The analysis of mesoscale eddies in the MC was conducted using the Mesoscale Eddy Trajectory Atlas Product (version 2.0, METAP), which is produced in delayed time by the SSALTO/DUACS multimission altimeter data processing system and distributed by AVISO+ (https://www.aviso.altimetry.fr/) following the methodology developed by Schlax and Chelton (2016). This product, which is reliable for recognizing mesoscale eddies and has been successfully applied in many studies (Dong et al., 2017; Sandalyuk et al., 2020), provides the daily cyclonic/anticyclonic type, central position, and radius of mesoscale eddies from 1993 to 2017 to facilitate the analysis of mesoscale eddies. The mesoscale eddy center is defined as the location of a Sea Level Anomaly (SLA) extremum within a predefined eddy area. The SLA field encompasses a broad spectrum of features, ranging from small to large-scale ones. Eddies are identified as features with diameters of 100-300 km; therefore, the initial step involves eliminating larger-scale variability (~1000 km) through the application of a low pass filter before detecting eddy centers. To compute large-scale variability, smoothing was performed using a Lanczos filter with a 1000 km half-power cutoff wavelength in both latitude and longitude dimensions. The resultant output was then subtracted from the original SLA data to generate a high-pass filtered grid exclusively containing mesoscale variability. Eddy radius is defined as the radius of a circle whose area matches that enclosed by the contour of the maximum circum-average geostrophic speed. In consideration of the ~35-day decorrelation time scale in the AVISO optimal interpolation procedure, METAP removes mesoscale eddies with lifetimes shorter than 28 d to prevent sporadic eddy events perhaps resulting from potential artifacts associated with the interpolation procedure.

An improved statistical processing of mesoscale eddies was established to avoid counting the same eddies repeatedly. The MC (34–49°E, 10–25°S) was first homogeneously divided into 1/2° grid meshes, the same as Halo et al. (2014). Then, the number of different types of eddies in each grid mesh was accumulated based on their identification. Note that each eddy has a unique identification, which is labeled as a serial number so that it would not be counted repeatedly.

Dipole eddies in the MC were extracted from METAP. Here, two adjacent eddies with eddy-center distances smaller than the sum of their radii are determined to be dipole eddies. The first step to extract dipole eddies from cyclonic eddies and anticyclonic eddies of METAP is to gain eddy information on each day. Subsequently, we conduct a comparison of the distances between eddy centers and the summation of their radii for each pair of eddies observed on the same day. Two eddies with eddy-center distances smaller than the sum of their radii are determined to be dipole eddies. The identity information of these two eddies and the day they form a dipole eddy is recorded as a dipole eddy record. By iteratively following this procedure, all dipole eddies in the MC will be found. Dipole eddies with the two eddies exhibiting consistent identity information on different days were identified as the same dipole eddy.

To investigate the characteristics of the southward branch of the NEMC, surface geostrophic velocity data processed by the SSALTO/DUACS multimission altimeter data processing system is used, which is provided by AVISO+ and distributed by the Copernicus Marine Environment Monitoring Service (CMEMS). The data have a homogeneous resolution of 0.25° in each direction.

To investigate the potential reach of the southward branch of the NEMC towards the middle MC, a methodology based on Ambe et al. (2004) was employed to precisely delineate the current axis of this southward branch by tracking and analyzing its maximum surface velocity. The schematic of this methodology is illustrated in Figure 2 . The initial subsidiary line was established at 14°S and 40°–42°E, intersecting the upstream of the NEMC southward branch in a nearly perpendicular manner. The first point along the current axis P V max ( 1 , t ) was determined by identifying the maximum velocity along this subsidiary line. The subsidiary line was then repositioned to search for the second point of the current axis. Prior to this, the subsidiary line underwent a rotation around the point P V max ( 1 , t ) to ensure its perpendicularity with respect to the mean flow direction. The determination of the mean flow direction involved averaging the flow direction of each point along the subsidiary line. Subsequently, the adjusted line was shifted southward along this mean flow direction by a displacement of Δr (20 km). The width of the new subsidiary line is 120 km, encompassing seven points whose velocities can be determined through interpolation. The second point of the current axis P V max ( 2 , t ) can be derived based on the maximum velocity observed along the new subsidiary line. By iteratively following this procedure, the concatenation of all points on the current axis may be considered as constituting the current axis of the southward branch of NEMC. The velocity threshold along the current axis was set to 60 cm/s, as this value corresponds to the maximum climatological mean velocity (based on AVISO data from 1993–2017) of the southward branch of the NEMC. Modifying this threshold would not impact the position of the current axis, but it could potentially alter its length by including more or less P V max ( i , t ) would be added to the current axis.

A hydrographic survey was conducted by the China–Mozambique International Joint Cruise involving R/V Xiang Yang Hong 10 from June 1 to 23, 2016. The CTD measurements of Seabird 911 at nine sampling stations ( Figure 1 ) and Acoustic Doppler Current Profiler (ADCP) data were used to verify the reliability of the HYCOM data before its application. Along the cruise track ( Figure 1 ), the current profile was measured via a Shipboard ADCP, namely, a 38-kHz Ocean Surveyor (OS38). The ADCP parameter settings were configured as follows: the data-sampling rate was set to one ping per 3 s, bin length was set to 24 m, and bin number was set to 40. The depth of the first ADCP bin is approximately 41 m (=sensor depth (7 m) + blank distance (22 m) + half of the bin length (24 m/2). The blank distance is set to 22m, which exceeds the default setting of the ADCP (16 m), effectively mitigating potential ship noise interference. To obtain the true currents, the navigation trajectory was used as the velocity reference for post-processing, which was provided by the NavCom SF-3050 DGPS system. Abnormal records exceeding three times the standard deviation of the mean current was excluded. The current profile was derived by averaging over 3 km intervals (not shown) to reduce the influence of noise. No specific tidal correction was applied to the ADCP data because tidal noise is less than 4–7 cm s-1 (Di Marco et al., 2002). The associated error in current calculations, when not accounting for tidal effects, is approximately 10%, as we utilize a reference velocity of 60 cm s-1 for the southward branch of the NEMC.

The global 1/12° reanalysis data from HYCOM (Bleck, 2002) was utilized to diagnose the energy conversion between the southward branch of the NEMC and mesoscale eddies, providing three-dimensional temperature, salinity, and current data at three-hour intervals. Baroclinic energy conversion terms as well as barotropic energy conversion terms were defined in accordance with Equations 1 and 2 (Böning and Budich, 1992):

Here u ′ = u − u ¯ and v ′ = v − v ¯ , u ¯ and v ¯ denote the mean velocity components computed by averaging over the time period from January 1993 to December 2017. ρ ˜ ( x , y , z , t ) = ρ ( x , y , z , t ) − ρ b ( z ) , ρ b ( z ) is the background density computed by temporally averaging over the same time period above and horizontally averaging over the domain in (34°E–52°E, 10°S–25°S), ρ ¯ ′ = ρ ˜ − ρ ˜ ¯ ,   ρ ˜ ¯ is the temporal mean value of ρ ˜ over the same averaging period, and ρ ¯ θ ( z ) is the annual and horizontal mean potential density (Böning and Budich, 1992; Biastoch and Krauss, 1999; Collins et al., 2014). PeKe is the conversion between the mean potential energy (MPE) and eddy potential energy (EPE). Positive values for PeKe correspond to baroclinic instability. KmKe is the conversion between the mean kinetic energy (MKE) and EKE. Positive values for KmKe correspond to barotropic instability owing to the work of Reynolds stresses against the mean shear. Given the substantial disparity in current velocity between the deep ocean (~0.1 m/s) and the upper ocean (~1 m/s), the energy budget was calculated only for the upper 1500 m. We compared the model simulated results with the in-situ ADCP and CTD data to verify the simulation ability of the HYCOM. The results show that the HYCOM outputs well reproduced the velocities of the ADCP observation at 100 m with correlation coefficient reaching 0.56 for the zonal velocity and 0.71 for the meridional velocity (Figures 3A, B). Temperature and salinity simulated by HYCOM displays high agreement with that of CTD observation with their determination coefficients keeping over than 0.95 (Figures 3C, D).

After eliminating duplicate counts, the distribution of anticyclonic and cyclonic eddies was obtained, as shown in Figure 4 . Both anticyclonic and cyclonic eddies are more active in the western MC section ( Figures 4B, C ) than in the eastern part. Anticyclonic and cyclonic eddies with occurrence frequencies higher than once per year mostly emerge in the western MC, which exhibits a northeast-southwest distribution. The northeast-southwest distribution covers the region from 15°S to 25°S and indicates a southward movement trend for both cyclonic eddies and anticyclonic eddies. In addition to the western MC, anticyclonic eddies are also observed in proximity to 20°S and 43°E, while cyclonic eddies occur near 23°S and 42°E, as previously reported by Halo et al. (2014). Both cyclonic and anticyclonic eddies are also observed in the Comoros Basin, which was not reported by Halo et al. (2014) because their study did not include this area.

The variations in the occurrence frequency of mesoscale eddies during their southward movement in the western MC are shown in Figure 5 . The occurrence frequencies of anticyclonic and cyclonic eddies are four (Ridderinkhof and De Ruijter, 2003; Schouten et al., 2003; Ridderinkhof et al., 2010) and three times per year, respectively, at 15°S ( Figure 5 ) in the MC. The occurrence frequency of anticyclonic eddies in the region between 15°S and 20°S is approximately four times per year, peaking at around five times per year at 18.5°S, and subsequently decreasing to approximately two times per year at 25°S ( Figure 5 ). In comparison, the frequency of cyclonic eddies first decreases to approximately two times per year at 17°S, then increases to approximately five times per year at 18.5°S, and then again decreases to approximately two times per year at 25°S.

The radius and lifespans of these southward-propagating mesoscale eddies in the western MC are depicted in Figure 6 . Notably, anticyclonic eddies in this region exhibit larger sizes compared to cyclonic eddies. Specifically, a majority of anticyclonic eddies have radii ranging from 90 to 140 km, while most cyclonic eddies have radii between 60 and 110 km ( Figures 6A, C ). Furthermore, the number of cyclonic eddies surpasses that of anticyclonic ones. Both types of eddies demonstrate similar lifespan distributions within the range of 30–80 days ( Figures 6B, D ). Overall, these findings align with Halo et al. (2014), indicating that cyclonic eddies in the western MC are more abundant but smaller in size than anticyclonic eddies.

Due to the similarity in spatial distributions of anticyclonic and cyclonic eddies in the MC ( Figure 4 ), dipole eddies may form, as observed by Kolasinski et al. (2012); Malauene et al. (2014); Roberts et al. (2014), and Lamont and Barlow (2017). The distribution of dipole eddies is shown in Figure 7 . Here, two adjacent eddies with eddy-center distances smaller than the sum of their radii are determined to be dipole eddies. Dipole eddies are predominantly observed in the middle MC between 17°S and 20°S, with a frequency of occurrence approximately twice per year. The highest frequency of occurrence is found around 18°S, with three events per year. Ninety-five percent of these dipole eddies consist of an anticyclonic eddy and a cyclonic eddy. The remaining dipole eddies are comprised of two anticyclonic eddies or two cyclonic eddies.

The radius and lifespans of dipole eddies in the MC are depicted in Figure 8 . As almost all dipole eddies consist of an anticyclonic eddy and a cyclonic eddy, we utilized the extracted radii of these individual components to represent the radius properties of dipole eddies. Both anticyclonic and cyclonic eddies predominantly exhibit radii ranging from 110–160 km ( Figures 8A, B ). A substantial number of dipole eddies have been observed in the MC (Figure 8C). Although most dipole eddies have lifespans shorter than 30 days, there still exists a considerable proportion with lifespans exceeding 30 days.

The sources of mesoscale eddies passing through the narrowest part of the MC were investigated using METAP ( Figure 9A ). Here we define the region between 15°S and 16°S in the MC as the narrowest part of the MC. The results indicate that these mesoscale eddies are all generated in the Comoros Basin, with a majority of approximately 70% originating in the western Comoros Basin, specifically west of 44°E. It is noteworthy that while numerous mesoscale eddies are observed in the Comoros Basin, most fail to traverse through the narrowest section of the MC. Only around 43% of mesoscale eddies generated within the Comoros Basin successfully pass through this narrow region. Among those unable to do so, an overwhelming majority of approximately 90% are formed east of 44°E in the Comoros Basin. Consequently, it can be inferred that the current field prevailing in the western Comoros Basin plays a crucial role in both generation and propagation processes associated with mesoscale eddies within the MC. The speed of mesoscale eddies in the Comoros basin is significantly higher compared to those located south of the Comoros basin, providing further evidence ( Figure 9B ). In addition, the disparity in velocity may facilitate the convergence of mesoscale eddies within the Comoros basin with those located to its south, subsequently giving rise to dipole eddies. A significant proportion of anticyclonic eddies (86%) and cyclonic eddies (77%), capable of traversing the narrowest section of the Channel and transporting southward, subsequently develop into dipole eddies.

The current field in the western Comoros Basin was investigated using the AVISO geostrophic velocity data ( Figure 10 ). From a climatological perspective, the southward branch of the NEMC is the main ocean current in the western Comoros Basin ( Figure 10A ). However, this branch is not a persistent and steady current, as its velocity ranges from 0 to 0.9 m/s, and it sometimes flows northward ( Figure 10C ). The velocity of the southward branch of the NEMC exhibits a 50-day oscillation period ( Figure 10B ). A similar 50-day oscillation period is also found for the NEMC (Quadfasel and Swallow, 1986). A countercurrent is located east of the southward branch of the NEMC (red box; Figure 10A ). Once the southward branch of the NEMC is strengthened, the current amplitude of the countercurrent increases ( Figure 10C ). This countercurrent is not caused by the presence of eddies since the velocity of the countercurrent is always much lower than the NEMC southward branch ( Figure 10C ). The correlation coefficient between the southward branch of the NEMC and the countercurrent reaches -0.7 with a lag of 5 days. The countercurrent also exhibits a 50-day oscillation period, which is the same as that of the southward branch of the NEMC.

The energy conversion when these mesoscale eddies generated is shown in Figures 11A, B . The vertically integrated values of PeKe and KmKe were computed during the periods when mesoscale eddies generated. Subsequently, these results were averaged to obtain the mean values of PeKe and KmKe. The results depicted in Figure 11 demonstrate that both PeKe and KmKe exhibited positive values along the Mozambique coast below 14°S, which corresponds to the downstream region of the southward branch of NEMC. Furthermore, it is noteworthy that KmKe displayed a greater magnitude compared to PeKe. The findings demonstrate the prevalence of barotropic instabilities in the generation of mesoscale eddies, while also highlighting the significance of baroclinic instabilities.

The formation of mesoscale eddies is likely influenced by another process, as depicted in Figure 5 , occurring between 17°S and 19°S. Notably, there is an observed increase in the frequency of cyclonic eddies from two to four occurrences per year. The cyclonic eddies are predominantly generated in the eastern middle MC ( Figure 12A ) and initially propagate westward before turning southward along the Mozambique coast. The current axis of the southward branch of the NEMC during cyclonic eddy generation is depicted in Figure 12A to elucidate the potential relationship between the eddies in the middle MC and the southern branch of NEMC. When the southward branch of NEMC exhibits sufficient intensity, it has the potential to extend further towards the southern region and exert influence on dynamic processes within the middle MC. Given the prevalence of dipole eddies in the middle MC, we investigated the relationship between dipole eddies and the generation of cyclonic eddies by normalizing cyclonic eddy positions to the coordinate origin ( Figure 12B ). Subsequently, we identified the nearest anticyclonic eddies on the same day. Cyclonic eddies are predominantly generated in the vicinity of anticyclonic eddies located within a distance of less than 2°. Moreover, 26% of these cyclonic eddies exhibit dipole structures with adjacent anticyclonic eddies upon their formation, while 98% of these cyclonic eddies persist as dipole structures throughout their lifespans.

The energy conversion when cyclonic eddies generated between 17°S and 19°S was diagnosed in Figures 13A, B . The magnitudes of both PeKe and KmKe in the middle MC are comparable to those observed in the Comoros Basin ( Figure 11 ), indicating a same strong interaction between eddies and mean flow within the middle MC. Positive KmKe dominates the region between 17°S and 19°S, suggesting that the generation of cyclonic eddies is mainly influenced by barotropic instability.