The mooring data were collected at site M1 (~1900 m water depth) on the continental slope south of the Dongsha Island in the northeastern SCS ( Figure 1A ). The mooring was equipped with a McLane Moored Profiler (MMP), consisting of a CTD (SBE 52-MP CTD, Sea-Bird Scientific, USA) and a current meter (FSI 3D-MP ACM) which were used to measure temperature, conductivity, and horizontal velocity at a sampling rate of 1 Hz between depths of 385 and 1840 m ( Figure 1B ). The MMP completed a single upward or downward profile every 4 hours. Its observation period was from July 15, 2018, to October 20, 2018. However, since typhoon Mangkhut had a great influence on the instruments after mid-September, data from September 5 to October 20 were not used in this study. In addition, an upward-looking 75-kHz RDI Acoustic Doppler Current Profile (ADCP) was deployed at a depth of 270 m. The ADCP recorded data every 30 min with 8-m vertical depth bins from July 18, 2018, to September 15, 2019. The horizontal velocity is decomposed into along-slope (x) and cross-slope (y) components ([u, v]). The positive x and y directions are defined as 42° and 312° at M1, measured clockwise from the true north direction ( Figure 1A ).

In this study, the bathymetry is obtained from the General Bathymetric Chart of the Oceans’ gridded bathymetric data with a 30-arc sec resolution (http://www.gebco.net/). We also use the climatological temperature and salinity of the 2018 World Ocean Atlas (http://www.nodc.noaa.gov/OC5/WOA18) to obtain the full-depth buoyancy frequency N_w ( Figure 2A ). This buoyancy frequency profile N_w shows good consistency with N_m computed from MMP data at 385 m and 1840 m. Based on the full-depth N_w , the ray path of internal waves with frequency ω can be computed by

where β is the slope of the internal wave group velocity with respect to the horizontal direction and f is the local inertial frequency. Near M1, the topographic slope is near-critical and subcritical with respect to diurnal and semidiurnal internal tides, respectively ( Figure 2B ).

We focus on diurnal internal tides and low-frequency flow. The diurnal component is extracted by a second-order Butterworth band-pass filter, with the cutoff frequency of [0.85, 1.15] cpd (cycles per day), while the low-frequency flow is extracted using the low-pass filter with a cutoff period of 3 days.

The baroclonic velocity signals (that is, the raw velocity minus the barotropic velocity [u_T(t), v_T(t)] defined as the depth-averaged velocity) are projected into vertical modes. The baroclinic signals can be represented by a superposition of discrete vertical modes that depend on N ² (z).

where Φ_n(z) and Π_n(z) are the vertical structure of modes for vertical displacement and horizontal velocity, respectively, c_n is the eigenspeed and n is the mode number (Gill, 1982). The least square mode fitting method is used to calculate the time-varying velocity of the first three baroclinic modes [u′_n(t), v′_n(t)] from the observed velocity profiles (Alford, 2003; Nash et al., 2005). The baroclinic velocities u′(z, t) and v′(z,t) are expressed as

High mode velocities (n≥4) are obtained by the raw baroclinic velocities minus the sum of the first three mode velocities.

Overturning from Thorpe-sorted profiles (Thorpe, 1977) is used to calculate the turbulent dissipation rate ϵ at M1. Klymak et al. (2011) suggested that stratification in the SCS largely depends on temperature, and there are no salinity-compensated intrusions. Therefore, to eliminate data errors from the salinity sensor, potential temperature profiles are directly used to identify overturning. In the original profile, each potential temperature is associated with a depth D_o . After sorted vertically, the sorted temperature is associated with another depth D_r . L_T is the Thorpe scale and is calculated from the root-mean-square of L_d ,

where N_i is N_m under the sorting and C is a constant of proportionality. Following Dillon (1982), C is set to be 0.8.

Strong internal tidal motions are clearly visible at M1 ( Figure 3A ). The near-bottom isotherms show large vertical excursions with diurnal period, whose maximum displacement exceeds 100 m ( Figure 3A ). In the band-pass-filtered diurnal velocity field, the near-bottom intensification of diurnal internal tides are also observed, with the maximum velocity exceeding 0.1 m/s. These bottom-enhanced diurnal internal tides show a clear ~14-day spring-neap cycle, whose phase lags that of the local barotropic tides for ~3 days ( Figure 3B ), suggesting that internal tides do not result from the local barotropic forcing. Instead, the 3-day time difference is approximately equal to the propagation time of the mode-1 diurnal internal tides from the Luzon Strait to M1 ( Figures 3A, B ), suggesting their generation source of the Luzon Strait, as previously reported in Zhao (2014); Zhao (2020). However, the bottom-enhanced diurnal internal tides observed at the mooring site are mainly composed of higher modes (n≥4; Figure 4 ). This indicates that low-mode internal tides are scattered into higher modes when they travel westward from the Luzon Strait to the near-critical continental slope (Klymak et al., 2011; Xie et al., 2018).

To identify the propagating direction of diurnal internal tides, the modal decomposition of the velocity field is performed based on equation (2). The mode-1 and mode-2 are dominant, occupying more than 55% of the total energy ( Figures 5A, B ). The mode-1 diurnal internal tide shows an elongated current ellipse, while the mode-2 wave is near-circularly polarized ( Figure 5C ). Since mode-1 is larger than mode-2, the major axis of its current ellipse is regarded as the along-beam direction of internal tides (Alford and Zhao, 2007). Assuming that diurnal internal tides westward from the Luzon Strait to the slope, their incident angles with respect to positive y direction during four diurnal springs are γ₁ =23°, γ₂ =40°, γ₃ =51°and γ₄=43°, respectively ( Figure 5C ). This is consistent with the satellite altimeter observations near M1 for mode-1 internal tides (γ = 46°; Zhao et al., 2020), except at the first spring during which the modal decomposition may have large errors due to the absence of the upper ADCP data.

Below 1600 m, strong dissipation is observed due to overturning and breaking of high-mode internal tides, with the maximum dissipation rate exceeding 3.9×10^-7 W/kg ( Figures 6A, B ). Enhanced dissipation rate is often phase-locked to diurnal internal tides. The depth-integrated dissipation rate D near the bottom layer largely depends on diurnal velocity amplitude ( Figure 7A ), and elevated D also shows a spring-neap cycle whose phase is the same as that of diurnal tides ( Figures 6A, B ). Clearly, the near-bottom enhancement of diurnal internal tides and strong turbulent dissipation can be attributed to their critical reflection on the continental slope ( Figure 2B ), as shown in the previous studies (Klymak et al., 2011; Xie et al., 2018). The depth-integrated dissipation rate D (= ρ 0 ∫ H H − h ϵ d h ) averaged over available data due to near-bottom dissipation of diurnal internal tides is 4.8×10^-3 W/m². This turbulent dissipation is one order of magnitude lower than that (D = 7×10^-2 W/m²) estimated by Klymak et al. (2011) based on the similar MMP measurements on the continental slope east of the Dongsha Island, where diurnal internal tides were much stronger than those observed at M1.

Since diurnal internal tides obliquely impinge on the near-critical continental slope, enhanced bottom dissipation due to their breaking is expected to generate a southwestward along-slope bottom current (Xie et al., 2018). To confirm it, along-slope (U) and cross-slope (V) low-frequency velocities are shown in Figures 6C, D , respectively. A southwestward low-frequency flow (U<0) is observed below 1600 m where the turbulent dissipation rate is elevated due to breaking internal tides ( Figure 6B ), with the maximum velocities reaching 6 cm/s ( Figure 6C ). Note that the along-slope velocity is often much larger than the cross-slope velocity, suggesting dominant along-slope currents (compare Figures 6C, D ). The southwestward flow is enhanced at diurnal springs (compare Figures 6A, C ), whose magnitude shows a correlation with near-bottom diurnal velocity ( Figure 7B ). The correlation between enhanced U and diurnal velocities suggests that the southwestward bottom current may be generated by breaking diurnal internal tides on the near-critical continental slope, as reported in Xie et al. (2018). However, as shown in Figure 7B , the along-slope current velocity does not increase when V_it is larger than 6.5 cm/s. It may be because U in equation (11) is inversely proportional to V_it although the bottom-enhanced dissipation always increases as V_it increases ( Figure 7A ).

The southwestward on the deep slope may also be caused by the deep western boundary current (hereafter referred to DWBC; Wang et al., 2011; Zhou et al., 2017; Zhao et al., 2020; Zhou et al., 2020). Using mooring data collected near our mooring site M1, Zheng et al. (2022) estimated that the DWBC was weak during August, 2018 corresponding to our observation period, with a velocity of 0.54 cm/s. This small velocity is consistent with our observations (~0.6 cm/s) at neap tides. Therefore, DWBC may affect the southwestward bottom flow near M1, but their effects are secondary at diurnal spring tides.

The above observations have suggested near-bottom dissipation of diurnal internal tides and the subsequent generation of the southwestward bottom currents on the near-critical continental slope. Based on equation (11), it is possible to estimate internal wave-induced along-slope current. Since the phase speed C_p of high-mode internal tides (C_p< 1 m/s for n≥4) are much smaller than that of low-mode internal tides (C_p = 3.2 m/s for mode-1 internal tides), the choice of C_p can significantly affect the estimation in equation (11). Although it is assumed that low-mode internal tides are obliquely incident to the continental slope, breaking of high modes (n≥4) are essential to the bottom-enhanced dissipation ( Figure 4 ). Here we use the following dispersion relation to estimate C_p :

where k is the horizontal wavenumber and m is the vertical wavenumber. The vertical wave number m can be deduced from the near-bottom diurnal velocity ( Figures 4A, B ) and is approximately 2π/1000 m. Taking N =1.5×10^-3 s^-1 below 1600 m ( Figure 2A ), C_p is approximately equal to 0.35 m/s. The depth integrated dissipation rate ϵ from 1600 m to the seafloor (h = 300 m) during four diurnal springs are used to compute the along-slope flow velocity, respectively. The result is shown in Table 1 .

As shown in Table 1 , the estimated U are in magnitude consistent with the observational values at all diurnal springs. Note that observed U in Table 1 have removed the background velocity at neap tides (~0.6 cm/s). If C_p of high-mode internal tides in equation (11) is replaced by that of low-mode internal tides (e.g., mode-1), the predicted along-slope bottom velocity is one order of magnitude smaller than the observed value, even smaller than the background velocities during neap tides.

Using the full-depth MMP measurements at a mooring site on the continental slope east of the Dongsha Island (i.e., site K11; Figure 1A ), Klymak et al. (2011) showed that near-bottom breaking of diurnal internal tides caused energy dissipation of ~7×10^-2 W/m² on the near-critical slope. Their mooring site was close to X18 ( Figure 1A ), where the along-slope bottom current caused by near-bottom dissipation of diurnal internal tides was also observed, with velocity amplitude of ~0.1 m/s (Xie et al., 2018). Using the dissipation rate (D = ~7×10^-2 W/m²) estimated by Klymak et al. (2011), U at X18 is estimated to be 0.11 m/s based on equation (11), where |u| = 0.2 m/s, γ= 20°, and C_p = 0.5 m/s (Xie et al., 2018). The result is also consistent with the along-slope (southwestward) bottom velocity observed at X18. It should be pointed out that energy dissipation of internal tides cannot be completely converted into the mean flow. Parts of them may drive the local turbulent mixing and increase mean potential energy (Klymak et al., 2011). Osborn (1980) estimated that the upper limit mixing efficient was ~0.2. Such mixing efficient does not essentially change the estimated result in equation (11).