Measurements of temperature, salinity, and pressure were obtained using a conductivity–temperature–depth (CTD) system with Sea-Bird Electronics (SBE) 911plus implemented in a survey conducted in August 2015. The accuracies of the CTD sensors were 0.003 psu for salinity and 0.001°C for temperature. There were fifty-six CTD stations in the YS ( Figure 1 ). The velocity profile was measured using a bottom-mounted 300-kHz Sentinel Acoustic Doppler Current Profiler (ADCP) located in the western YS (122.75°E, 34°N) from April to December, 2015. The depth of the mooring system was 74 m. The bin size of the ADCP observation was 2 m, with a sampling output interval of 30 minutes. In addition, SBE 37 CTD was mounted on the mooring system to simultaneously measure the bottom temperature, salinity, and pressure. Velocity data above a depth of 8m with poor quality were removed because of the effect of bubbles (Thorne and Hurther, 2014). The trajectory and intensity of the cyclone is downward from the Japan Meteorological Agency. (https://www.jma.go.jp/jma/index.html).

Regional Ocean Modeling System (ROMS) is a widely used free-surface, terrain-following, three-dimensional primitive equations ocean model that assumes hydrostatic and incompressible conditions (Shchepetkin and McWilliams, 2005). ROMS was used to study the response process of near-inertial flow in the YS during a cyclone transit and the model domain encompassed 22–42°N, 117.0–140.0°E ( Figure 1A ). The horizontal resolution was 1/18°× 1/18°. We adopt a 32-level stretched terrain-following vertical s-coordinates with control the surface and bottom parameters of θ_s=4.3, θ_b=0.4 to enhance the resolution near the surface and bottom (Shchepetkin and McWilliams, 2005). The minimum and the maximum water depths were set at 10 and 5, 000 m, respectively. The time steps for the inner and outer modes were 360 and 12 s, respectively. The outputs were stored every 1 h. Generic length scale (GLS) turbulence closure scheme was used to determine the vertical turbulent viscosity and diffusion coefficients for horizontal momentum equations and tracer equations. Background mixing coefficient for momentum is 1×10^-5 m²/s. Model was first integrated over 5 years for spin-up, from 1^st January, 2010 to 31^th December, 2014. Model continue to count to 31^th August, 2015.

The surface forcing fields include the wind field, atmospheric temperature, shortwave radiation, longwave radiation, atmospheric pressure, precipitation rate, and relative humidity derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) through the Interim ECMWF re-analysis dataset with a temporal resolution of 1 h and a spatial resolution of 0.25° × 0.25° (http://apps.ecmwf.int/datasets). Based on these data, the net heat flux and freshwater fluxes in the model were calculated using the bulk formulation. The daily average sea surface temperature (SST) data were derived from the National Oceanic and Atmospheric Administration (NOAA)’s Optimum Interpolation Sea Surface Temperature v2.1, and Sea surface salinity was derived from the World Ocean Atlas 2013 (https://www.ncei.noaa.gov/). During model a spin-up period, SST and SSS are used to calibrate the model. Temperature, salinity, current velocity, and elevation of the open boundary and initial field were determined from the monthly average data set of the Simple Ocean Data Assimilation (SODA 3.4.1). The tidal constituents M2, S2, N2, K2, K1, O1, P1, and Q1 were introduced at the boundary. Their amplitudes and phases were interpolated from the 1/30°-resolution TPXO8-atlas solution of Oregon State University (OSU) Tidal Inversion Software (http://volkov.oce.orst.edu/tides/). Model bathymetry data were extracted from the General Bathymetric Chart of the Oceans (GEBCO) database with a resolution of 15 arc-second (http://www.gebco.net/). The topography was corrected using charts in shallow areas.

Two noticeable near-inertial velocity peaks are found in the upper mixed layer and below the maximum stratification, with a velocity of up to 0.15 m/s ( Figures 5 , 6A ). From the mixed layer to the thermocline, the near-inertial velocity decreases rapidly. The vertical structure of the near-inertial flow was dominated by a 180° phase difference with one zero-crossing at the depth of the maximum stratification (the blue line in Figure 5A ). A near-inertial peak occurs from the depth of the maximum stratification to a depth of 20 m. In the bottom boundary layer, the near-inertial velocity was very weak at approximately 0.03 m/s.

The vertical structure of the antiphase of near-inertial flow is closely dependent on the stratification and can be explained by the traditional two-layer model (Millot and Crépon, 1981; Kelly, 2019). The wind-generated near-inertial flow was confined within the mixed layer and could not pass through the thermocline, due to the strong stratification which suppresses the downward transfer of near-inertial energy (Davies and Xing, 2005; Yang et al., 2015). Below the thermocline, however, owing to the presence of the coast, the pressure gradient force formed by the convergence and divergence of seawater induces a near-inertial flow with an opposite phase to satisfy the cross-shelf flux conservation (Millot and Crépon, 1981; Davies and Xing, 2005; Shearman, 2005). However, the phenomenon of strong near-inertial velocity peaks at the base of the thermocline, which should be homogeneous below the thermocline according to the two-layer model, has not been explained.

While triggering near-inertial oscillations, the cyclone also has an influence on the stratification of the YS. Firstly, the model shows ~2°C cooling of the SST at the observation site associated with the arrival of the cyclone ( Figure 6B ). ln contrast to surface heat flux that dominates over the open ocean, the entrainment term is the dominant process for significant SST cooling in the YS (Moon and Kwon, 2012; Lee et al., 2016; Yang et al., 2019). Then, the deepening of the mixed layer caused by wind stirring results in the compression of the thermocline which then intensifies and deepens the maximum stratification strength and depth, respectively. Prior to the arrival of the cyclone, N ², which represents the strength of the maximum stratification, was ~4×10^-3 s^-2 located at 10m, while after the cyclone the N ² strengthened to ~6×10^-3 s^-2 and deepened to 13m. Note that the maximum depth of stratification become shallower first, which can be related to cyclone-induced upwelling (Jacob et al., 2000) which can be confirmed by the lifting of temperature contours on the 11^th of August ( Figure 6B ). The maximum depth of stratification is deepening after the cyclone.

The first baroclinic mode can explain the flow structure of the upper and lower opposite phase, but the theoretical maximum flow velocities in the first baroclinic mode occurring at the surface and the bottom layers are inconsistent with observations (i.e. strong near-inertial flow occurs below the thermocline in the observations and model). To examine the vertical structure of the near-inertial velocity, the modelled near-inertial velocity was projected onto the first five baroclinic modes using a least-squares regression at each time according to Equations (1) - (4).

The vertical structure of the first three modes and the percentage of each mode’s energy to the total energy were calculated and shown in Figure 7 . It was found that the near-inertial energy was dominated by the first model energy, accounting for 60% of the total energy, and was mainly distributed in the mixed layer and below a depth of 20m. However, at depths below the maximum stratification from 10 to 20m, the second modal energy dominated rather than the first mode; and the first and the second mode velocities were in phase, causing the peak of near-inertial energy at this depth (purple and red lines in Figure 7A ). The near-inertial velocity peak is not revealed by the first-mode structure solely, but by the increase in higher-order mode energy due to other physical processes. The higher modal energy was associated with strong friction under the influence of the tides and was significantly reduced when the tidal currents disappeared, which will be clarified in the following discussion.

To elucidate the sources and sinks of energy in each mode, the energy gain and loss of each mode from the wind and bottom friction are calculated using Equations (12) –(13). The energy of the modes 1 and 2 gained or lost from bottom friction is shown in Figure 8A . Although the cumulative work done by the bottom friction in mode 2 was weak, the positive work suggested that the bottom friction was a source of energy in mode 2 (blue line in Figure 8A ). However, the negative cumulative work done by the bottom friction in mode 1 indicated that the bottom friction was a sink of energy for mode 1 (red line in Figure 8A ). The energy of mode 1 and 2 gained or lost from wind is shown in Figure 8B . The work done by wind in mode 1 increased rapidly and positively on 11^th August indicating that wind was a source of energy for mode 1. The work done by wind in mode 2 was minor but positive, indicating that the wind also input a slight amount of energy for mode 2.

The near-inertial velocity with opposite phase led to the maximum shear value at the thermocline (at depths of 10m-20m), while the higher modal energy contributed to the sub-peak in shear below the thermocline ( Figure 9A ). The normalised Richardson number (Ri _n) is used to justify the shear instability according to Equation (6). Although the shear was the strongest within the thermocline, the Ri _n greater than zero indicated the development of the shear instability inhibited by strong stratification ( Figure 9B ). Below the thermocline, the Ri _n decreased and was even less than zero relative to that within the thermocline, suggesting the occurrences of the shear instability due to the stratification below the thermocline being at its weakest. On August 11^th, Ri _n was less than 0 at a depth of 20-30m, which indicates the occurrence of shear instability ( Figure 9B ). This shear instability may cause the underlying cold water to mix into the thermocline.

The horizontal distribution of near-inertial velocity is shown in Figure 10A . In the coastal region, tidal-induced mixing led to the disappearance of the stratification, and the near-inertial oscillation was in phase throughout the water column. In shelf seas, with the increase in the depth and the enhancement of the stratification, the near-inertial velocity is in antiphase above and below the thermocline, with one zero-crossing at the depth of the maximum stratification (bold black line in Figures 10A, B ).

In the coastal region (121°-122.2°E), despite the strong influence of wind stress, the near-inertial flow was very small, at 0.02 m/s. This value can be attributed to the friction caused by the shallow water depth in this region ( Figures 10A–C ),which causes the wind energy input to be dissipated in the form of seiches on a much smaller scale (Anderson et al., 1983; Sobarzo et al., 2007; Chen et al., 2017). In the mixed layer of the shelf region from 122.5° to 123°E, the near-inertial kinetic energy (NIKE) was enhanced with the increasing of the wind work, indicating that the NIKE was related to wind work. Below the thermocline of the shelf region from 122.2° to 123°E, the location of the maximum NIKE was at the shelf break (122.4°E). To satisfy cross-shelf flux conservation, the near-inertial velocity below the thermocline is related to that in the mixed layer and the water depth below the thermocline. The NIKE below the thermocline of the region from 122°E to the shelf break and from the shelf break to the 123°E was weaker than that at the shelf break because of the weak NIKE in the mixed layer and the deep water depth below the thermocline,respectively. As shown in Figure 10B , the maximum NIKE in the mixed layer occurred at 123°E, where wind energy input was greatest, and the maximum NIKE energy below the thermocline occurred at the shelf break.

The clockwise rotation of the near-inertial velocity indicated a decreasing phase with time and downward transmission of near-inertial energy. Owing to the rapid propagation of the barotropic wave, the phase was almost uniform in the region of 122.2°E to 124°E, with the offshore phase slightly lagging behind the nearshore phase ( Figure 10D ).

The YS is a strongly tidally-driven shallow shelf sea, dominated by the M₂, with a maximum value of up to 0.5 m/s. Tides have a significant influence on the hydrological environment and circulation structure of the YS (Xia et al., 2019; Meng et al., 2020); therefore, an understanding of the effect of tides on the near-inertial flow is crucial.

To investigate the influence of tides on the near-inertial velocity, we simulated the near-inertial velocity with and without the tides ( Figures 5A , 11 ). The most striking phenomenon is the variation in the vertical structure of the near-inertial current. Under the influence of the tides, the strong near-inertial velocity below the maximum stratification were mainly concentrated between 10-20 m. However, in the absence of tides, the strong near-inertial response extended to 40 m with a significant weakening within the bottom 10 m. The results suggest that the near-inertial energy was dominated by the second modal energy between 10-20 m below the thermocline with the influence of tides. However, the near-inertial energy was dominated by the first modal energy without the influence of tides according to the model analysis. As analysed in result 3.2, an increasing of tides increases bottom friction, which is a source of higher modal energy and a sink for first modal energy. The absence of tidal currents decreases bottom friction resulting in a decrease in higher modal energy and an increase in first modal energy.

To investigate how tides affect the near-inertial flow, eddy viscosities with and without tides were simulated. Within the mixed layer, the near-inertial energy input from wind energy became homogeneous under the influence of the eddy viscosity during the period of wind energy input from 10^th to 12^th August. Below the thermocline, eddy viscosity was mainly related to the influence of tides. As shown in Figures 6A , 11 , during the presence of tides, the eddy viscosity is uniform up to 20 m depth, where it corresponds to a weak near-inertial velocity. Strong peak near-inertial velocities correspond to weak eddy viscosity at 10-20 m depth. In the absence of tides, eddy viscosity in the lower layer was mainly confined within 10 m of the bottom boundary, resulting in a significant reduction in near-inertial flow ( Figures 11 , 12B ). From the depth of the maximum stratification to 40 m, the eddy viscosity is low corresponding to strong near-inertial flow velocities. In brief, mixing leads to rapid diffusion of near-inertial energy above the thermocline, which is generated by wind stress. Below the thermocline, the near-inertial energy is suppressed by the eddy viscosity. The effect of eddy viscosity is pronounced in the existence of tides.

In different shelf seas, the vertical structure of the near-inertial current may differ due to different tidally induced eddy viscosities. In strongly tidally-driven shelf seas, a narrower depth near-inertia peak occurs due to the deep influence of eddy viscosity ( Figures 5A , 12A ). When the tide is not strong or disappears, the eddy viscosity affects a limited range of depths, and a near-inertia peak with a wider depth occurs ( Figures 11 , 12B ). Further observations are needed to confirm this view.

The traditional two-layer model assumes that the time-varying wind field induces a near-inertial flow at the surface layer and the energy input from the wind cannot break through the thermocline to propagate downward. During the forcing phase, the wind causes the seawater to accumulate along the coast. The accumulated seawater is released during the geostrophic adjustment process and barotropic waves are generated at the coast and propagate offshore, which suppress the near-inertial flow response in the upper layer but generate the near-inertial flow in the lower layer (Millot and Crépon, 1981; Shearman, 2005).

Previously, the non-linear and eddy viscosity were not considered in the control equations of the two-layer model. Although, the two-layer model can appropriately account for the relationship between the inertial velocity inversions above and below the thermocline, the dynamical process of the two velocity peaks in the mixed layer and below the thermocline remains unclear. Given that the pressure gradient forces are uniform throughout the water column, it is unclear why the inertial velocity within the thermocline and bottom boundary layer is small compared with the inertial velocity peaks in the mixed layer and below the thermocline. In the YS, the ocean should be divided into four layers according to the characterstics of near-inertial velocity: the mixed layer with velocity peaks at depths above 10 m, the thermocline, the lower mixed layer with velocity peaks at depths of 10-20 m, and the bottom boundary layer with rapidly decreasing velocity ( Figures 5 , 11 ). To investigate the response of the ocean to time-varying wind fields, the original N-S equation is given as:

In Equation (15), ɤ and K_M denote molecular viscosity coefficient and eddy viscosity coefficien, respectively. The terms of acceleration ∂ u ∂ t , horizontal advection u ∂ u ∂ x and v ∂ u ∂ y , convection w ∂ u ∂ z , Coriolis force -fv, pressure gradient force − 1 ρ ∂ p ∂ x , eddy viscosity − 1 ∂ z ( − K M ∂ u ∂ z ) , and molecular viscosity term 1 ∂ z   ( ɤ ∂ u ∂ z ) are shown in order from left to right in Equation (15). The minor terms of the horizontal advection are ignored relative to the convection term. In addition, the molecular viscosity term can also be ignored relative to the eddy viscosity term.

Therefore, Equation (15) can be rewritten as follows:

In the absence of tide, the diagnostic analysis of each layer is illustrated in Figure 13 . The response of the ocean to time-varying wind fields first appeared in the mixed layer ( Figure 13A ). During the wind-forced period from 12:00 on the 10^th to 00:00 on the 11^th August, the velocity increased with the increased in wind stress, and the acceleration term and the Coriolis force combined to balance the wind stress. During the wind-forced period, wind-driven currents caused seawater to accumulate on the shore, creating enhanced offshore pressure gradient forces at all depths. As the wind stress decreased on 11^th August, seawater at the shore was released and propagated offshore, causing a decrease in pressure gradient force (blue line in Figure 14 ). A barotropic wave was first generated at the coast at 00:00 on 11^th August and propagated offshore. A comparsion of the variation in pressure gradient force with time at different positions reflects the gradual decrease in amplitude during the wave propagation ( Figure 14 ). As the barotropic wave propagated to 124°E, the pressure gradient force decreased significantly so that near-inertial kinetic energy below the thermocline became almost zero ( Figure 10B ). From 00:00 on 11^th to 00:00 on 12^th August, the magnitude of the wind stress gradually decreased, and the pressure gradient force gradually increased. At this stage, the terms of acceleration, Coriolis force, pressure gradient force, and eddy viscosity were balanced. When the wind stress disappeared completely at 20:00 on 11^th August, the pressure gradient force was at its maximum, and the Coriolis force was smaller than that when the wind stress was at its maximum. In other words, the arrival of a barotropic wave will weaken the near-inertial flow of the mixed layer (Millot and Crépon, 1981). Finally, the seawater motions were mainly balanced by the terms of acceleration, Coriolis force, and the pressure gradient force. Therefore, the motions appeared in the form of a near-inertial frequency. When the pressure gradient force disappeared from 00:00 on 15^th August, the motions became fully inertial motion that was, the acceleration term balanced with the Coriolis force term ( Figure 13A ).

Below the mixed layer, the seawater began to respond to the pressure gradient force at 12:00 on 11^th August, promoting the evident variation in the terms of acceleration, Coriolis force, convection, and eddy viscosity ( Figures 13B–D ). In the strongly stratified thermocline, although the near-inertial wave was generated, it was not evident in the observations and model. Strong nonlinear phenomena were observed in the thermocline by Davies (2005), suggesting that the enhancement of the convection term contributes to a cascade of near-inertial energy to smaller scales, as a result of the weakening of the near-inertial energy. It can be clarified that the convection term (magenta line in Figure 13B ), owing to velocity shear increased to the same magnitude as Coriolis force around 12:00 on 11^th August and balanced part of the pressure gradient force, resulting in a reduction in the near-inertial flow. The terms of acceleration, vertical advection, and Coriolis force together balanced the pressure gradient force. It is worth noting that the convective term caused by velocity shear only appears in the thermocline, which is the main reason for the weakening of near-inertial flow in the thermocline.

In the lower mixed layer, the motion of seawater is driven by pressure gradient force, which is balanced only by acceleration and Coriolis forces together ( Figure 13C ). Therefore, this motion behaves as a near-inertial motion and the near-inertial flow was greater than that in the thermocline, owing to the fact that it is not modulated by the advection term. After the disappearance of the pressure gradient force, the motion evolves into inertial motion.

At the boundary layer, a portion of the pressure gradient force was balanced by the eddy viscosity (black line in Figure 13D ), resulting in the rapid decrease in the near-inertial velocity relative to that in the lower mixed layer. Thus, the two velocity peaks occur in the upper and lower mixed layers, and the weak inertial velocities in the thermocline and bottom boundary layers are influenced by the convective and eddy viscosity terms respectively.