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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Mar. Sci.</journal-id>
<journal-title-group>
<journal-title>Frontiers in Marine Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mar. Sci.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">2296-7745</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fmars.2026.1756034</article-id>
<article-version article-version-type="Version of Record" vocab="NISO-RP-8-2008"/>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Original Research</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Different types of cyclic steps nearby Manila Trench of northern South China Sea and analysis of forming mechanism</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name><surname>Yang</surname><given-names>Yuping</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
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<name><surname>Zhang</surname><given-names>Shuwei</given-names></name>
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<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
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<name><surname>Li</surname><given-names>Shuang</given-names></name>
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<name><surname>Yu</surname><given-names>Kaiqi</given-names></name>
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<name><surname>Qian</surname><given-names>Xuesheng</given-names></name>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="aff" rid="aff5"><sup>5</sup></xref>
<xref ref-type="aff" rid="aff6"><sup>6</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>*</sup></xref>
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<name><surname>Wang</surname><given-names>Chenghao</given-names></name>
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<name><surname>Xu</surname><given-names>Jingping</given-names></name>
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<aff id="aff1"><label>1</label><institution>National Engineering Research Center of Port Hydraulic Construction Technology, Tianjin Research Institute for Water Transport Engineering, M.O.T.</institution>, <city>Tianjin</city>,&#xa0;<country country="cn">China</country></aff>
<aff id="aff2"><label>2</label><institution>Department of Ocean Science and Engineering, Southern University of Science and Technology</institution>, <city>Shenzhen</city>,&#xa0;<country country="cn">China</country></aff>
<aff id="aff3"><label>3</label><institution>Department of Earth System Science, Ministry of Education Key Laboratory for Earth System Modeling, Institute for Global Change Studies, Tsinghua University</institution>, <city>Beijing</city>,&#xa0;<country country="cn">China</country></aff>
<aff id="aff4"><label>4</label><institution>CAS Key Laboratory of Ocean and Marginal Sea Geology, South China Sea Institute of Oceanology, Chinese Academy of Sciences</institution>, <city>Guangzhou</city>,&#xa0;<country country="cn">China</country></aff>
<aff id="aff5"><label>5</label><institution>Guangdong Provincial Key Laboratory of Green Construction and Intelligent Operation &amp; Maintenance for Offshore Infrastructure, School of Future Transportation, Guangzhou Maritime University/Guangzhou Jiaotong University (Under Construction)</institution>, <city>Guangzhou</city>,&#xa0;<country country="cn">China</country></aff>
<aff id="aff6"><label>6</label><institution>Guangdong Provincial Engineering Research Center for Resilient Offshore Infrastructure, School of Future Transportation, Guangzhou Maritime University/Guangzhou Jiaotong University (Under Construction)</institution>, <city>Guangzhou</city>,&#xa0;<country country="cn">China</country></aff>
<author-notes>
<corresp id="c001"><label>*</label>Correspondence: Xuesheng Qian, <email xlink:href="mailto:qianxuesheng@gzmtu.edu.cn">qianxuesheng@gzmtu.edu.cn</email></corresp>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-01-28">
<day>28</day>
<month>01</month>
<year>2026</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2026</year>
</pub-date>
<volume>13</volume>
<elocation-id>1756034</elocation-id>
<history>
<date date-type="received">
<day>28</day>
<month>11</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>13</day>
<month>01</month>
<year>2026</year>
</date>
<date date-type="rev-recd">
<day>13</day>
<month>01</month>
<year>2026</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2026 Yang, Zhang, Li, Yu, Qian, Wang and Xu.</copyright-statement>
<copyright-year>2026</copyright-year>
<copyright-holder>Yang, Zhang, Li, Yu, Qian, Wang and Xu</copyright-holder>
<license>
<ali:license_ref start_date="2026-01-28">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</license-p>
</license>
</permissions>
<abstract>
<p>High-resolution multibeam bathymetric enables detailed morphological investigation of the area of Manila Trench on the northeastern South China Sea margin, where twenty-three cyclic steps are observed. The identified cyclic steps can be further divided into two groups (Types A and B), namely, thirteen net-erosional and ten net-depositional cyclic steps, based on their sizes and relative locations. Type A cyclic steps occur downstream of the South Taiwan Shoal Canyon and Penghu Canyon, whereas Type B cyclic steps distribute outside the South Taiwan Shoal Canyon levees adjacent to the canyon bend. Principal component analysis (PCA) distinctly identifies the two cyclic step clusters (Types A and B), with cyclic steps length (<italic>L</italic><sub>step</sub>) and height (<italic>H</italic><sub>step</sub>) are key explanatory variables. The significant differences in flow properties between confined and unconfined turbidity currents crossing cyclic steps are considered to control the formation of Types A and B cyclic steps. Furthermore, net- erosional (Type A) cyclic steps will likely evolve into new submarine canyon-channel systems under continued turbidity currents erosion, altering material transport and deposition patterns to the deep sea in the Manila Trench. Our results improve understanding of the origin and formation of cyclic steps in global submarine canyons.</p>
</abstract>
<kwd-group>
<kwd>cyclic steps</kwd>
<kwd>Manila trench</kwd>
<kwd>northern South China Sea</kwd>
<kwd>submarine canyons</kwd>
<kwd>turbidity currents</kwd>
</kwd-group>
<funding-group>
<funding-statement>The author(s) declared that financial support was received for this work and/or its publication. This study was supported by the Research Innovation Fund of Tianjin Research Institute for Water Transport Engineering, Ministry of Transport, China (Grant No. TKS20250704), the National Natural Science Foundation of China (Grant Nos. 42106198, 42350710199) and the Guangdong Provincial Key Discipline Research Capacity Enhancement Initiative (Grant Nos. 2024ZDJS060, 2024ZDJS053).</funding-statement>
</funding-group>
<counts>
<fig-count count="10"/>
<table-count count="5"/>
<equation-count count="12"/>
<ref-count count="45"/>
<page-count count="17"/>
<word-count count="8694"/>
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<custom-meta-group>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Deep-Sea Environments and Ecology</meta-value>
</custom-meta>
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</front>
<body>
<sec id="s1" sec-type="intro">
<label>1</label>
<title>Introduction</title>
<p>Deep-water sedimentary processes, which encompass those regulated by gravity-driven downslope currents and alongslope currents, exert a pivotal control on the geomorphical evolution and morphological shaping of continental margins (<xref ref-type="bibr" rid="B28">Mosher et&#xa0;al., 2017</xref>). Turbidity currents, a type of gravity-driven downslope flow, are capable of transporting substantial volumes of sediment and plastic litter from continental shelf margins to the deep sea (<xref ref-type="bibr" rid="B35">Talling et&#xa0;al., 2013</xref>; <xref ref-type="bibr" rid="B39">Xu et&#xa0;al., 2014</xref>; <xref ref-type="bibr" rid="B40">Yang et&#xa0;al., 2024</xref>). A single turbidity current can transport over 100 km&#xb3; of sediment, which more than ten times the annual sediment load of all the world&#x2019;s rivers combined (<xref ref-type="bibr" rid="B36">Talling et&#xa0;al., 2007</xref>) and such currents are capable of modifying the morphology of continental margins, thereby facilitating the formation of submarine canyons, channels, sediment waves and scours (<xref ref-type="bibr" rid="B4">Cartigny et&#xa0;al., 2014</xref>; <xref ref-type="bibr" rid="B8">Covault et&#xa0;al., 2014</xref>). Turbidity currents, together with their associated seafloor morphological features, are regarded as fundamental factors in the formation of submarine channels (<xref ref-type="bibr" rid="B8">Covault et&#xa0;al., 2014</xref>, <xref ref-type="bibr" rid="B9">2016</xref>).</p>
<p>Cyclic steps are long-wavelength, upstream-migrating, step-like upper-flow-regime bedforms in turbidity currents that are bounded by internal hydraulic jumps, and they exhibit Froude-supercritical flow conditions (densimetric Froude number &gt; 1) over their lee sides and Froude-subcritical flow conditions (densimetric Froude number&lt; 1) over their stoss sides (<xref ref-type="bibr" rid="B45">Zhong et&#xa0;al., 2015</xref>; <xref ref-type="bibr" rid="B9">Covault et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B26">Li and Gong, 2018</xref>; <xref ref-type="bibr" rid="B27">Li et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B32">Slootman and Cartigny, 2020</xref>). Cyclic steps are generally classified as net-erosional or net-depositional, with the distinction determined by whether erosion or deposition acts as the dominant process across the entire bedform (<xref ref-type="bibr" rid="B16">Fildani et&#xa0;al., 2006</xref>; <xref ref-type="bibr" rid="B8">Covault et&#xa0;al., 2014</xref>; <xref ref-type="bibr" rid="B45">Zhong et&#xa0;al., 2015</xref>; <xref ref-type="bibr" rid="B26">Li and Gong, 2018</xref>; <xref ref-type="bibr" rid="B5">Cerrillo-Escoriza et&#xa0;al., 2024</xref>). Net-depositional cyclic steps manifest as upstream-migrating sediment waves (<xref ref-type="bibr" rid="B16">Fildani et&#xa0;al., 2006</xref>; <xref ref-type="bibr" rid="B21">Kostic and Parker, 2006</xref>; <xref ref-type="bibr" rid="B45">Zhong et&#xa0;al., 2015</xref>), while net-erosional cyclic steps develop as trains of upstream-migrating scours, scarps, or headcuts (<xref ref-type="bibr" rid="B20">Kostic, 2011</xref>; <xref ref-type="bibr" rid="B45">Zhong et&#xa0;al., 2015</xref>). Based on their geometric characteristics, cyclic steps can be further categorized as downstream-asymmetric (steep lee side and gentle stoss side), symmetric (equal slopes of the lee and stoss sides), or upstream-asymmetric (gentle lee side and steep stoss side) (<xref ref-type="bibr" rid="B8">Covault et&#xa0;al., 2014</xref>; <xref ref-type="bibr" rid="B32">Slootman and Cartigny, 2020</xref>).</p>
<p>Cyclic steps are ubiquitous in natural settings, ranging from high mountain rivers to deep-water basins (<xref ref-type="bibr" rid="B22">Kostic et&#xa0;al., 2010</xref>). They have been documented along the thalwegs and overbank areas of numerous submarine canyons and channels, such as the Monterey East Channel System in California (<xref ref-type="bibr" rid="B16">Fildani et&#xa0;al., 2006</xref>), the submarine distributary channel in the Rio Muni Basin (<xref ref-type="bibr" rid="B26">Li and Gong, 2018</xref>), Carchuna Canyon in the Alboran Sea (<xref ref-type="bibr" rid="B5">Cerrillo-Escoriza et&#xa0;al., 2024</xref>), the Foix Canyon System in the northwestern Mediterranean Sea (<xref ref-type="bibr" rid="B38">Tubau et&#xa0;al., 2013</xref>), Pearl River Mouth Canyon Group (<xref ref-type="bibr" rid="B33">Sun et&#xa0;al., 2024</xref>) and the West Penghu Submarine Canyons in the South China Sea (<xref ref-type="bibr" rid="B23">Kuang et&#xa0;al., 2014</xref>; <xref ref-type="bibr" rid="B45">Zhong et&#xa0;al., 2015</xref>; <xref ref-type="bibr" rid="B27">Li et&#xa0;al., 2020</xref>).</p>
<p>Some cyclic steps distributed in the South Taiwan Shoal Canyon and the West Penghu Canyon in the South China Sea have been reported and investigated (<xref ref-type="bibr" rid="B23">Kuang et&#xa0;al., 2014</xref>; <xref ref-type="bibr" rid="B45">Zhong et&#xa0;al., 2015</xref>). However, the detailed morphological characteristics of the cyclic steps downstream of these canyons remain enigmatic, and the flow properties of the turbidity currents that generate the cyclic steps downstream of the canyon mouths are still poorly understood.</p>
<p>In this study, two types of cyclic steps were identified downstream of the South Taiwan Shoal Canyon and the adjacent Penghu Canyon near the Manila Trench. These were designated as Types A and B cyclic steps, and their characteristics were quantified using high-resolution multibeam bathymetry to address three key objectives: (1) investigating the morphological and geometric parameters of cyclic steps in the vicinity of the Manila Trench; (2) determining the flow properties of turbidity currents traversing these cyclic steps; and (3) identifying the formation processes of different cyclic step types and the factors controlling their morphology.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Geological background</title>
<p>The Manila Trench is situated in the northeastern South China Sea and tectonically belongs to a subduction system, where the Sunda Plate (part of the Eurasian Plate) is subducted beneath the Luzon Volcanic Island Arc (<xref ref-type="bibr" rid="B24">Lallemand, 2016</xref>; <xref ref-type="bibr" rid="B31">Qiu et&#xa0;al., 2019</xref>; <xref ref-type="bibr" rid="B14">Fan et&#xa0;al., 2025</xref>; <xref ref-type="bibr" rid="B37">Tian et&#xa0;al., 2026</xref>). The Manila Trench lies downstream of the confluence of a submarine canyon system, including the Gaoping, Penghu, and South Taiwan Shoal Canyons (<xref ref-type="fig" rid="f1"><bold>Figure&#xa0;1</bold></xref>). As the northern extension of the Manila Trench, the Penghu Canyon is interpreted as a geomorphological expression of the transition zone between the northwestward-thrusting Taiwan orogenic wedge and the southeastward-subducting South China Sea Plate margin (<xref ref-type="bibr" rid="B42">Yu and Hong, 2006</xref>). The South Taiwan Shoal Canyon extends in a northwest&#x2013;southeast (NW-SE) direction in its upper-middle reaches, but bends eastward in its lower segment, where is blocked by a seamount (<xref ref-type="bibr" rid="B12">Ding et&#xa0;al., 2010</xref>; <xref ref-type="bibr" rid="B23">Kuang et&#xa0;al., 2014</xref>). Within the South Taiwan Shoal Canyon, approximately 51 cyclic steps have been identified, while around 19 cyclic steps are distributed in the West Penghu Canyon (<xref ref-type="bibr" rid="B45">Zhong et&#xa0;al., 2015</xref>). Additionally, roughly 25,000 km&#xb2; of sediment waves have been documented on the western wall of the north-south (N-S) trending Manila Trench, which is located in the northeastern South China Sea basin (<xref ref-type="bibr" rid="B10">Damuth, 1979</xref>).</p>
<fig id="f1" position="float">
<label>Figure&#xa0;1</label>
<caption>
<p>High-resolution multibeam bathymetric map of the study area. The bottom map is slope gradient of the study area within the northeast South China Sea (<ext-link ext-link-type="uri" xlink:href="https://download.gebco.net/">https://download.gebco.net/</ext-link>) and the red dotted lines represent the canyons and trench axis. The two black oval areas represent the location of the Types A and B cyclic steps (<xref ref-type="fig" rid="f3"><bold>Figure&#xa0;3</bold></xref>).</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-13-1756034-g001.tif">
<alt-text content-type="machine-generated">Map of the South Taiwan region displaying submarine canyons including Gaoping, Penghu, and South Taiwan Shoal Canyons. The study area is highlighted near the Manila Trench between types A and B zones. An inset shows the regional location in East Asia. Depths range from 2,500 to 4,000 meters, with a color gradient for depth and slope gradient scale.</alt-text>
</graphic></fig>
<p>The study area is situated at the confluence of the South Taiwan Shoal Canyon and the Penghu Canyon, near the Manila Trench, where water depths range from 2500&#xa0;m to 4000&#xa0;m.</p>
</sec>
<sec id="s3">
<label>3</label>
<title>Data and methods</title>
<sec id="s3_1">
<label>3.1</label>
<title>Data collection</title>
<p>The high-resolution multibeam data used in this study, covering a total area of approximately 3950 km&#xb2;, was collected in 2022 by the research vessel &#x201c;Dongfanghong 3&#x201d; in the South China Sea. This multibeam bathymetric data was acquired via an EM 122 multibeam echo sounder, which operates at a frequency of 12 kHz with a beamwidth of 0.5&#xb0;&#xd7;1&#xb0;. The maximum swath width of the system is six times the water depth (up to ~30 km), and the vertical sounding accuracy is 3&#x2030; of the water depth. The multibeam bathymetric data were imported into and analyzed using Global Mapper<sup>&#xae;</sup> software.</p>
</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Statistical analysis</title>
<p>Principal component analysis (PCA) is one of the statistical analysis methods used to identify the variables that best explain the variance in a dataset (<xref ref-type="bibr" rid="B18">Jolliffe, 2014</xref>). In this study, we applied the PCA method to determine the key controlling parameters for the dimensional characteristics of the two cyclic step types (Types A and B). Additionally, we analyzed the correlations between the variables and the principal components, with the aim of clarifying which variables should be prioritized for subsequent in-depth analysis.</p>
</sec>
<sec id="s3_3">
<label>3.3</label>
<title>Estimating turbidity currents conditions from hydraulic geometries</title>
<p>Multibeam bathymetry was used to investigate the morphological and architectural characteristics of the studied cyclic steps. As graphically illustrated in <xref ref-type="fig" rid="f2"><bold>Figure&#xa0;2</bold></xref>, individual cyclic steps consist of three discrete, geometrically defined zones: steep headcuts (corresponding to their lee sides), flat or gently sloping stoss sides, and a topographic depression (or trough) between these two zones (<xref ref-type="bibr" rid="B3">Cartigny et&#xa0;al., 2011</xref>; <xref ref-type="bibr" rid="B45">Zhong et&#xa0;al., 2015</xref>; <xref ref-type="bibr" rid="B26">Li and Gong, 2018</xref>). Individual cyclic steps have been quantitatively documented in terms of (1) length, height, and slope of the cyclic step (<italic>L</italic><sub>step</sub>, <italic>H</italic>, and <italic>&#x3b8;</italic>, respectively); (2) length of stoss and lee sides (<italic>L</italic><sub>stoss</sub> and <italic>L</italic><sub>lee</sub>, respectively); (3) slope of stoss and lee sides (&#x430; and &#x3b2;, respectively); (4) cross-sectional asymmetry (<italic>A</italic><sub>y</sub>, computed as <italic>L</italic><sub>stoss</sub>/<italic>L</italic><sub>lee</sub>); and (5) aspect ratio (calculated as <italic>L</italic><sub>step</sub>/<italic>H</italic>).</p>
<fig id="f2" position="float">
<label>Figure&#xa0;2</label>
<caption>
<p><bold>(A)</bold> Schematic illustration of cyclic step longitudinal profiles (modified from <xref ref-type="bibr" rid="B3">Cartigny et&#xa0;al., 2011</xref>) <bold>(B)</bold> Schematic illustration of a single cyclic step showing morphologic parameters (modified from <xref ref-type="bibr" rid="B3">Cartigny et&#xa0;al., 2011</xref>; <xref ref-type="bibr" rid="B26">Li and Gong, 2018</xref>; <xref ref-type="bibr" rid="B27">Li et&#xa0;al., 2020</xref>). <bold>(C)</bold> Flow chart showing the calculations of cyclic step forming turbidity currents conditions (modified from <xref ref-type="bibr" rid="B26">Li and Gong, 2018</xref>).</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-13-1756034-g002.tif">
<alt-text content-type="machine-generated">Diagram illustrating hydraulic flow. (A) Shows supercritical flow, subcritical flow, and hydraulic jump over a terrain. (B) Details the parameters and geometry of flow regions, labeled as lee side, crest, and stoss side, with indications of flow depth and velocity. (C) Presents a table of input parameters, numerical computations, and output parameters, explaining flow estimation using various equations and models.</alt-text>
</graphic></fig>
<p>Flow properties of turbidity currents moving along the seabed near the Manila Trench were calculated based on the morphological parameters of the cyclic steps. These parameters include the channel bed slope (<italic>S</italic>), as well as the length and slope gradient of the lee and stoss sides of the cyclic steps. In Part I of the analysis, morphological parameters of the cyclic steps were used to compute the turbidity current conditions upstream of hydraulic jumps, following <xref ref-type="disp-formula" rid="eq1">Equations 1</xref>&#x2013;<xref ref-type="disp-formula" rid="eq5">5</xref>.</p>
<disp-formula id="eq1"><label>(1)</label>
<mml:math display="block" id="M1"><mml:mrow><mml:mn>0</mml:mn><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>S</mml:mi><mml:msubsup><mml:mi>C</mml:mi><mml:mrow><mml:mi>f</mml:mi><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>0.5</mml:mn><mml:msub><mml:mi>R</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>f</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mfrac><mml:mo>&#x2212;</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq2"><label>(2)</label>
<mml:math display="block" id="M2"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>0.0075</mml:mn></mml:mrow><mml:mrow><mml:msqrt><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>718</mml:mn><mml:msubsup><mml:mi>R</mml:mi><mml:mi>i</mml:mi><mml:mrow><mml:mn>2.4</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:msqrt></mml:mrow></mml:mfrac></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq3"><label>(3)</label>
<mml:math display="block" id="M3"><mml:mrow><mml:mi>F</mml:mi><mml:msubsup><mml:mi>r</mml:mi><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mtext>sin</mml:mtext><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mtext>&#x3b3;</mml:mtext><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>f</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq4"><label>(4)</label>
<mml:math display="block" id="M4"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mtext>L</mml:mtext><mml:mrow><mml:mn>2</mml:mn><mml:mtext>&#x3c0;</mml:mtext><mml:mi>F</mml:mi><mml:msubsup><mml:mi>r</mml:mi><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq5"><label>(5)</label>
<mml:math display="block" id="M5"><mml:mrow><mml:msubsup><mml:mi>U</mml:mi><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mi>&#x394;</mml:mi><mml:mi>&#x3c1;</mml:mi><mml:mi>g</mml:mi><mml:mi>C</mml:mi><mml:mi>h</mml:mi><mml:mi>F</mml:mi><mml:msubsup><mml:mi>r</mml:mi><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im1"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the dimensionless coefficient of the entrainment of ambient water into turbidity currents; <inline-formula>
<mml:math display="inline" id="im2"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>f</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the coefficient of friction at channel bed (ranging from 0.002 to 0.005, as suggested by (<xref ref-type="bibr" rid="B19">Konsoer et&#xa0;al., 2013</xref>)); <italic>S</italic> denotes the slope of the channel bed; <italic>Fr</italic> is the densimetric Froude number; <inline-formula>
<mml:math display="inline" id="im3"><mml:mtext>&#x3b3;</mml:mtext></mml:math></inline-formula> is the slope gradient of the stoss side or lee side of cyclic steps (<inline-formula>
<mml:math display="inline" id="im4"><mml:mrow><mml:mi>&#x3b1;</mml:mi><mml:mo>&#xa0;</mml:mo><mml:mtext>or</mml:mtext><mml:mo>&#xa0;</mml:mo><mml:mi>&#x3b2;</mml:mi></mml:mrow></mml:math></inline-formula>); L is the length of stoss (<italic>L</italic><sub>stoss</sub>) and lee sides (<italic>L</italic><sub>lee</sub>); <italic>h</italic> is the thickness of turbidity currents; <italic>C</italic> is the volume sediment concentration (ranging from 0.2% to 0.6%, as suggested by <xref ref-type="bibr" rid="B19">Konsoer et&#xa0;al., 2013</xref>); <inline-formula>
<mml:math display="inline" id="im5"><mml:mrow><mml:mi>&#x394;</mml:mi><mml:mi>&#x3c1;</mml:mi></mml:mrow></mml:math></inline-formula> is the density difference between the sediment and the ambient water, usually taken as 1650 kg/m<sup>3</sup> (<xref ref-type="bibr" rid="B29">Piper and Savoye, 1993</xref>); <italic>g</italic> is gravitational acceleration (9.8 m/s<sup>2</sup>).</p>
<p>In part II, the Froude number, flow depth, and velocity of formative turbidity currents downstream of hydraulic jumps (<italic>Fr</italic><sub>2</sub>, <italic>h</italic><sub>2</sub>, and <italic>U</italic><sub>2</sub>) were computed, respectively, by the momentum principles of <xref ref-type="bibr" rid="B6">Chanson (2004)</xref> (<xref ref-type="disp-formula" rid="eq6">Equations 6</xref>&#x2013;<xref ref-type="disp-formula" rid="eq8">8</xref>).</p>
<disp-formula id="eq6"><label>(6)</label>
<mml:math display="block" id="M6"><mml:mrow><mml:mi>F</mml:mi><mml:msub><mml:mi>r</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mn>2</mml:mn><mml:mrow><mml:mn>1.5</mml:mn></mml:mrow></mml:msup><mml:mi>F</mml:mi><mml:msub><mml:mi>r</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msqrt><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>8</mml:mn><mml:mi>F</mml:mi><mml:msubsup><mml:mi>r</mml:mi><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:msqrt><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>1.5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mfrac></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq7"><label>(7)</label>
<mml:math display="block" id="M7"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:mfrac><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msqrt><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>8</mml:mn><mml:mi>F</mml:mi><mml:msubsup><mml:mi>r</mml:mi><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:msqrt><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq8"><label>(8)</label>
<mml:math display="block" id="M8"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:msub><mml:mi>U</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:math>
</disp-formula>
<p>where <italic>h</italic><sub>1</sub>, <italic>U</italic><sub>1</sub> and <italic>Fr</italic><sub>1</sub> are the flow depth, the velocity and Froude number of turbidity currents before hydraulic jumps, respectively.</p>
<p>The energy loss (<inline-formula>
<mml:math display="inline" id="im6"><mml:mrow><mml:mtext>&#x394;</mml:mtext><mml:msub><mml:mi>E</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and the length of the hydraulic jump (<inline-formula>
<mml:math display="inline" id="im7"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mi>u</mml:mi><mml:mi>m</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) can be calculated by the approach of <xref ref-type="bibr" rid="B6">Chanson (2004)</xref> (<xref ref-type="disp-formula" rid="eq9">Equations 9</xref>, <xref ref-type="disp-formula" rid="eq10">10</xref>).</p>
<disp-formula id="eq9"><label>(9)</label>
<mml:math display="block" id="M9"><mml:mrow><mml:mtext>&#x394;</mml:mtext><mml:msub><mml:mi>E</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mn>3</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn>4</mml:mn><mml:msub><mml:mi>h</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq10"><label>(10)</label>
<mml:math display="block" id="M10"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mi>u</mml:mi><mml:mi>m</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>160</mml:mn><mml:mi>tan</mml:mi><mml:mi>h</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mfrac><mml:mrow><mml:mi>F</mml:mi><mml:msub><mml:mi>r</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mn>20</mml:mn></mml:mrow></mml:mfrac></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>12</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>
</disp-formula>
<p>In Part III of the analysis, a two-equation model-derived from mass and momentum balance considerations was used to calculate the flow depth and velocity at the crests of the cyclic steps. This model incorporates gravitational forces, frictional forces, and pressure forces induced by variations in flow thickness (<xref ref-type="bibr" rid="B3">Cartigny et&#xa0;al., 2011</xref>) (<xref ref-type="disp-formula" rid="eq11">Equations 11</xref>, <xref ref-type="disp-formula" rid="eq12">12</xref>).</p>
<disp-formula id="eq11"><label>(11)</label>
<mml:math display="block" id="M11"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>&#x3b1;</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mn>8</mml:mn><mml:mo>*</mml:mo><mml:mi>F</mml:mi><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>F</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq12"><label>(12)</label>
<mml:math display="block" id="M12"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>U</mml:mi></mml:mrow><mml:mi>h</mml:mi></mml:mfrac><mml:mo>*</mml:mo><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im8"><mml:mi>&#x3b1;</mml:mi></mml:math></inline-formula> is the slope gradient of the stoss side and <italic>f</italic> is the friction coefficient. The friction coefficient seems to be far less important by sensitivity analysis. The accuracy of the model depends mainly on and is almost proportional to the accuracy of the slope measurements used (<xref ref-type="bibr" rid="B3">Cartigny et&#xa0;al., 2011</xref>).</p>
</sec>
</sec>
<sec id="s4" sec-type="results">
<label>4</label>
<title>Results</title>
<sec id="s4_1">
<label>4.1</label>
<title>Two types of cyclic steps</title>
<p>A total of twenty-three (23) long-wavelength, upstream-migrating, crescentic bedforms have been identified near the Manila Trench. Based on their locations and dimensions, these bedforms-recognized as cyclic steps-can be categorized into two types: (1) Lines 1 and 2, with lengths of 27&#xa0;km and 36&#xa0;km respectively, exhibit profiles of Type A cyclic steps. These Type A cyclic steps are developed at the downstream confluence between the South Taiwan Shoal Canyon and the West Penghu Canyon (<xref ref-type="fig" rid="f3"><bold>Figures&#xa0;3A, C, D</bold></xref>); (2) Line 3, which is 22.4&#xa0;km long, shows profiles of cyclic steps developed in the overbank areas of the South Taiwan Channel, these are herein designated as Type B cyclic steps (<xref ref-type="fig" rid="f3"><bold>Figures&#xa0;3B, E</bold></xref>). In this section, the morphological and geometric parameters of the two cyclic step types are compared and discussed.</p>
<fig id="f3" position="float">
<label>Figure&#xa0;3</label>
<caption>
<p><bold>(A, B)</bold> Multibeam bathymetric map illustrating the morphology and distribution of cyclic steps. Two yellow lines (Line 1 and Line 2) are the depth profiles of Type A cyclic steps (E1-E6 and E7-E13) in <bold>(C, D)</bold>, which almost parallel in distribution. Black line (Line 3) is the profile of Type B cyclic steps (S1-S10).</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-13-1756034-g003.tif">
<alt-text content-type="machine-generated">Two colored maps (panels A and B) display different types of cyclic steps, with white dashed lines indicating step patterns. Panel C shows an elevation profile for Line 1, highlighting six peaks (E1 to E6). Panel D presents the elevation for Line 2, showing peaks E7 to E13. Panel E displays a smoother elevation line for Line 3. Depth is color-coded from shallow (red) to deep (dark blue). The maps illustrate net-erosional and net-depositional features, with depths in meters and distances in kilometers.</alt-text>
</graphic></fig>
<sec id="s4_1_1">
<label>4.1.1</label>
<title>Morphological and architectural characteristics of type A cyclic steps</title>
<p>Type A cyclic steps occur at the downstream confluence of the South Taiwan Shoal Canyon and the West Penghu Canyon, in water depths ranging from 3430&#xa0;m to 3596&#xa0;m. The average slope gradient in this area is 0.27&#xb0;. These cyclic steps have a wavelength of 2.7-6.1&#xa0;km and a height of 20.1-68.1&#xa0;m (<xref ref-type="table" rid="T1"><bold>Table&#xa0;1</bold></xref>). For the dimensional parameters of their sides: the length of the stoss side (<italic>L</italic><sub>stoss</sub>) ranges from 1350&#xa0;m to 4800&#xa0;m, with a mean of 2495&#xa0;m; the length of the lee side (<italic>L</italic><sub>lee</sub>) ranges from 700&#xa0;m to 3850&#xa0;m, with an average of 2139&#xa0;m (<xref ref-type="table" rid="T1"><bold>Table&#xa0;1</bold></xref>). In terms of slope gradients: the stoss side slope (<italic>&#x3b1;</italic>) varies from 0.72&#xb0; to 1.44&#xb0;, with a mean value of 1.10&#xb0;. By contrast, the lee side slope (<italic>&#x3b2;</italic>) ranges from 1.06&#xb0; to 2.88&#xb0;, with an average of 1.65&#xb0; (<xref ref-type="table" rid="T1"><bold>Table&#xa0;1</bold></xref>, <xref ref-type="fig" rid="f4"><bold>Figure&#xa0;4</bold></xref>). Additionally, Type A cyclic steps have an asymmetry index (<italic>A</italic><sub>y</sub>) ranging from 0.35 to 2.93 (mean = 1.34) and an aspect ratio ranging from 57.34 to 136.88 (mean = 94.73) (<xref ref-type="table" rid="T1"><bold>Table&#xa0;1</bold></xref>, <xref ref-type="fig" rid="f4"><bold>Figure&#xa0;4</bold></xref>).</p>
<table-wrap id="T1" position="float">
<label>Table&#xa0;1</label>
<caption>
<p>Morphological characteristics of thirteen Type A cyclic steps.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center">Type A</th>
<th valign="middle" align="center"><italic>&#x3b1;</italic></th>
<th valign="middle" align="center"><italic>&#x3b2;</italic></th>
<th valign="middle" align="center"><italic>&#x3b8;</italic></th>
<th valign="middle" align="center"><italic>L</italic><sub>stoss</sub></th>
<th valign="middle" align="center"><italic>L</italic><sub>lee</sub></th>
<th valign="middle" align="center"><italic>L</italic><sub>step</sub></th>
<th valign="middle" align="center"><italic>H</italic><sub>step</sub></th>
<th valign="middle" align="center"><italic>A</italic><sub>y</sub></th>
<th valign="middle" align="center">Aspect ratio</th>
</tr>
<tr>
<th valign="middle" align="center">No.</th>
<th valign="middle" align="center">(&#xb0;)</th>
<th valign="middle" align="center">(&#xb0;)</th>
<th valign="middle" align="center">(&#xb0;)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(-)</th>
<th valign="middle" align="center">(-)</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" align="center">E1</td>
<td valign="middle" align="center">0.87</td>
<td valign="middle" align="center">1.81</td>
<td valign="middle" align="center">0.19</td>
<td valign="middle" align="center">3700</td>
<td valign="middle" align="center">2400</td>
<td valign="middle" align="center">6100</td>
<td valign="middle" align="center">68.13</td>
<td valign="middle" align="center">1.54</td>
<td valign="middle" align="center">89.53</td>
</tr>
<tr>
<td valign="middle" align="center">E2</td>
<td valign="middle" align="center">1.03</td>
<td valign="middle" align="center">2.02</td>
<td valign="middle" align="center">0.01</td>
<td valign="middle" align="center">3390</td>
<td valign="middle" align="center">1760</td>
<td valign="middle" align="center">5150</td>
<td valign="middle" align="center">61.66</td>
<td valign="middle" align="center">1.93</td>
<td valign="middle" align="center">83.52</td>
</tr>
<tr>
<td valign="middle" align="center">E3</td>
<td valign="middle" align="center">0.98</td>
<td valign="middle" align="center">1.23</td>
<td valign="middle" align="center">0.42</td>
<td valign="middle" align="center">2050</td>
<td valign="middle" align="center">700</td>
<td valign="middle" align="center">2750</td>
<td valign="middle" align="center">20.09</td>
<td valign="middle" align="center">2.93</td>
<td valign="middle" align="center">136.88</td>
</tr>
<tr>
<td valign="middle" align="center">E4</td>
<td valign="middle" align="center">1.02</td>
<td valign="middle" align="center">2.17</td>
<td valign="middle" align="center">0.57</td>
<td valign="middle" align="center">1400</td>
<td valign="middle" align="center">1400</td>
<td valign="middle" align="center">2800</td>
<td valign="middle" align="center">39.00</td>
<td valign="middle" align="center">1.00</td>
<td valign="middle" align="center">71.79</td>
</tr>
<tr>
<td valign="middle" align="center">E5</td>
<td valign="middle" align="center">1.21</td>
<td valign="middle" align="center">1.06</td>
<td valign="middle" align="center">0.01</td>
<td valign="middle" align="center">2350</td>
<td valign="middle" align="center">2750</td>
<td valign="middle" align="center">5100</td>
<td valign="middle" align="center">50.46</td>
<td valign="middle" align="center">0.85</td>
<td valign="middle" align="center">101.07</td>
</tr>
<tr>
<td valign="middle" align="center">E6</td>
<td valign="middle" align="center">0.99</td>
<td valign="middle" align="center">1.42</td>
<td valign="middle" align="center">0.09</td>
<td valign="middle" align="center">1800</td>
<td valign="middle" align="center">1450</td>
<td valign="middle" align="center">3250</td>
<td valign="middle" align="center">33.77</td>
<td valign="middle" align="center">1.24</td>
<td valign="middle" align="center">96.24</td>
</tr>
<tr>
<td valign="middle" align="center">E7</td>
<td valign="middle" align="center">1.64</td>
<td valign="middle" align="center">2.38</td>
<td valign="middle" align="center">0.5</td>
<td valign="middle" align="center">1750</td>
<td valign="middle" align="center">2000</td>
<td valign="middle" align="center">3750</td>
<td valign="middle" align="center">65.40</td>
<td valign="middle" align="center">0.88</td>
<td valign="middle" align="center">57.34</td>
</tr>
<tr>
<td valign="middle" align="center">E8</td>
<td valign="middle" align="center">0.82</td>
<td valign="middle" align="center">1.23</td>
<td valign="middle" align="center">0.09</td>
<td valign="middle" align="center">4800</td>
<td valign="middle" align="center">2650</td>
<td valign="middle" align="center">7450</td>
<td valign="middle" align="center">61.27</td>
<td valign="middle" align="center">1.81</td>
<td valign="middle" align="center">121.59</td>
</tr>
<tr>
<td valign="middle" align="center">E9</td>
<td valign="middle" align="center">1.15</td>
<td valign="middle" align="center">1.55</td>
<td valign="middle" align="center">0.14</td>
<td valign="middle" align="center">2200</td>
<td valign="middle" align="center">2000</td>
<td valign="middle" align="center">4200</td>
<td valign="middle" align="center">49.24</td>
<td valign="middle" align="center">1.10</td>
<td valign="middle" align="center">85.30</td>
</tr>
<tr>
<td valign="middle" align="center">E10</td>
<td valign="middle" align="center">1.33</td>
<td valign="middle" align="center">1.18</td>
<td valign="middle" align="center">0.21</td>
<td valign="middle" align="center">1900</td>
<td valign="middle" align="center">3000</td>
<td valign="middle" align="center">4900</td>
<td valign="middle" align="center">50.98</td>
<td valign="middle" align="center">0.63</td>
<td valign="middle" align="center">96.12</td>
</tr>
<tr>
<td valign="middle" align="center">E11</td>
<td valign="middle" align="center">0.72</td>
<td valign="middle" align="center">1.19</td>
<td valign="middle" align="center">0.11</td>
<td valign="middle" align="center">3100</td>
<td valign="middle" align="center">2400</td>
<td valign="middle" align="center">5500</td>
<td valign="middle" align="center">45.20</td>
<td valign="middle" align="center">1.29</td>
<td valign="middle" align="center">121.68</td>
</tr>
<tr>
<td valign="middle" align="center">E12</td>
<td valign="middle" align="center">1.44</td>
<td valign="middle" align="center">1.35</td>
<td valign="middle" align="center">0.63</td>
<td valign="middle" align="center">1350</td>
<td valign="middle" align="center">3850</td>
<td valign="middle" align="center">5200</td>
<td valign="middle" align="center">48.80</td>
<td valign="middle" align="center">0.35</td>
<td valign="middle" align="center">106.56</td>
</tr>
<tr>
<td valign="middle" align="center">E13</td>
<td valign="middle" align="center">1.04</td>
<td valign="middle" align="center">2.88</td>
<td valign="middle" align="center">0.35</td>
<td valign="middle" align="center">2650</td>
<td valign="middle" align="center">1450</td>
<td valign="middle" align="center">4100</td>
<td valign="middle" align="center">64.16</td>
<td valign="middle" align="center">1.83</td>
<td valign="middle" align="center">63.90</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="f4" position="float">
<label>Figure&#xa0;4</label>
<caption>
<p>Graphical plots of the morphological characteristics of cyclic steps. <bold>(A)</bold> Length of cyclic steps comparison between Type A (marked in red) and Type B (marked in blue). <bold>(B)</bold> Asymmetry of cyclic steps comparison between Type A (marked in red) and Type B (marked in blue). <bold>(C)</bold> Slope angle of cyclic steps comparison between Type A and Type B. Slope gradients of the stoss side (<italic>&#x3b1;</italic>), the lee side (<italic>&#x3b2;</italic>) and the scour (<italic>&#x3b8;</italic>) are marked in red, azure and blue, respectively. Note that the triangles represent Type A cyclic steps and the circles indicate Type B cyclic steps in <xref ref-type="fig" rid="f4"><bold>Figure&#xa0;4C</bold></xref>.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-13-1756034-g004.tif">
<alt-text content-type="machine-generated">Three graphs show relationships for Type A and Type B data. (A) Plots length of cyclic step versus number of steps; red dots for Type A, blue for Type B. (B) Shows asymmetry versus number of steps; similar color coding. (C) Displays slope angle using different colored shapes for each type and parameter.</alt-text>
</graphic></fig>
</sec>
<sec id="s4_1_2">
<label>4.1.2</label>
<title>Morphological and architectural characteristics of Type B cyclic steps</title>
<p>Type B cyclic steps are located in the overbank areas of the South Taiwan Channel, in water depths ranging from 3235&#xa0;m to 3598&#xa0;m. The average slope gradient of this region is 0.90&#xb0;. These cyclic steps have a wavelength of 1.0-2.6&#xa0;km and a height of 4.86-29.21&#xa0;m (<xref ref-type="table" rid="T2"><bold>Table&#xa0;2</bold></xref>). For their side-specific parameters: the length of the stoss side (<italic>L</italic><sub>stoss</sub>) ranges from 450&#xa0;m to 850&#xa0;m, with a mean of 610&#xa0;m; the length of the lee side (<italic>L</italic><sub>lee</sub>) ranges from 450&#xa0;m to 2000&#xa0;m, with an average of 1110&#xa0;m (<xref ref-type="table" rid="T2"><bold>Table&#xa0;2</bold></xref>). In terms of slope gradients: the stoss side slope (<italic>&#x3b1;</italic>) varies from 0.10&#xb0; to 1.40&#xb0;, with a mean value of 0.73&#xb0;. In contrast, the lee side slope (<italic>&#x3b2;</italic>) ranges from 0.89&#xb0; to 2.86&#xb0;, with an average of 1.75&#xb0; (<xref ref-type="table" rid="T2"><bold>Table&#xa0;2</bold></xref>; <xref ref-type="fig" rid="f4"><bold>Figure&#xa0;4</bold></xref>). Additionally, Type B cyclic steps have an asymmetry index (<italic>A</italic><sub>y</sub>) ranging from 0.30 to 1.33 (mean = 0.64) and an aspect ratio ranging from 74.82 to 216.05 (mean = 118.11) (<xref ref-type="table" rid="T2"><bold>Table&#xa0;2</bold></xref>; <xref ref-type="fig" rid="f4"><bold>Figure&#xa0;4</bold></xref>).</p>
<table-wrap id="T2" position="float">
<label>Table&#xa0;2</label>
<caption>
<p>Morphological characteristics of ten Type B cyclic steps.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center">Type B</th>
<th valign="middle" align="center"><italic>&#x3b1;</italic></th>
<th valign="middle" align="center"><italic>&#x3b2;</italic></th>
<th valign="middle" align="center"><italic>&#x3b8;</italic></th>
<th valign="middle" align="center"><italic>L</italic><sub>stoss</sub></th>
<th valign="middle" align="center"><italic>L</italic><sub>lee</sub></th>
<th valign="middle" align="center"><italic>L</italic><sub>step</sub></th>
<th valign="middle" align="center"><italic>H</italic><sub>step</sub></th>
<th valign="middle" align="center"><italic>A</italic><sub>y</sub></th>
<th valign="middle" align="center">Aspect ratio</th>
</tr>
<tr>
<th valign="middle" align="center">No.</th>
<th valign="middle" align="center">(&#xb0;)</th>
<th valign="middle" align="center">(&#xb0;)</th>
<th valign="middle" align="center">(&#xb0;)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(-)</th>
<th valign="middle" align="center">(-)</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" align="center">S1</td>
<td valign="middle" align="center">1.40</td>
<td valign="middle" align="center">2.18</td>
<td valign="middle" align="center">1.07</td>
<td valign="middle" align="center">450</td>
<td valign="middle" align="center">1000</td>
<td valign="middle" align="center">1450</td>
<td valign="middle" align="center">19.38</td>
<td valign="middle" align="center">0.45</td>
<td valign="middle" align="center">74.82</td>
</tr>
<tr>
<td valign="middle" align="center">S2</td>
<td valign="middle" align="center">0.10</td>
<td valign="middle" align="center">1.20</td>
<td valign="middle" align="center">0.74</td>
<td valign="middle" align="center">550</td>
<td valign="middle" align="center">1000</td>
<td valign="middle" align="center">1550</td>
<td valign="middle" align="center">8.10</td>
<td valign="middle" align="center">0.55</td>
<td valign="middle" align="center">191.36</td>
</tr>
<tr>
<td valign="middle" align="center">S3</td>
<td valign="middle" align="center">0.94</td>
<td valign="middle" align="center">1.78</td>
<td valign="middle" align="center">1.03</td>
<td valign="middle" align="center">550</td>
<td valign="middle" align="center">1450</td>
<td valign="middle" align="center">2000</td>
<td valign="middle" align="center">18.90</td>
<td valign="middle" align="center">0.38</td>
<td valign="middle" align="center">105.82</td>
</tr>
<tr>
<td valign="middle" align="center">S4</td>
<td valign="middle" align="center">0.19</td>
<td valign="middle" align="center">0.89</td>
<td valign="middle" align="center">0.27</td>
<td valign="middle" align="center">600</td>
<td valign="middle" align="center">450</td>
<td valign="middle" align="center">1050</td>
<td valign="middle" align="center">4.86</td>
<td valign="middle" align="center">1.33</td>
<td valign="middle" align="center">216.05</td>
</tr>
<tr>
<td valign="middle" align="center">S5</td>
<td valign="middle" align="center">0.72</td>
<td valign="middle" align="center">1.15</td>
<td valign="middle" align="center">0.44</td>
<td valign="middle" align="center">400</td>
<td valign="middle" align="center">650</td>
<td valign="middle" align="center">1050</td>
<td valign="middle" align="center">8.05</td>
<td valign="middle" align="center">0.62</td>
<td valign="middle" align="center">130.43</td>
</tr>
<tr>
<td valign="middle" align="center">S6</td>
<td valign="middle" align="center">0.67</td>
<td valign="middle" align="center">1.31</td>
<td valign="middle" align="center">0.4</td>
<td valign="middle" align="center">600</td>
<td valign="middle" align="center">700</td>
<td valign="middle" align="center">1300</td>
<td valign="middle" align="center">11.15</td>
<td valign="middle" align="center">0.86</td>
<td valign="middle" align="center">116.59</td>
</tr>
<tr>
<td valign="middle" align="center">S7</td>
<td valign="middle" align="center">0.61</td>
<td valign="middle" align="center">2.23</td>
<td valign="middle" align="center">0.89</td>
<td valign="middle" align="center">850</td>
<td valign="middle" align="center">950</td>
<td valign="middle" align="center">1800</td>
<td valign="middle" align="center">22.22</td>
<td valign="middle" align="center">0.89</td>
<td valign="middle" align="center">81.01</td>
</tr>
<tr>
<td valign="middle" align="center">S8</td>
<td valign="middle" align="center">1.22</td>
<td valign="middle" align="center">1.84</td>
<td valign="middle" align="center">0.88</td>
<td valign="middle" align="center">750</td>
<td valign="middle" align="center">1650</td>
<td valign="middle" align="center">2400</td>
<td valign="middle" align="center">27.56</td>
<td valign="middle" align="center">0.45</td>
<td valign="middle" align="center">87.08</td>
</tr>
<tr>
<td valign="middle" align="center">S9</td>
<td valign="middle" align="center">0.69</td>
<td valign="middle" align="center">2.06</td>
<td valign="middle" align="center">1.03</td>
<td valign="middle" align="center">750</td>
<td valign="middle" align="center">1250</td>
<td valign="middle" align="center">2000</td>
<td valign="middle" align="center">22.50</td>
<td valign="middle" align="center">0.60</td>
<td valign="middle" align="center">88.89</td>
</tr>
<tr>
<td valign="middle" align="center">S10</td>
<td valign="middle" align="center">0.76</td>
<td valign="middle" align="center">2.86</td>
<td valign="middle" align="center">2.03</td>
<td valign="middle" align="center">600</td>
<td valign="middle" align="center">2000</td>
<td valign="middle" align="center">2600</td>
<td valign="middle" align="center">29.21</td>
<td valign="middle" align="center">0.30</td>
<td valign="middle" align="center">89.01</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s4_1_3">
<label>4.1.3</label>
<title>Morphological properties comparison between Types A and B cyclic steps</title>
<p>The average wavelength of Type A cyclic steps is 2.7 times that of Type B cyclic steps, and their average wave height is 2.9 times greater (<xref ref-type="table" rid="T1"><bold>Tables&#xa0;1</bold></xref>, <xref ref-type="table" rid="T2"><bold>2</bold></xref>). In terms of side lengths: the average stoss side length (<italic>L</italic><sub>stoss</sub>) of Type A is 4.1 times that of Type B, while the average lee side length (<italic>L</italic><sub>lee</sub>) of Type A is 1.9 times that of Type B (<xref ref-type="table" rid="T1"><bold>Tables&#xa0;1</bold></xref>, <xref ref-type="table" rid="T2"><bold>2</bold></xref>). Regarding slope gradients: the average stoss side slope (<italic>&#x3b1;</italic>) of Type A is 1.5 times that of Type B. In contrast, the average lee side slope (<italic>&#x3b2;</italic>) and the overall slope (<italic>&#x3b8;</italic>) of Type A are 0.94 times and 0.29 times those of Type B, respectively (<xref ref-type="table" rid="T1"><bold>Tables&#xa0;1</bold></xref>, <xref ref-type="table" rid="T2"><bold>2</bold></xref>). In terms of morphological indices: the average asymmetry index (<italic>A</italic><sub>y</sub>) of Type A is 2.1 times that of Type B, whereas the average aspect ratio of Type A is 0.8 times that of Type B (<xref ref-type="table" rid="T1"><bold>Tables&#xa0;1</bold></xref>, <xref ref-type="table" rid="T2"><bold>2</bold></xref>).</p>
</sec>
</sec>
<sec id="s4_2">
<label>4.2</label>
<title>Flow properties of turbidity currents generating the cyclic steps</title>
<sec id="s4_2_1">
<label>4.2.1</label>
<title>Flow properties of turbidity currents of Type A cyclic steps</title>
<p>Prior to hydraulic jumps, the velocity of turbidity currents passing over Type A cyclic steps (<italic>U</italic><sub>1</sub>) ranges from 2.60&#xa0;m/s to 6.08&#xa0;m/s, with an average of 4.47&#xa0;m/s (<xref ref-type="table" rid="T3"><bold>Table&#xa0;3</bold></xref>; <xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5A</bold></xref>). For these turbidity currents, the flow thickness (<italic>h</italic><sub>1</sub>) ranges from 36.73&#xa0;m to 124.64&#xa0;m (average: 66.27&#xa0;m), and the Froude number (<italic>Fr</italic><sub>1</sub>) ranges from 2.01 to 3.01 (average: 2.41) (<xref ref-type="table" rid="T3"><bold>Table&#xa0;3</bold></xref>).</p>
<table-wrap id="T3" position="float">
<label>Table&#xa0;3</label>
<caption>
<p>Estimated hydraulic properties of turbidity currents flowing through the thirteen Type A cyclic steps.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center">Type A</th>
<th valign="middle" rowspan="2" align="center">Values</th>
<th valign="middle" align="center"><italic>U</italic><sub>1</sub></th>
<th valign="middle" align="center"><italic>h</italic><sub>1</sub></th>
<th valign="middle" align="center"><italic>Fr</italic><sub>1</sub></th>
<th valign="middle" align="center"><italic>U</italic><sub>2</sub></th>
<th valign="middle" align="center"><italic>h</italic><sub>2</sub></th>
<th valign="middle" align="center"><italic>Fr</italic><sub>2</sub></th>
<th valign="middle" align="center">&#x394;<italic>E</italic><sub>L</sub></th>
<th valign="middle" align="center"><italic>L</italic><sub>jump</sub></th>
<th valign="middle" align="center"><italic>U</italic><sub>3</sub></th>
<th valign="middle" align="center"><italic>h</italic><sub>3</sub></th>
<th valign="middle" align="center"><italic>Fr</italic><sub>3</sub></th>
</tr>
<tr>
<th valign="middle" align="center">No.</th>
<th valign="middle" align="center">(m/s)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(-)</th>
<th valign="middle" align="center">(m/s)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(-)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(m/s)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(-)</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" rowspan="2" align="center">E1</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">2.96-5.13</td>
<td valign="middle" align="center">36.62-59.87</td>
<td valign="middle" align="center">2.13-2.72</td>
<td valign="middle" align="center">0.88-2.01</td>
<td valign="middle" align="center">123.65-152.53</td>
<td valign="middle" align="center">0.44-0.52</td>
<td valign="middle" align="center">21.78-36.39</td>
<td valign="middle" align="center">295.94-352.00</td>
<td valign="middle" align="center">1.58-3.53</td>
<td valign="middle" align="center">24.38-37.34</td>
<td valign="middle" align="center">1.78-1.85</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">4.05</td>
<td valign="middle" align="center">48.25</td>
<td valign="middle" align="center">2.43</td>
<td valign="middle" align="center">1.39</td>
<td valign="middle" align="center">138.09</td>
<td valign="middle" align="center">0.48</td>
<td valign="middle" align="center">29.09</td>
<td valign="middle" align="center">323.97</td>
<td valign="middle" align="center">2.47</td>
<td valign="middle" align="center">30.86</td>
<td valign="middle" align="center">1.82</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">E2</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">3.52-6.09</td>
<td valign="middle" align="center">43.99-71.92</td>
<td valign="middle" align="center">2.30-2.95</td>
<td valign="middle" align="center">0.95-2.18</td>
<td valign="middle" align="center">162.64-201.18</td>
<td valign="middle" align="center">0.41-0.49</td>
<td valign="middle" align="center">37.32-58.36</td>
<td valign="middle" align="center">457.10-501.69</td>
<td valign="middle" align="center">1.56-3.45</td>
<td valign="middle" align="center">59.15-83.13</td>
<td valign="middle" align="center">1.12-1.22</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">4.81</td>
<td valign="middle" align="center">57.96</td>
<td valign="middle" align="center">2.63</td>
<td valign="middle" align="center">1.51</td>
<td valign="middle" align="center">181.91</td>
<td valign="middle" align="center">0.45</td>
<td valign="middle" align="center">47.84</td>
<td valign="middle" align="center">457.10</td>
<td valign="middle" align="center">2.43</td>
<td valign="middle" align="center">71.14</td>
<td valign="middle" align="center">1.17</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">E3</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">3.01-5.22</td>
<td valign="middle" align="center">28.91-47.26</td>
<td valign="middle" align="center">2.43-3.11</td>
<td valign="middle" align="center">0.77-1.75</td>
<td valign="middle" align="center">113.62-140.79</td>
<td valign="middle" align="center">0.40-0.47</td>
<td valign="middle" align="center">30.75-46.28</td>
<td valign="middle" align="center">348.82-367.24</td>
<td valign="middle" align="center">1.16-2.56</td>
<td valign="middle" align="center">55.58-75.35</td>
<td valign="middle" align="center">0.86-0.95</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">4.12</td>
<td valign="middle" align="center">38.09</td>
<td valign="middle" align="center">2.77</td>
<td valign="middle" align="center">1.22</td>
<td valign="middle" align="center">127.21</td>
<td valign="middle" align="center">0.44</td>
<td valign="middle" align="center">38.52</td>
<td valign="middle" align="center">358.03</td>
<td valign="middle" align="center">1.80</td>
<td valign="middle" align="center">65.47</td>
<td valign="middle" align="center">0.91</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">E4</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">1.90-3.29</td>
<td valign="middle" align="center">18.88-30.86</td>
<td valign="middle" align="center">1.9-2.43</td>
<td valign="middle" align="center">0.64-1.47</td>
<td valign="middle" align="center">56.10-68.92</td>
<td valign="middle" align="center">0.47-0.57</td>
<td valign="middle" align="center">6.48-12.17</td>
<td valign="middle" align="center">97.34-138.55</td>
<td valign="middle" align="center">1.18-2.69</td>
<td valign="middle" align="center">9.02-12.2</td>
<td valign="middle" align="center">2.18-2.47</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">2.60</td>
<td valign="middle" align="center">24.87</td>
<td valign="middle" align="center">2.17</td>
<td valign="middle" align="center">1.02</td>
<td valign="middle" align="center">62.51</td>
<td valign="middle" align="center">0.52</td>
<td valign="middle" align="center">9.33</td>
<td valign="middle" align="center">117.95</td>
<td valign="middle" align="center">1.87</td>
<td valign="middle" align="center">10.61</td>
<td valign="middle" align="center">2.33</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">E5</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">2.69-4.65</td>
<td valign="middle" align="center">21.41-34.99</td>
<td valign="middle" align="center">2.52-3.23</td>
<td valign="middle" align="center">0.66-1.5</td>
<td valign="middle" align="center">87.55-108.60</td>
<td valign="middle" align="center">0.39-0.46</td>
<td valign="middle" align="center">26.23-38.60</td>
<td valign="middle" align="center">282.76-290.88</td>
<td valign="middle" align="center">1.26-2.75</td>
<td valign="middle" align="center">6.56-17.69</td>
<td valign="middle" align="center">2.1-2.74</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">3.67</td>
<td valign="middle" align="center">28.20</td>
<td valign="middle" align="center">2.88</td>
<td valign="middle" align="center">1.04</td>
<td valign="middle" align="center">98.08</td>
<td valign="middle" align="center">0.43</td>
<td valign="middle" align="center">32.42</td>
<td valign="middle" align="center">286.82</td>
<td valign="middle" align="center">1.95</td>
<td valign="middle" align="center">12.13</td>
<td valign="middle" align="center">2.42</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">E6</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">3.76-6.52</td>
<td valign="middle" align="center">86.06-140.69</td>
<td valign="middle" align="center">1.76-2.26</td>
<td valign="middle" align="center">1.38-3.19</td>
<td valign="middle" align="center">234.79-287.57</td>
<td valign="middle" align="center">0.50-0.60</td>
<td valign="middle" align="center">19.58-40.70</td>
<td valign="middle" align="center">291.75-513.35</td>
<td valign="middle" align="center">1.74-4.04</td>
<td valign="middle" align="center">172.98-210.83</td>
<td valign="middle" align="center">0.74-0.89</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">5.14</td>
<td valign="middle" align="center">113.38</td>
<td valign="middle" align="center">2.01</td>
<td valign="middle" align="center">2.20</td>
<td valign="middle" align="center">261.18</td>
<td valign="middle" align="center">0.55</td>
<td valign="middle" align="center">30.14</td>
<td valign="middle" align="center">402.55</td>
<td valign="middle" align="center">2.78</td>
<td valign="middle" align="center">191.91</td>
<td valign="middle" align="center">0.82</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">E7</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">2.64-4.57</td>
<td valign="middle" align="center">30.06-49.14</td>
<td valign="middle" align="center">2.09-2.67</td>
<td valign="middle" align="center">0.8-1.83</td>
<td valign="middle" align="center">99.61-122.80</td>
<td valign="middle" align="center">0.44-0.53</td>
<td valign="middle" align="center">16.56-28.09</td>
<td valign="middle" align="center">229.37-278.41</td>
<td valign="middle" align="center">1.51-3.39</td>
<td valign="middle" align="center">10-17.63</td>
<td valign="middle" align="center">2.59-2.66</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">3.61</td>
<td valign="middle" align="center">39.60</td>
<td valign="middle" align="center">2.38</td>
<td valign="middle" align="center">1.27</td>
<td valign="middle" align="center">111.21</td>
<td valign="middle" align="center">0.49</td>
<td valign="middle" align="center">22.33</td>
<td valign="middle" align="center">253.89</td>
<td valign="middle" align="center">2.37</td>
<td valign="middle" align="center">13.82</td>
<td valign="middle" align="center">2.63</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">E8</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">3.21-5.56</td>
<td valign="middle" align="center">27.88-45.58</td>
<td valign="middle" align="center">2.64-3.38</td>
<td valign="middle" align="center">0.75-1.7</td>
<td valign="middle" align="center">120.02-149.08</td>
<td valign="middle" align="center">0.38-0.45</td>
<td valign="middle" align="center">40.78-58.43</td>
<td valign="middle" align="center">411.08-411.99</td>
<td valign="middle" align="center">1.43-3.09</td>
<td valign="middle" align="center">10.24-27.32</td>
<td valign="middle" align="center">1.90-2.48</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">4.39</td>
<td valign="middle" align="center">36.73</td>
<td valign="middle" align="center">3.01</td>
<td valign="middle" align="center">1.18</td>
<td valign="middle" align="center">134.55</td>
<td valign="middle" align="center">0.42</td>
<td valign="middle" align="center">49.61</td>
<td valign="middle" align="center">411.54</td>
<td valign="middle" align="center">2.19</td>
<td valign="middle" align="center">18.78</td>
<td valign="middle" align="center">2.19</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">E9</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">3.7-6.4</td>
<td valign="middle" align="center">71.47-116.84</td>
<td valign="middle" align="center">1.90-2.43</td>
<td valign="middle" align="center">1.24-2.87</td>
<td valign="middle" align="center">212.39-260.91</td>
<td valign="middle" align="center">0.47-0.57</td>
<td valign="middle" align="center">24.52-46.08</td>
<td valign="middle" align="center">368.50-524.51</td>
<td valign="middle" align="center">1.73-3.97</td>
<td valign="middle" align="center">128.90-160.19</td>
<td valign="middle" align="center">0.85-1.01</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">5.05</td>
<td valign="middle" align="center">94.16</td>
<td valign="middle" align="center">2.17</td>
<td valign="middle" align="center">1.98</td>
<td valign="middle" align="center">236.65</td>
<td valign="middle" align="center">0.52</td>
<td valign="middle" align="center">35.30</td>
<td valign="middle" align="center">446.51</td>
<td valign="middle" align="center">2.75</td>
<td valign="middle" align="center">144.55</td>
<td valign="middle" align="center">0.93</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">E10</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">3.21-5.56</td>
<td valign="middle" align="center">42.81-69.98</td>
<td valign="middle" align="center">2.13-2.73</td>
<td valign="middle" align="center">0.95-2.17</td>
<td valign="middle" align="center">145.06-178.96</td>
<td valign="middle" align="center">0.44-0.52</td>
<td valign="middle" align="center">25.84-43.04</td>
<td valign="middle" align="center">349.73-414.41</td>
<td valign="middle" align="center">1.46-3.28</td>
<td valign="middle" align="center">67.07-88.08</td>
<td valign="middle" align="center">0.99-1.12</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">4.39</td>
<td valign="middle" align="center">56.40</td>
<td valign="middle" align="center">2.43</td>
<td valign="middle" align="center">1.51</td>
<td valign="middle" align="center">162.01</td>
<td valign="middle" align="center">0.48</td>
<td valign="middle" align="center">34.44</td>
<td valign="middle" align="center">382.07</td>
<td valign="middle" align="center">2.29</td>
<td valign="middle" align="center">77.58</td>
<td valign="middle" align="center">1.06</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">E11</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">3.93-6.81</td>
<td valign="middle" align="center">84.34-137.88</td>
<td valign="middle" align="center">1.86-2.38</td>
<td valign="middle" align="center">1.35-3.13</td>
<td valign="middle" align="center">244.74-300.40</td>
<td valign="middle" align="center">0.48-0.58</td>
<td valign="middle" align="center">25.91-49.98</td>
<td valign="middle" align="center">392.19-585.77</td>
<td valign="middle" align="center">1.77-4.06</td>
<td valign="middle" align="center">170.35-210.62</td>
<td valign="middle" align="center">0.75-0.90</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">5.37</td>
<td valign="middle" align="center">111.11</td>
<td valign="middle" align="center">2.12</td>
<td valign="middle" align="center">2.16</td>
<td valign="middle" align="center">272.57</td>
<td valign="middle" align="center">0.53</td>
<td valign="middle" align="center">37.95</td>
<td valign="middle" align="center">488.98</td>
<td valign="middle" align="center">2.81</td>
<td valign="middle" align="center">190.49</td>
<td valign="middle" align="center">0.83</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">E12</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">3.52-6.09</td>
<td valign="middle" align="center">66.9-109.37</td>
<td valign="middle" align="center">1.87-2.39</td>
<td valign="middle" align="center">1.21-2.78</td>
<td valign="middle" align="center">195.09-239.50</td>
<td valign="middle" align="center">0.48-0.58</td>
<td valign="middle" align="center">21.03-40.34</td>
<td valign="middle" align="center">317.94-469.99</td>
<td valign="middle" align="center">1.61-3.70</td>
<td valign="middle" align="center">130.17-160.49</td>
<td valign="middle" align="center">0.78-0.94</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">4.81</td>
<td valign="middle" align="center">88.14</td>
<td valign="middle" align="center">2.13</td>
<td valign="middle" align="center">1.92</td>
<td valign="middle" align="center">217.30</td>
<td valign="middle" align="center">0.53</td>
<td valign="middle" align="center">30.69</td>
<td valign="middle" align="center">393.97</td>
<td valign="middle" align="center">2.56</td>
<td valign="middle" align="center">145.33</td>
<td valign="middle" align="center">0.86</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">E13</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">4.45-7.71</td>
<td valign="middle" align="center">94.61-154.66</td>
<td valign="middle" align="center">1.99-2.54</td>
<td valign="middle" align="center">1.42-3.27</td>
<td valign="middle" align="center">296.47-364.84</td>
<td valign="middle" align="center">0.46-0.55</td>
<td valign="middle" align="center">41.14-73.31</td>
<td valign="middle" align="center">598.72-780.54</td>
<td valign="middle" align="center">1.84-4.21</td>
<td valign="middle" align="center">208.15-260.12</td>
<td valign="middle" align="center">0.71-0.84</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">6.08</td>
<td valign="middle" align="center">124.64</td>
<td valign="middle" align="center">2.27</td>
<td valign="middle" align="center">2.26</td>
<td valign="middle" align="center">330.66</td>
<td valign="middle" align="center">0.51</td>
<td valign="middle" align="center">57.23</td>
<td valign="middle" align="center">689.63</td>
<td valign="middle" align="center">2.92</td>
<td valign="middle" align="center">234.14</td>
<td valign="middle" align="center">0.78</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="f5" position="float">
<label>Figure&#xa0;5</label>
<caption>
<p>Graphical plots of the hydraulic characteristics of cyclic steps. <bold>(A)</bold> Velocity of cyclic steps comparison between Type A and Type B. The red represents <italic>U</italic><sub>1</sub> (velocity at the trough), the azure represents <italic>U</italic><sub>2</sub> (velocity after the hydraulic jumps) and the blue represents <italic>U</italic><sub>3</sub> (velocity at the crest). <bold>(B)</bold> Froude number of cyclic steps comparison between Type A and Type B. The red, azure and blue represent <italic>Fr</italic><sub>1</sub> (Froude number at the trough), <italic>Fr</italic><sub>2</sub> (Froude number after the hydraulic jumps) and <italic>Fr</italic><sub>3</sub> (Froude number at the crest). <bold>(C)</bold> Energy loss of cyclic steps comparison between Type A (marked in red) and Type B (marked in blue). <bold>(D)</bold> Length of the hydraulic jump of cyclic steps comparison between Type A (marked in red) and Type B (marked in blue).</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-13-1756034-g005.tif">
<alt-text content-type="machine-generated">Four charts display measurements related to cyclic steps differentiated by Type A and Type B. Chart (A) shows velocity plotted against the number of cyclic steps; Chart (B) illustrates the Froude number. Chart (C) presents energy loss, and Chart (D) depicts the length of the hydraulic jump, both also against the number of cyclic steps. Triangles represent Type A data, while circles denote Type B.</alt-text>
</graphic></fig>
<p>Downstream of hydraulic jumps, the velocity of turbidity currents decreases significantly. For Type A cyclic steps, the post-jump velocity (<italic>U</italic><sub>2</sub>) ranges from 1.02&#xa0;m/s to 2.26&#xa0;m/s (average: 1.59&#xa0;m/s) (<xref ref-type="table" rid="T3"><bold>Table&#xa0;3</bold></xref>; <xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5A</bold></xref>). Corresponding changes in other flow properties are observed: the post-jump flow thickness (<italic>h</italic><sub>2</sub>) ranges from 62.51&#xa0;m to 330.66&#xa0;m (average: 179.53&#xa0;m), and the post-jump Froude number (<italic>Fr</italic><sub>2</sub>) ranges from 0.42 to 0.55 (average: 0.49) (<xref ref-type="table" rid="T3"><bold>Table&#xa0;3</bold></xref>; <xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5B</bold></xref>). During hydraulic jumps, the energy loss (&#x394;<italic>E</italic><sub>L</sub>) of turbidity currents over Type A cyclic steps ranges from 9.33&#xa0;m to 57.23&#xa0;m, with a mean of 34.99&#xa0;m (<xref ref-type="table" rid="T3"><bold>Table&#xa0;3</bold></xref>; <xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5C</bold></xref>). Additionally, the length of these hydraulic jumps (<italic>L</italic><sub>jump</sub>) ranges from 117.95&#xa0;m to 689.63&#xa0;m, with an average of 387.33&#xa0;m (<xref ref-type="table" rid="T3"><bold>Table&#xa0;3</bold></xref>; <xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5D</bold></xref>).</p>
<p>In Stage III of the flow process, the turbidity current properties at the crests of Type A cyclic steps (<italic>U</italic><sub>3</sub>, <italic>h</italic><sub>3</sub>, <italic>Fr</italic><sub>3</sub>) are as follows: velocity (<italic>U</italic><sub>3</sub>) ranges from 1.80&#xa0;m/s to 2.92&#xa0;m/s (average: 2.40&#xa0;m/s), flow thickness (<italic>h</italic><sub>3</sub>) ranges from 10.61&#xa0;m to 234.14&#xa0;m (average: 92.83&#xa0;m), and Froude number (<italic>Fr</italic><sub>3</sub>) ranges from 0.78 to 2.42 (average: 1.44) (<xref ref-type="table" rid="T3"><bold>Table&#xa0;3</bold></xref>).</p>
</sec>
<sec id="s4_2_2">
<label>4.2.2</label>
<title>Flow properties of turbidity currents of Type B cyclic steps</title>
<p>Prior to hydraulic jumps, the velocity of turbidity currents passing over Type B cyclic steps (<italic>U</italic><sub>1</sub>) ranges from 2.08&#xa0;m/s to 3.99&#xa0;m/s, with an average of 3.14&#xa0;m/s (<xref ref-type="table" rid="T4"><bold>Table&#xa0;4</bold></xref>; <xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5A</bold></xref>). For these currents, the flow thickness (<italic>h</italic><sub>1</sub>) ranges from 18.62&#xa0;m to 67.74&#xa0;m (average: 31.43&#xa0;m), and the Froude number (<italic>Fr</italic><sub>1</sub>) ranges from 1.85 to 2.92 (average: 2.41) (<xref ref-type="table" rid="T4"><bold>Table&#xa0;4</bold></xref>).</p>
<table-wrap id="T4" position="float">
<label>Table&#xa0;4</label>
<caption>
<p>Estimated hydraulic properties of turbidity currents flowing through the ten Type B cyclic steps.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center">Type B</th>
<th valign="middle" rowspan="2" align="center">Values</th>
<th valign="middle" align="center"><italic>U</italic><sub>1</sub></th>
<th valign="middle" align="center"><italic>h</italic><sub>1</sub></th>
<th valign="middle" align="center"><italic>Fr</italic><sub>1</sub></th>
<th valign="middle" align="center"><italic>U</italic><sub>2</sub></th>
<th valign="middle" align="center"><italic>h</italic><sub>2</sub></th>
<th valign="middle" align="center"><italic>Fr</italic><sub>2</sub></th>
<th valign="middle" align="center">&#x394;<italic>E</italic><sub>L</sub></th>
<th valign="middle" align="center"><italic>L</italic><sub>jump</sub></th>
<th valign="middle" align="center"><italic>U</italic><sub>3</sub></th>
<th valign="middle" align="center"><italic>h</italic><sub>3</sub></th>
<th valign="middle" align="center"><italic>Fr</italic><sub>3</sub></th>
</tr>
<tr>
<th valign="middle" align="center">No.</th>
<th valign="middle" align="center">(m/s)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(-)</th>
<th valign="middle" align="center">(m/s)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(-)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(m/s)</th>
<th valign="middle" align="center">(m)</th>
<th valign="middle" align="center">(-)</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" rowspan="2" align="center">S1</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">2.83-4.89</td>
<td valign="middle" align="center">51.42-84.06</td>
<td valign="middle" align="center">1.71-2.19</td>
<td valign="middle" align="center">1.07-2.48</td>
<td valign="middle" align="center">135.63-165.91</td>
<td valign="middle" align="center">0.51-0.62</td>
<td valign="middle" align="center">9.83-21.41</td>
<td valign="middle" align="center">140.51-280.4</td>
<td valign="middle" align="center">1.25-2.9</td>
<td valign="middle" align="center">113.25-137.60</td>
<td valign="middle" align="center">0.65-0.79</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">3.86</td>
<td valign="middle" align="center">67.74</td>
<td valign="middle" align="center">1.95</td>
<td valign="middle" align="center">1.71</td>
<td valign="middle" align="center">150.77</td>
<td valign="middle" align="center">0.57</td>
<td valign="middle" align="center">15.62</td>
<td valign="middle" align="center">210.46</td>
<td valign="middle" align="center">2.00</td>
<td valign="middle" align="center">125.43</td>
<td valign="middle" align="center">0.72</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">S2</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">2.27-3.93</td>
<td valign="middle" align="center">15.22-24.88</td>
<td valign="middle" align="center">2.53-3.23</td>
<td valign="middle" align="center">0.55-1.26</td>
<td valign="middle" align="center">62.41-77.42</td>
<td valign="middle" align="center">0.39-0.46</td>
<td valign="middle" align="center">18.82-27.66</td>
<td valign="middle" align="center">202.19-207.7</td>
<td valign="middle" align="center">0.57-1.29</td>
<td valign="middle" align="center">60.92-75.93</td>
<td valign="middle" align="center">0.40-0.47</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">3.10</td>
<td valign="middle" align="center">20.05</td>
<td valign="middle" align="center">2.88</td>
<td valign="middle" align="center">0.88</td>
<td valign="middle" align="center">69.92</td>
<td valign="middle" align="center">0.43</td>
<td valign="middle" align="center">23.24</td>
<td valign="middle" align="center">204.95</td>
<td valign="middle" align="center">0.90</td>
<td valign="middle" align="center">68.43</td>
<td valign="middle" align="center">0.44</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">S3</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">2.27-3.93</td>
<td valign="middle" align="center">27.64-45.19</td>
<td valign="middle" align="center">1.88-2.4</td>
<td valign="middle" align="center">0.77-1.79</td>
<td valign="middle" align="center">81.00-99.45</td>
<td valign="middle" align="center">0.48-0.57</td>
<td valign="middle" align="center">8.89-16.96</td>
<td valign="middle" align="center">134.18-196.38</td>
<td valign="middle" align="center">0.94-2.16</td>
<td valign="middle" align="center">63.82-78.69</td>
<td valign="middle" align="center">0.65-0.78</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">3.10</td>
<td valign="middle" align="center">36.42</td>
<td valign="middle" align="center">2.14</td>
<td valign="middle" align="center">1.23</td>
<td valign="middle" align="center">90.23</td>
<td valign="middle" align="center">0.53</td>
<td valign="middle" align="center">12.93</td>
<td valign="middle" align="center">165.28</td>
<td valign="middle" align="center">1.50</td>
<td valign="middle" align="center">71.26</td>
<td valign="middle" align="center">0.72</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">S4</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">2.73-4.73</td>
<td valign="middle" align="center">27.03-44.18</td>
<td valign="middle" align="center">2.29-2.92</td>
<td valign="middle" align="center">0.75-1.71</td>
<td valign="middle" align="center">98.99-122.41</td>
<td valign="middle" align="center">0.42-0.50</td>
<td valign="middle" align="center">22.13-34.82</td>
<td valign="middle" align="center">274.13-303.02</td>
<td valign="middle" align="center">0.77-1.76</td>
<td valign="middle" align="center">95.68-118.83</td>
<td valign="middle" align="center">0.44-0.52</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">3.73</td>
<td valign="middle" align="center">35.61</td>
<td valign="middle" align="center">2.61</td>
<td valign="middle" align="center">1.19</td>
<td valign="middle" align="center">110.70</td>
<td valign="middle" align="center">0.46</td>
<td valign="middle" align="center">28.48</td>
<td valign="middle" align="center">288.58</td>
<td valign="middle" align="center">1.22</td>
<td valign="middle" align="center">107.26</td>
<td valign="middle" align="center">0.48</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">S5</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">1.52-2.64</td>
<td valign="middle" align="center">16.77-27.42</td>
<td valign="middle" align="center">1.62-2.07</td>
<td valign="middle" align="center">0.62-1.43</td>
<td valign="middle" align="center">41.34-50.44</td>
<td valign="middle" align="center">0.53-0.65</td>
<td valign="middle" align="center">2.21-5.35</td>
<td valign="middle" align="center">24.71-75.02</td>
<td valign="middle" align="center">0.78-1.83</td>
<td valign="middle" align="center">30.67-36.63</td>
<td valign="middle" align="center">0.78-0.97</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">2.08</td>
<td valign="middle" align="center">22.10</td>
<td valign="middle" align="center">1.85</td>
<td valign="middle" align="center">0.99</td>
<td valign="middle" align="center">45.89</td>
<td valign="middle" align="center">0.59</td>
<td valign="middle" align="center">3.78</td>
<td valign="middle" align="center">49.87</td>
<td valign="middle" align="center">1.25</td>
<td valign="middle" align="center">33.65</td>
<td valign="middle" align="center">0.88</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">S6</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">1.83-3.17</td>
<td valign="middle" align="center">18.75-30.65</td>
<td valign="middle" align="center">1.84-2.35</td>
<td valign="middle" align="center">0.64-1.48</td>
<td valign="middle" align="center">53.61-65.77</td>
<td valign="middle" align="center">0.49-0.58</td>
<td valign="middle" align="center">5.73-10.54</td>
<td valign="middle" align="center">81.40-125.72</td>
<td valign="middle" align="center">0.80-1.84</td>
<td valign="middle" align="center">40.11-49.41</td>
<td valign="middle" align="center">0.70-0.84</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">2.50</td>
<td valign="middle" align="center">24.70</td>
<td valign="middle" align="center">2.10</td>
<td valign="middle" align="center">1.02</td>
<td valign="middle" align="center">59.69</td>
<td valign="middle" align="center">0.54</td>
<td valign="middle" align="center">7.96</td>
<td valign="middle" align="center">103.56</td>
<td valign="middle" align="center">1.27</td>
<td valign="middle" align="center">44.76</td>
<td valign="middle" align="center">0.77</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">S7</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">1.90-3.29</td>
<td valign="middle" align="center">17.73-28.98</td>
<td valign="middle" align="center">1.96-2.51</td>
<td valign="middle" align="center">0.62-1.42</td>
<td valign="middle" align="center">54.61-67.16</td>
<td valign="middle" align="center">0.46-0.56</td>
<td valign="middle" align="center">7.15-12.95</td>
<td valign="middle" align="center">105.36-140.95</td>
<td valign="middle" align="center">0.80-1.84</td>
<td valign="middle" align="center">37.92-47.46</td>
<td valign="middle" align="center">0.73-0.86</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">2.60</td>
<td valign="middle" align="center">23.36</td>
<td valign="middle" align="center">2.24</td>
<td valign="middle" align="center">0.98</td>
<td valign="middle" align="center">60.89</td>
<td valign="middle" align="center">0.51</td>
<td valign="middle" align="center">10.05</td>
<td valign="middle" align="center">123.16</td>
<td valign="middle" align="center">1.27</td>
<td valign="middle" align="center">42.69</td>
<td valign="middle" align="center">0.80</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">S8</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">2.21-3.83</td>
<td valign="middle" align="center">14.13-23.11</td>
<td valign="middle" align="center">2.56-3.27</td>
<td valign="middle" align="center">0.53-1.22</td>
<td valign="middle" align="center">58.69-72.83</td>
<td valign="middle" align="center">0.39-0.46</td>
<td valign="middle" align="center">18.26-26.66</td>
<td valign="middle" align="center">193.02-196.95</td>
<td valign="middle" align="center">0.77-1.70</td>
<td valign="middle" align="center">32.78-43.81</td>
<td valign="middle" align="center">0.75-0.82</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">3.02</td>
<td valign="middle" align="center">18.62</td>
<td valign="middle" align="center">2.92</td>
<td valign="middle" align="center">0.84</td>
<td valign="middle" align="center">65.76</td>
<td valign="middle" align="center">0.43</td>
<td valign="middle" align="center">22.46</td>
<td valign="middle" align="center">194.99</td>
<td valign="middle" align="center">1.20</td>
<td valign="middle" align="center">38.30</td>
<td valign="middle" align="center">0.79</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">S9</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">2.92-5.05</td>
<td valign="middle" align="center">29.75-48.64</td>
<td valign="middle" align="center">2.32-2.97</td>
<td valign="middle" align="center">0.78-1.79</td>
<td valign="middle" align="center">111.01-137.35</td>
<td valign="middle" align="center">0.41-0.49</td>
<td valign="middle" align="center">26.13-40.61</td>
<td valign="middle" align="center">316.43-344.95</td>
<td valign="middle" align="center">0.89-2.01</td>
<td valign="middle" align="center">95.77-120.10</td>
<td valign="middle" align="center">0.50-0.59</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">3.99</td>
<td valign="middle" align="center">39.20</td>
<td valign="middle" align="center">2.65</td>
<td valign="middle" align="center">1.24</td>
<td valign="middle" align="center">124.18</td>
<td valign="middle" align="center">0.45</td>
<td valign="middle" align="center">33.73</td>
<td valign="middle" align="center">330.69</td>
<td valign="middle" align="center">1.40</td>
<td valign="middle" align="center">107.94</td>
<td valign="middle" align="center">0.55</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">S10</td>
<td valign="middle" align="center">Range</td>
<td valign="middle" align="center">2.54-4.40</td>
<td valign="middle" align="center">20.13-32.91</td>
<td valign="middle" align="center">2.46-3.14</td>
<td valign="middle" align="center">0.64-1.46</td>
<td valign="middle" align="center">80.00-99.16</td>
<td valign="middle" align="center">0.40-0.47</td>
<td valign="middle" align="center">22.27-33.31</td>
<td valign="middle" align="center">249.15-260.58</td>
<td valign="middle" align="center">0.74-1.68</td>
<td valign="middle" align="center">66.90-84.47</td>
<td valign="middle" align="center">0.51-0.58</td>
</tr>
<tr>
<td valign="middle" align="center">Mean</td>
<td valign="middle" align="center">3.47</td>
<td valign="middle" align="center">26.52</td>
<td valign="middle" align="center">2.80</td>
<td valign="middle" align="center">1.01</td>
<td valign="middle" align="center">89.58</td>
<td valign="middle" align="center">0.44</td>
<td valign="middle" align="center">27.79</td>
<td valign="middle" align="center">254.87</td>
<td valign="middle" align="center">1.17</td>
<td valign="middle" align="center">75.69</td>
<td valign="middle" align="center">0.55</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>After hydraulic jumps, the velocity of turbidity currents decreases significantly. For Type B cyclic steps, the post-jump velocity (<italic>U</italic><sub>2</sub>) ranges from 0.84&#xa0;m/s to 1.71&#xa0;m/s (average: 1.11&#xa0;m/s) (<xref ref-type="table" rid="T4"><bold>Table&#xa0;4</bold></xref>; <xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5A</bold></xref>). Corresponding changes in other flow properties include: post-jump flow thickness (<italic>h</italic><sub>2</sub>) ranging from 45.89&#xa0;m to 150.77&#xa0;m (average: 86.76&#xa0;m) and post-jump Froude number (<italic>Fr</italic><sub>2</sub>) ranging from 0.43 to 0.57 (average: 0.49) (<xref ref-type="table" rid="T4"><bold>Table&#xa0;4</bold></xref>; <xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5B</bold></xref>). During hydraulic jumps, the energy loss (&#x394;<italic>E</italic><sub>L</sub>) of turbidity currents over Type B cyclic steps ranges from 3.78&#xa0;m to 33.37&#xa0;m, with a mean of 18.57&#xa0;m (<xref ref-type="table" rid="T4"><bold>Table&#xa0;4</bold></xref>; <xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5C</bold></xref>). Additionally, the length of these hydraulic jumps (<italic>L</italic><sub>jump</sub>) ranges from 49.87&#xa0;m to 330.69&#xa0;m, with an average of 192.64&#xa0;m (<xref ref-type="table" rid="T4"><bold>Table&#xa0;4</bold></xref>; <xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5D</bold></xref>).</p>
<p>In Stage III of the flow process, the turbidity current properties at the crests of Type B cyclic steps (<italic>U</italic><sub>3</sub>, <italic>h</italic><sub>3</sub>, <italic>Fr</italic><sub>3</sub>) are as follows: velocity (<italic>U</italic><sub>3</sub>) ranges from 0.90&#xa0;m/s to 2.00&#xa0;m/s (average: 1.32&#xa0;m/s), flow thickness (<italic>h</italic><sub>3</sub>) ranges from 33.65&#xa0;m to 125.43&#xa0;m (average: 71.54&#xa0;m), and Froude number (<italic>Fr</italic><sub>3</sub>) ranges from 0.44 to 0.88 (average: 0.67) (<xref ref-type="table" rid="T4"><bold>Table&#xa0;4</bold></xref>).</p>
</sec>
<sec id="s4_2_3">
<label>4.2.3</label>
<title>Hydraulic properties comparison between Types A and B cyclic steps</title>
<p>In terms of the hydraulic characteristics of cyclic steps, the average values of pre-jump velocity (<italic>U</italic><sub>1</sub>) and pre-jump flow thickness (<italic>h</italic><sub>1</sub>) for turbidity currents forming Type A cyclic steps (E1 to E13) are 1.4 times and 2.1 times those of the currents forming Type B cyclic steps (S1 to S10), respectively (<xref ref-type="table" rid="T3"><bold>Tables&#xa0;3</bold></xref>, <xref ref-type="table" rid="T4"><bold>4</bold></xref>). After hydraulic jumps, the average post-jump velocity (<italic>U</italic><sub>2</sub>) of turbidity currents over Type A cyclic steps is 1.4 times that of those over Type B, and the average post-jump flow thickness (<italic>h</italic><sub>2</sub>) of Type A is 2.1 times that of Type B. Additionally, the average energy loss (&#x394;<italic>E</italic><sub>L</sub>) of turbidity currents during hydraulic jumps for Type A is 1.9 times that of Type B, and the average hydraulic jump length (<italic>L</italic><sub>jump</sub>) for Type A is 2.0 times that of Type B. In Stage III, the average values of flow velocity (U<sub>3</sub>) and flow thickness (<italic>h</italic><sub>3</sub>) of turbidity currents at the crests of Type A cyclic steps are 1.8 times and 1.3 times those of Type B, respectively (<xref ref-type="table" rid="T3"><bold>Table&#xa0;3</bold></xref>).</p>
<p>Notably, the average pre-jump (<italic>Fr</italic><sub>1</sub>) and post-jump (<italic>Fr</italic><sub>2</sub>) Froude numbers of turbidity currents are nearly identical between Type A and Type B cyclic steps. However, the average Froude number at the crests (<italic>Fr</italic><sub>3</sub>) of Type A is 2.1 times that of Type B. From a flow regime perspective: in Stage I (prior to hydraulic jumps), turbidity currents over both Types A and B cyclic steps are supercritical (<italic>Fr</italic><sub>1</sub>&gt;1); after hydraulic jumps (Stage II), the flow transitions to subcritical (<italic>Fr</italic><sub>2</sub>&lt;1) for both types. In Stage III, however, a distinct difference emerges: turbidity currents at the crests of Type A cyclic steps remain supercritical (<italic>Fr</italic><sub>3</sub>&gt;1), whereas those at the crests of Type B are subcritical (<italic>Fr</italic><sub>3</sub>&lt;1).</p>
</sec>
</sec>
</sec>
<sec id="s5" sec-type="discussion">
<label>5</label>
<title>Discussion</title>
<sec id="s5_1">
<label>5.1</label>
<title>Origin and formation process of cyclic steps</title>
<p>Thirteen (13) Type A cyclic steps and ten (10) Type B cyclic steps were identified near the Manila Trench. Their morphological features, as well as the flow properties of the inferred turbidity currents that could generate them were compared in Section 4. <xref ref-type="bibr" rid="B34">Symons et&#xa0;al. (2016)</xref> conducted a statistical analysis of numerous sediment waves and scours across a broad range of water depths and environmental settings (<xref ref-type="fig" rid="f6"><bold>Figure&#xa0;6</bold></xref>). In the study area, despite the morphological differences between Types A and B cyclic steps, their wavelengths and wave heights are comparable to those of large-scale bedforms with mixed relief documented in <xref ref-type="bibr" rid="B34">Symons et&#xa0;al. (2016)</xref> and <xref ref-type="bibr" rid="B7">Clare et&#xa0;al. (2023)</xref>. In this section, the origin and formation processes of these cyclic steps are discussed.</p>
<fig id="f6" position="float">
<label>Figure&#xa0;6</label>
<caption>
<p>Log-Log plots of aspect ratios (wavelength versus wave height) for thirteen (13) Type A and ten (10) Type B cyclic steps, compared to those described in <xref ref-type="bibr" rid="B34">Symons et&#xa0;al. (2016)</xref> and <xref ref-type="bibr" rid="B7">Clare et&#xa0;al. (2023)</xref>.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-13-1756034-g006.tif">
<alt-text content-type="machine-generated">Graph illustrating wave height against wavelength, highlighting bedform types. A cyan area represents small-scale bedforms with mixed relief. A green area denotes large-scale bedforms, overlapping a magenta section marked as large-scale scours comprising enclosed depressions. Red dots indicate Type A cyclic steps, and blue dots indicate Type B cyclic steps, as referenced in the legend. Arrows and labels provide context for each area.</alt-text>
</graphic></fig>
<p>In previous studies, the formation of cyclic steps along submarine canyons has been attributed to hydraulic jumps in turbidity currents (<xref ref-type="bibr" rid="B5">Cerrillo-Escoriza et&#xa0;al., 2024</xref>; <xref ref-type="bibr" rid="B13">Dorrell et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B32">Slootman and Cartigny, 2020</xref>). In the present study area, the formation of both Type A and Type B cyclic steps is linked to the transition of turbidity currents from supercritical flow (<italic>Fr</italic><sub>1</sub>&gt;1) to subcritical flow (<italic>Fr</italic><sub>2</sub>&lt;1) (<xref ref-type="table" rid="T3"><bold>Tables&#xa0;3</bold></xref>, <xref ref-type="table" rid="T4"><bold>4</bold></xref>). Cyclic steps along the Penghu Canyon and South Taiwan Shoal Canyon have been classified as net-erosional cyclic steps, based on their columnar arrangement, upstream migration direction, and crescentic morphology (<xref ref-type="bibr" rid="B27">Li et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B44">Zhang et&#xa0;al., 2022</xref>). Given these characteristics, we infer that Type A cyclic steps are net-erosional cyclic steps, associated with confined turbidity currents that propagate along the submarine canyons-specifically, the South Taiwan Shoal Canyon and the Penghu Canyon (<xref ref-type="fig" rid="f7"><bold>Figure&#xa0;7</bold></xref>).</p>
<fig id="f7" position="float">
<label>Figure&#xa0;7</label>
<caption>
<p>Illustration of the origin and formation mechanism of Types A and B cyclic steps.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-13-1756034-g007.tif">
<alt-text content-type="machine-generated">Three-dimensional diagram showing underwater topography with labeled features. The South Taiwan Shoal Canyon and Penghu Canyon indicate flow directions. Seamount is highlighted, with &#x201c;Type A cyclic steps&#x201d; and &#x201c;Type B cyclic steps&#x201d; marked in red. The map also references the Manila Trench and describes overflow driven by inertial centrifugal force.</alt-text>
</graphic></fig>
<p>Type B cyclic steps in this study are distributed outside the levees of the South Taiwan Shoal Canyon, adjacent to canyon bends (<xref ref-type="fig" rid="f1"><bold>Figures&#xa0;1</bold></xref>, <xref ref-type="fig" rid="f7"><bold>7</bold></xref>). At these bends, turbidity currents overflow due to superelevation (<xref ref-type="bibr" rid="B25">Lamb et&#xa0;al., 2008</xref>) and inertial centrifugal force (<xref ref-type="bibr" rid="B23">Kuang et&#xa0;al., 2014</xref>), these overspilling currents exhibit supercritical flow and typically undergo successive downslope hydraulic jumps (<xref ref-type="bibr" rid="B5">Cerrillo-Escoriza et&#xa0;al., 2024</xref>; <xref ref-type="bibr" rid="B16">Fildani et&#xa0;al., 2006</xref>). A process that generates sheet-shaped, net-depositional cyclic steps on canyon levees, as documented in the Shepard Bend of Monterey Canyon, Eel Canyon, and West Mariana Ridge (<xref ref-type="bibr" rid="B5">Cerrillo-Escoriza et&#xa0;al., 2024</xref>; <xref ref-type="bibr" rid="B16">Fildani et&#xa0;al., 2006</xref>; <xref ref-type="bibr" rid="B25">Lamb et&#xa0;al., 2008</xref>; <xref ref-type="bibr" rid="B43">Zhang et&#xa0;al., 2023</xref>). Type B cyclic steps show downslope-decreasing dimensions (<xref ref-type="fig" rid="f3"><bold>Figure&#xa0;3E</bold></xref>), consistent with the traits of sediment waves formed by unconfined turbidity currents (<xref ref-type="bibr" rid="B34">Symons et&#xa0;al., 2016</xref>).</p>
</sec>
<sec id="s5_2">
<label>5.2</label>
<title>Factors controlling the Types A and B cyclic steps</title>
<p>Based on their location and dimensions, the cyclic steps in the study area can be categorized into two main types (Types A and B): Type A occurs downstream of canyon mouths, while Type B is distributed outside the levees of the South Taiwan Shoal Canyon, adjacent to canyon bends. In plan view, Type B cyclic steps are significantly smaller than Type A (<xref ref-type="fig" rid="f3"><bold>Figure&#xa0;3</bold></xref>). Results from principal component analysis (PCA) indicate that the first three principal components (PC1, PC2, PC3) capture 98.33% of the total variance (<xref ref-type="table" rid="T5"><bold>Table&#xa0;5</bold></xref>), so these three components are the focus of subsequent analysis. PC1, explaining 85.4% of total variance, is strongly negatively correlated with step length (<italic>L</italic><sub>step</sub>) (correlation coefficient: -0.86) and step height (<italic>H</italic><sub>step</sub>) (-0.60; <xref ref-type="table" rid="T5"><bold>Table&#xa0;5</bold></xref>). PC2 accounts for an additional 8.1% of variance and shows strong positive correlations with water depth (0.84) and stoss side length (<italic>L</italic><sub>stoss</sub>) (<italic>-</italic>0.56; <xref ref-type="table" rid="T5"><bold>Table&#xa0;5</bold></xref>). PC3 explains a further 4.8% of variance, with a strong positive correlation with <italic>H</italic><sub>step</sub> (0.80) and a negative correlation with <italic>L</italic><sub>stoss</sub> (-0.60; <xref ref-type="table" rid="T5"><bold>Table&#xa0;5</bold></xref>). The strongest correlations are observed for <italic>L</italic><sub>step</sub> (-0.86 with PC1, 0.46 with PC2) and <italic>H</italic><sub>step</sub> (-0.60 with PC1, 0.80 with PC3). Thus, these two parameters are prioritized for further discussion.</p>
<table-wrap id="T5" position="float">
<label>Table&#xa0;5</label>
<caption>
<p>Correlation coefficients determined from principal component analysis.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" rowspan="2" align="center">Principal component</th>
<th valign="middle" rowspan="2" align="center">Proportion of variance</th>
<th valign="middle" colspan="4" align="center">Correlation coefficient determined from principal component analysis</th>
</tr>
<tr>
<th valign="middle" align="center"><italic>L</italic><sub>stoss</sub></th>
<th valign="middle" align="center"><italic>L</italic><sub>step</sub></th>
<th valign="middle" align="center"><italic>H</italic><sub>step</sub></th>
<th valign="middle" align="center">Water Depth</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" align="center">PC1</td>
<td valign="middle" align="center">0.8536</td>
<td valign="middle" align="center">-0.5755</td>
<td valign="middle" align="center">-0.8633</td>
<td valign="middle" align="center">-0.6031</td>
<td valign="middle" align="center">0.3982</td>
</tr>
<tr>
<td valign="middle" align="center">PC2</td>
<td valign="middle" align="center">0.0814</td>
<td valign="middle" align="center">0.5591</td>
<td valign="middle" align="center">0.4589</td>
<td valign="middle" align="center">-0.0580</td>
<td valign="middle" align="center">0.8387</td>
</tr>
<tr>
<td valign="middle" align="center">PC3</td>
<td valign="middle" align="center">0.0483</td>
<td valign="middle" align="center">-0.5968</td>
<td valign="middle" align="center">-0.2101</td>
<td valign="middle" align="center">0.7956</td>
<td valign="middle" align="center">0.3714</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The two cyclic step types (Type A and Type B) are distinctly distinguishable in cross-plots of PC1 vs. PC2, PC1 vs. PC3, and PC2 vs. PC3 (<xref ref-type="fig" rid="f8"><bold>Figure&#xa0;8</bold></xref>). For PC1, the absolute correlation coefficient is largest for step length (<italic>L</italic><sub>step</sub>), followed by step height (<italic>H</italic><sub>step</sub>). For PC2, the largest absolute correlation coefficient corresponds to water depth (<xref ref-type="table" rid="T5"><bold>Table&#xa0;5</bold></xref>). Both Types A and B cyclic steps exhibit wide variance in PC1 but relatively narrow variance in PC2, indicating a broad range of <italic>L</italic><sub>step</sub> and <italic>H</italic><sub>step</sub> values yet minimal variation in water depth (<xref ref-type="table" rid="T5"><bold>Table&#xa0;5</bold></xref>; <xref ref-type="fig" rid="f8"><bold>Figure&#xa0;8</bold></xref>). Thus, <italic>L</italic><sub>step</sub> and <italic>H</italic><sub>step</sub> are the key variables driving the clustering of the two types, whereas water depth is less influential. Therefore, subsequent discussion will focus on the factors contributing to morphological differences (i.e., variations in <italic>L</italic><sub>step</sub> and <italic>H</italic><sub>step</sub>) between the two cyclic step types.</p>
<fig id="f8" position="float">
<label>Figure&#xa0;8</label>
<caption>
<p>Biplots of principal component analysis. Correlation coefficients for variables are highlighted in <xref ref-type="table" rid="T5"><bold>Table&#xa0;5</bold></xref>. The two clusters (Types A and B) cyclic steps distinctly identified, marked in red and blue circle dots, respectively. The length of the arrow represents the importance of the component in the principal component. A correlation coefficient of 1 indicates perfect correlation, -1 indicates perfect negative correlation, and 0 indicates no correlation.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-13-1756034-g008.tif">
<alt-text content-type="machine-generated">Three scatterplots labeled A, B, and C show principal component analyses with data points in red and blue. Arrows represent variables: orange (L stoss), green (L step), black (H step), blue (Water Depth). Plot A compares Principal Components 1 (85.4% variance) and 2 (8.14% variance). Plot B uses Principal Components 1 (85.4%) and 3 (4.83%). Plot C uses Principal Components 2 and 3. Each plot includes ellipses around the data points indicating variance.</alt-text>
</graphic></fig>
<p><xref ref-type="fig" rid="f9"><bold>Figure&#xa0;9</bold></xref> illustrates the relationship between the morphological parameters of cyclic steps (<italic>L</italic><sub>step</sub> and <italic>H</italic><sub>step</sub>) and the properties of turbidity currents (<italic>U</italic><sub>1</sub> and &#x394;<italic>E</italic><sub>L</sub>). Specifically, turbidity currents crossing Type B cyclic steps exhibit significantly lower <italic>U</italic><sub>1</sub> (1.86&#xa0;m/s vs. 2.82&#xa0;m/s) and &#x394;<italic>E</italic><sub>L</sub> (18.57&#xa0;m vs. 34.99&#xa0;m) compared to those crossing Type A. These differences in flow characteristics likely drive the distinct morphological traits of the two cyclic step types, including variations in <italic>L</italic><sub>step</sub> and <italic>H</italic><sub>step</sub>.</p>
<fig id="f9" position="float">
<label>Figure&#xa0;9</label>
<caption>
<p>Graphical plots highlighting the morphological characteristics and properties of turbidity currents in the study area. <bold>(A, B)</bold> showing relationships of length of cyclic steps (<italic>L</italic><sub>step</sub>) and height of cyclic steps (<italic>H</italic><sub>step</sub>) versus velocity of turbidity currents (<italic>U</italic><sub>1</sub>). <bold>(C, D)</bold> showing relationships of length of cyclic steps (<italic>L</italic><sub>step</sub>) and height of cyclic steps (<italic>H</italic><sub>step</sub>) versus loss of energy in turbidity currents (&#x394;<italic>E</italic><sub>L</sub>). Red and blue circle dots denote Types A and B cyclic steps, respectively.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-13-1756034-g009.tif">
<alt-text content-type="machine-generated">Four scatter plots depict relations in cyclic steps data. (A) plots the length versus velocity before a hydraulic jump. (B) shows height versus velocity. (C) illustrates length versus energy loss. (D) presents height versus energy loss. Red and blue dots indicate Types A and B, respectively.</alt-text>
</graphic></fig>
<p>The flow regime of turbidity currents is strongly influenced by slope gradient, sediment concentration, bed roughness, and sediment grain size (<xref ref-type="bibr" rid="B20">Kostic, 2011</xref>). Recent physical experiments have shown that the abrupt loss of lateral confinement in a canyon triggers turbidity current relaxation manifested as a velocity decrease, marking the transition from confined to unconfined flow (<xref ref-type="bibr" rid="B11">de Leeuw et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B30">Pohl et&#xa0;al., 2019</xref>). Additionally, spatiotemporal variations in flow velocity regulate the sediment transport and deposition capacity of turbidity currents (<xref ref-type="bibr" rid="B40">Yang et&#xa0;al., 2024</xref>). In this study, Type A cyclic steps are net-erosional features associated with confined turbidity currents flowing along submarine canyons, whereas Type B cyclic steps are net-depositional and form in open settings under unconfined turbidity currents. This distinction corresponds to a dramatic difference in the flow regime of turbidity currents interacting with the two cyclic step types. We hypothesize that the significant disparities in the flow characteristics of turbidity currents across Types A and B cyclic steps are linked to their respective confined and unconfined seafloor environments.</p>
<p>In summary, the difference in flow properties between confined and unconfined turbidity currents is the primary control on the morphological differences between Types A and B cyclic steps.</p>
</sec>
<sec id="s5_3">
<label>5.3</label>
<title>New submarine canyon-channel systems are being formed</title>
<p>Submarine canyon-channels act as critical conduits for transporting large volumes of sediment and particulate matter across continental margins to the deep ocean (<xref ref-type="bibr" rid="B1">Allen, 2008</xref>), numerous experiments and numerical simulations have investigated the development and formation of such channels (e.g., <xref ref-type="bibr" rid="B17">Hall et&#xa0;al., 2008</xref>; <xref ref-type="bibr" rid="B2">Cantelli et&#xa0;al., 2011</xref>; <xref ref-type="bibr" rid="B41">Yu, 2011</xref>). A key hypothesis is that incipient channels originate from net-erosional cyclic steps, which signal the initiation of a fully developed conduit (<xref ref-type="bibr" rid="B16">Fildani et&#xa0;al., 2006</xref>; <xref ref-type="bibr" rid="B21">Kostic and Parker, 2006</xref>; <xref ref-type="bibr" rid="B20">Kostic, 2011</xref>) and <xref ref-type="bibr" rid="B15">Fildani et&#xa0;al. (2013)</xref> used seismic data to document channel evolution, demonstrating that channels form during an initial erosive phase, driven by continuous turbidity current erosion (e.g., via net-erosional cyclic steps) and accompanied by levee aggradation, as observed in the Lucia Chica channel system. Building on this framework, we propose a three-stage model for the progressive development of mature canyon-channels in the Manila Trench: Stage I (Incipient Erosion), where turbidity currents undergo hydraulic jumps to generate a series of net-erosional cyclic steps (i.e., Type A cyclic steps) (<xref ref-type="fig" rid="f10"><bold>Figure&#xa0;10A</bold></xref>); Stage II (Channel Incision and Levee Construction), in which turbidity currents continue eroding the seabed (deepening the incipient channel) while promoting levee aggradation (widening and stabilizing channel margins) (<xref ref-type="fig" rid="f10"><bold>Figure&#xa0;10B</bold></xref>); and Stage III (Mature Conduit Formation), where fully developed canyon-channel systems evolve and connect to the Manila Trench (<xref ref-type="fig" rid="f10"><bold>Figure&#xa0;10C</bold></xref>). This formation process is expected to alter the pattern of material transport and deposition to the deep sea within the Manila Trench.</p>
<fig id="f10" position="float">
<label>Figure&#xa0;10</label>
<caption>
<p>Illustration of the formation mechanism of new submarine canyon-channel systems at the head of the Manila Trench. The diagram of time-step channel evolution of slope channels is modified from (<xref ref-type="bibr" rid="B15">Fildani et&#xa0;al., 2013</xref>).</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-13-1756034-g010.tif">
<alt-text content-type="machine-generated">Three panels display the geological development of canyons: (A) Stage I shows initial cyclic steps, with turbidity flows forming at South Taiwan Shoal Canyon. (B) Stage II depicts the formation of broad channels with persistent turbidity flows, highlighting thalweg development. (C) Stage III presents narrower channels with developed levees, showcasing further turbidity flow impact. Each stage includes a diagram illustrating flow direction and geological features labeled with key locations such as the Manila Trench and Gaoping Canyon.</alt-text>
</graphic></fig>
</sec>
</sec>
<sec id="s6" sec-type="conclusions">
<label>6</label>
<title>Conclusions</title>
<p>High-resolution multibeam bathymetry data allowed us to characterize the morphology and geometric parameters of two cyclic step types near the Manila Trench, quantify the flow properties of turbidity currents traversing these cyclic steps, and focus on their formation mechanisms and morphological controlling factors, with additional predictions of their future evolution. The main conclusions of this study are as follows:</p>
<list list-type="order">
<list-item>
<p>Based on location and dimensions, two cyclic step types (13 net-erosional Type A and 10 net-depositional Type B) were identified near the Manila Trench, specifically downstream of the South Taiwan Shoal Canyon and Penghu Canyon.</p></list-item>
<list-item>
<p>Principal component analysis (PCA) revealed distinct clustering of Types A and B cyclic steps, and correlation coefficients with principal components indicated that cyclic step length (<italic>L</italic><sub>step</sub>) and height (<italic>H</italic><sub>step</sub>) are the key variables driving this clustering.</p></list-item>
<list-item>
<p>Type A cyclic steps form under the control of submarine confined turbidity currents, whereas Type B cyclic steps are governed by unconfined turbidity currents that overflow canyon bends due to superelevation. The primary factor driving morphological differences between the two types is the significant disparity in flow properties of the confined versus unconfined turbidity currents traversing them.</p></list-item>
<list-item>
<p>Under sustained erosion by turbidity currents, Type A (net-erosional) cyclic steps are expected to evolve into new submarine canyon-channel systems, which will alter the pattern of material transport and deposition to the deep sea within the Manila Trench.</p></list-item>
</list>
</sec>
</body>
<back>
<sec id="s7" sec-type="data-availability">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material. Further inquiries can be directed to the corresponding author.</p></sec>
<sec id="s8" sec-type="author-contributions">
<title>Author contributions</title>
<p>YY: Conceptualization, Data curation, Formal Analysis, Funding acquisition, Investigation, Methodology, Validation, Visualization, Writing &#x2013; original draft, Writing &#x2013; review &amp; editing. SZ: Methodology, Writing &#x2013; review &amp; editing, Formal Analysis, Investigation. SL: Conceptualization, Formal Analysis, Methodology, Writing &#x2013; review &amp; editing, Investigation. KY:&#xa0;Conceptualization, Formal Analysis, Validation, Writing &#x2013; review &amp; editing, Data curation, Investigation. XQ: Resources, Formal Analysis, Project administration, Writing &#x2013; review &amp; editing, Funding acquisition, Validation, Conceptualization, Methodology, Investigation. CW: Formal Analysis, Methodology, Writing &#x2013; review &amp; editing, Conceptualization, Data curation. JX:&#xa0;Conceptualization, Data curation, Funding acquisition, Methodology, Project administration, Resources, Supervision, Visualization, Writing &#x2013; review &amp; editing, Writing &#x2013; original draft.</p></sec>
<ack>
<title>Acknowledgments</title>
<p>This study was supported by the Research Innovation Fund of Tianjin Research Institute for Water Transport Engineering, Ministry of Transport, China (Grant No. TKS20250704), the National Natural Science Foundation of China (Grant Nos. 42106198, 42350710199) and the Guangdong Provincial Key Discipline Research Capacity Enhancement Initiative (Grant Nos. 2024ZDJS060, 2024ZDJS053). We would like to thank everyone of the R/V &#x201c;Dongfanghong 3&#x201d; who contributed to the bathymetric survey in the Manila Trench.</p>
</ack>
<sec id="s10" sec-type="COI-statement">
<title>Conflict of interest</title>
<p>The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
<p>The reviewer YL declared a past collaboration with the authors YY to the handling editor.</p></sec>
<sec id="s11" sec-type="ai-statement">
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<fn id="n1" fn-type="custom" custom-type="edited-by">
<p>Edited by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1474732">Zhuangcai Tian</ext-link>, China University of Mining and Technology, China</p></fn>
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<p>Reviewed by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2281200">Yang Lu</ext-link>, Ocean University of China, China</p>
<p><ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3327798">Dongrui Han</ext-link>, Zhejiang University, China</p></fn>
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