Observation of Near-Inertial Waves Induced by Typhoon Mitag (2019) on the Southwestern East China Sea Continental Slope

Abstract

Based on horizontal velocity data recorded by a moored acoustic Doppler current profiler (ADCP) deployed on the southwestern continental slope of the East China Sea (ECS), this study investigates the characteristics of near-inertial waves (NIWs) induced by typhoon Mitag in October 2019. The results indicated that Mitag-induced near-inertial kinetic energy (NIKE) was mainly concentrated above 290 m and was subsurface-intensified; both the maximum velocity and kinetic energy of the NIWs occurred at a depth of 100 m and were 0.21 m/s and 23.01 J/m³, respectively. The rotary vertical wavenumber spectra suggested that both downward and upward energy propagation existed. However, upward energy propagation was much smaller than downward energy propagation, mainly in the 0.007–0.014 cpm wavenumber band. The NIWs had an e-folding timescale of 9.5 days and were red-shifted as a result of the Doppler shift of the Kuroshio. Normal mode analysis suggested that the NIWs were dominated by the first and fourth baroclinic modes, which together accounted for 76.7% of the total NIKE. Spectral analysis showed that although the spectral density of the semidiurnal internal tide (M₂) peak overwhelmed that of the NIWs by a factor of approximately 30, the shear strength generated by the NIWs was comparable to that of the semidiurnal internal tide (M₂), which plays an important role in upper ocean mixing on the southwestern continental slope of the ECS. In addition, the bicoherence analysis suggested that a harmonic wave (M₂–f) was generated via the nonlinear interaction between the NIWs and semidiurnal internal tide (M₂), which reflects the energy dissipation mechanism of semidiurnal tides and NIWs on the southwestern continental slope of the ECS.

1. Introduction

Near-inertial waves (NIWs) are a type of ocean internal wave whose frequency is close to the local inertial frequency f and is generally slightly larger than the local inertial frequency f [1]. NIWs can be observed in continental shelf areas, open oceans, and closed basins, and they are ubiquitous physical phenomena in the global ocean [2,3,4]. NIWs play an important role in promoting ocean turbulence mixing due to the strong shear they produce [5,6]. The resulting mixing effect has a significant impact on various processes, such as the diffusion of pollutants [7], biogeochemical variability, and the energy exchange between sea and air [8,9].

Previous studies have shown that NIWs can be generated by rapidly changing strong winds [10,11] and nonlinear wave–wave interactions [12,13]. Stable or slowly evolving geostrophic currents impact seafloor topography [14,15], geostrophic adjustments in the ocean [16], mesoscale eddies [17], etc. In addition, Alford et al. [1] mentioned that NIWs could be spontaneously generated by frontogenesis and radiation by time-dependent instabilities of low-frequency flow [18,19]. NIWs are also modulated by various ocean dynamic processes, such as background flow fields and mesoscale eddies [20,21,22,23,24,25].

Among these mechanisms that generate NIWs, wind forcing is considered the most important [1]. Wind-forced NIWs are mainly caused by the rapid passage of tropical cyclones or storms. Strong winds provide kinetic energy for the mixed layer of the ocean, resulting in strong ocean currents. After several Rossby adjustment cycles, NIWs are formed, which usually show upward (downward) propagation of phase (energy) and dissipate within several days [26,27,28]. Studies have shown that when the translation speed of a typhoon is greater than the phase velocity of the first baroclinic mode, NIWs are generated with the typhoon track and are characterized by low order, forced baroclinic modes [29]. The oceanic response generally exhibits rightward biased features, which are attributed to the asymmetry of typhoons [30]. NIWs generated by typhoons have been investigated in several previous studies [4,11,24,31,32,33,34,35,36,37,38]. However, the NIWs excited by different typhoons usually show different characteristics in terms of intensity, frequency, and propagation direction, owing to differences in the intensities and translation speeds of typhoons, distances between typhoon centers and observation sites, and local ocean environments. Based on mooring observations, Yang et al. [11] found that the near-inertial currents induced by typhoon Hagupit were surface-intensified with a maximum of 0.52 m/s in the northern South China Sea. Hou et al. [35] examined three NIW events excited by different typhoons in the northwest Pacific and reported that the maximum of near-inertial currents varied from 0.30 to 0.58 m/s. Research by Chen et al. [23] showed that the frequency of typhoon-induced NIWs was blue-shifted due to positive background vorticity. Jeon et al. [36] revealed the poleward propagation of typhoon-induced NIWs by the Kuroshio via observations and a numerical simulation. Moreover, compared with deep water, typhoon-induced NIWs generally have a longer e-folding timescale in shallow water, showing a low-mode pattern [34].

The southwestern continental slope of the East China Sea (ECS) is located on the northeastern side of Taiwan Island and has a complex topography. Moreover, the powerful Kuroshio enters the ECS through the East Taiwan Channel, and a significant invasion of the continental shelf occurs in this sea area. In addition, typhoons generated in the western Pacific often pass through the waters near the southwestern slope of the ECS [39,40], which is conducive to the generation of NIWs. However, due to the great difficulties and high costs of in situ observations, especially under extreme weather and ocean conditions, there are few observations of NIWs generated by typhoons in this region. Fortunately, a moored array captured a significant NIW event induced by typhoon Mitag, which provided an opportunity to investigate the characteristics of the NIWs on the southwestern continental slope of the ECS. It is helpful to advance the understanding of the propagation and dissipation of NIWs in the coastal oceans, which has important theoretical and practical value for revealing coastal material diffusion and ecosystems, as well as energy transfer and local parameterization of turbulent mixing [7,9,41,42]. In addition, NIWs, as a kind of ocean internal wave, are harmful to marine projects, such as oil drilling platforms. Therefore, our study has reference significance for the implementation of offshore engineering.

2. Data and Methodology

2.1. Typhoon Mitag

Typhoon Mitag was the 18th typhoon that occurred in 2019 in the Western Pacific Ocean. The best track of Mitag was obtained from the China Meteorological Administration tropical cyclone database [43,44], which is shown in Figure 1. The temporal evolutions of the translation speeds of typhoon Mitag and distances from the typhoon center to the mooring are shown in Figure 2. On 27 September 2019, typhoon Mitag formed as a tropical depression near the Northwest Pacific (138.9° E, 13.0° N) and moved to the northwest. At 12:00 on 29 September, it strengthened from a strong tropical storm to a typhoon with a maximum wind speed of 33 m/s. It continued northwest and entered the region near Taiwan Island, and the wind speed increased further. At 15:00 on 30 September, it was the closest to the mooring, with a distance of approximately 15 km. At the same time, the translation speed and the maximum wind speed reached 8.44 m/s and 40 m/s, respectively. At 12:00 on 1 October, typhoon Mitag reached the Yangtze River estuary and turned northeast. Finally, at 12:00 on 2 October, it landed on the Korean Peninsula and was reduced to a tropical storm, which dissipated at 24:00 on 4 October.

2.2. In Situ Observations

The horizontal velocity observation data were recorded by an upward-looking 75 kHz Teledyne RDI acoustic Doppler current profiler (ADCP). The instrument was carried out on a set of submersible buoy systems that were located at 122.60° E and 25.50° N (Figure 1). The average depth of the ADCP was 561 m, and the water depth at the mooring was approximately 620 m. The observation time covered the period of the passage of typhoon Mitag. The ADCP had temporal and spatial resolutions of 0.5 h and 8 m, respectively. The ADCP observed horizontal velocity from the sea surface to 540 m; however, the data near the sea surface were contaminated by surface reflections and were discarded. Therefore, in this study, the horizontal velocity data were linearly interpolated to 50–540 m in the vertical direction every 10 m. In this study, three months of continuous meridional observed velocity data covering the entire transit period of typhoon Mitag were selected for 10-day low-pass filtering as the background currents of the Kuroshio at the mooring ($\overrightarrow{v_h}$ in Equations (11) and (12)).

2.3. Satellite Altimeter Data

The gridded satellite altimeter data used in this study integrate multiple satellites (Jason-3, Sentinel-3A, HY-2A, Saral/AltiKa, Cryosat-2, Jason-2, Jason-1, TOPEX/Poseidon, ENVISAT, GFO, and ERS1/2) with a temporal resolution of 1 d and a spatial resolution of 1/4°. Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO) data were used to provide geostrophic velocities, and sea level anomalies before and after typhoon Mitag passed the main research area. Satellite altimeter data are now released by the Copernicus Marine Environment Monitoring Service (CMEMS). The version of the datasets used in this study is “Global Ocean Gridded L4 Sea Surface Heights and Derived Variables Reprocessed (1993-ongoing)”, which can be obtained from https://resources.marine.copernicus.eu/product-deail/SEALEVEL_GLO_PHY_L4_MY_008_047/DATA-ACCESS, and were accessed on 8 October 2021.

2.4. Analysis and Reanalysis Data

The buoyancy frequency of the observation period was calculated using the Global Ocean Forecasting System (GOFS) version 3.1 of the HYCOM Global Analysis dataset with a temporal resolution of 3 h, spatial resolution of 1/12°, and vertical division of 41 layers. The dataset is an operational, data-assimilative product that assimilates available satellite altimeter observations, satellite, and in situ sea surface temperatures, as well as in situ vertical temperature and salinity profiles from expendable bathythermograph (XBTs), Argo floats, and moored buoys. It has been widely used in studies on multiscale ocean phenomena off northeastern Taiwan Island [25,45,46]. The dataset is available for download from July 2014 to the present (http://www.hycom.org/data/glby0pt08/expt-93pt0, accessed on 23 July 2021). The temperature and salinity from 29 September 2019 to 15 October 2019, covering the NIW event, were selected to calculate the vertical profiles of seawater density and buoyancy frequency (later used to calculate the normal modes) at the mooring, as shown in Figure 3. Note that data on 1 October 2019 are missing.

Derived from the European Centre for Medium-Range Weather Forecasts (ECWMF), the ECWMF Reanalysis 5th Generation (ERA5) dataset was used to calculate the wind stress at 10 m over the sea surface with temporal and spatial resolutions of 1 h and 1/4°, respectively. The reanalysis wind dataset combines model data with global observations into a globally complete and consistent dataset using data assimilation. The dataset can be found here: https://www.ecmwf.int/en/forecasts/datasets/browse-reanalysis-datasets, and were accessed on 13 July 2021.

2.5. Methodology

The local inertial frequency f of the mooring is 0.0360 cph, which is similar to the frequencies of the diurnal internal tides (K₁ = 0.0418 cph, O₁ = 0.0387 cph, P₁ = 0.0416 cph, and Q₁ = 0.0372 cph). Therefore, to reduce the influence of the diurnal internal tides as much as possible, we first subtracted the diurnal internal tides (K₁, O₁, P₁, and Q₁) from the observed currents using the tidal harmonic analysis method. For convenience, the observed currents after removing the diurnal internal tides are referred to as residual currents. The rotary vertical wavenumber spectra were estimated to examine the vertical energy propagation of NIWs. First, vertical and temporal averages of the near-inertial currents were removed [47]. According to the method proposed by Leaman and Sanford [48], the near-inertial horizontal velocity can be written as $V_f\left(m\right)=u_f\left(m\right)+v_f\left(m\right)$, corresponding to the vertical wavenumber m. $u_f$ and $v_f$ are the zonal and meridional components of the near-inertial horizontal velocity. The Fourier transform of the near-inertial horizontal velocity $V_f$ can be expressed as follows:

$$V_f(m)=\frac{1}{H}{\displaystyle {\int }_0^H[u_f(z)+i{v}_f(z)]e^{-imz}}dz$$

(1)

where H is the water depth. This transform can be divided into two parts with positive and negative wavenumbers:

$$V_f(m)=u_{-}(m)e^{-imz}+u_{+}(m)e^{imz}$$

(2)

where $u_{-}$ and $u_{+}$ are velocity components that rotate clockwise and anticlockwise with depth, respectively. The spectra of the clockwise and anticlockwise rotating components are:

$$S_{-}=\frac{1}{2}<{u_{-}{u}_{-}}^{*}>,S_{+}=\frac{1}{2}<{u_{+}{u}_{+}}^{*}>$$

(3)

where $S_{-}$($S_{+}$) is the clockwise (anticlockwise) rotary spectrum, the angled brackets denote that the parameters within them are averaged, and the stars (*) denote the complex conjugate. $S_{-}$($S_{+}$) indicates downward (upward) propagation of energy, and the energy propagation direction is indicated by $S_{-}$ − $S_{+}$. A positive (negative) $S_{-}$ − $S_{+}$ indicates that the energy of NIWs propagates downward (upward).

In this study, the wind stress is calculated as follows:

$$\left({\tau }_x,{\tau }_y\right)={\rho }_a{C}_d\sqrt{u_{10}^2+v_{10}^2}\left(u_{10},v_{10}\right)$$

(4)

where ${\rho }_a$ = 1.29 kg/m³ is the air density, $C_d$ is the wind stress drag coefficient, which was calculated according to the formulation recommended by Oey et al. [49], and $u_{10}$ and $v_{10}$ are the zonal and meridional components of the wind speed at a height of 10 m, which were obtained from the ERA5 dataset.

The modal content of the Mitag-induced NIWs was investigated in this study. The zonal and meridional components of the near-inertial currents are expressed as follows [50]:

$$\left(u_f,v_f\right)={\displaystyle \sum _{n=0}^M\left(u_n,v_n\right)}{\mathsf{\Phi }}_n$$

(5)

where $u_n\left(t\right)$ and $v_n\left(t\right)$ are the modal components of $u_f\left(z,t\right)$ and $v_f\left(z,t\right)$ with respect to mode n (n = 0, 1..., M; n = 0 for the barotropic mode and n > 0 for baroclinic modes). ${\mathsf{\Phi }}_n\left(z\right)$ are the eigenfunctions of the eigenvalue problem for eigenspeed $c_n$:

$$\{\begin{array}{l}\frac{d^2{\mathsf{\Phi }}_n}{d{z}^2}+\frac{N^2}{c_n^2}{\mathsf{\Phi }}_n=0\\ {\mathsf{\Phi }}_n\left(0\right)=0,{\mathsf{\Phi }}_n\left(-h\right)=0\end{array}$$

(6)

$${\mathsf{\Pi }}_n={\rho }_0{c}_n^2\frac{d{\mathsf{\Phi }}_n}{dz}$$

(7)

where h is the water depth, and N is the buoyancy frequency. ${\mathsf{\Pi }}_n\left(z\right)$ are the normal modes corresponding to velocity, and ${\rho }_0$ = 1024 kg/m³ is the reference water density.

3. Results

3.1. Spectral Analysis

To investigate the near-inertial response of the upper ocean to typhoon Mitag, we first performed a spectral analysis of the residual current, as shown in Figure 4. A significant feature of NIWs is that the peak of their spectral density exists near the local inertial frequency f [1]. Figure 4a shows the continuous wavelet transformation of the zonal residual currents at a depth of 100 m at the mooring. Clearly, after typhoon Mitag passed the mooring, significant high-value energy appeared near the local inertial frequency f. On 2 October 2019, the energy was the highest. This indicates that the NIWs were excited by typhoon Mitag. The time evolution of the wavelet spectrum energy of the zonal residual current also shows that strong near-inertial spectrum energy existed only a few days after the passage of typhoon Mitag, while the spectral energy of the semidiurnal internal tides was almost strong during this period, reflecting the intermittent nature of NIWs, which is also an important feature to distinguish NIWs from internal tides. The depth-averaged power spectra of the zonal and meridional residual currents are shown in Figure 4b. There were significant peaks near the local inertial frequency f and the semidiurnal internal M₂ tides. However, the spectral density of the near-inertial frequency was much smaller than that of the semidiurnal internal M₂ tides, and the spectral peak of the former was approximately 1/30 of the latter. This is consistent with previous studies that showed strong semidiurnal tides in the East China Sea [51,52]. In addition, there was also a significant spectral peak at the frequency of M₂–f, which implies that nonlinear interactions between waves occur at the mooring. Note that there was no peak at the diurnal frequency, and the spectral density was very small, as shown in Figure 4. This indicates that the de-tide process using the tidal harmonic analysis method successfully reduced the interference of the diurnal signals.

3.2. Near-Inertial Currents

According to the spectral analysis results (Figure 4), with the cutoff frequency close to the troughs on both sides of the near-inertial spectrum peak as the standard, we selected the 0.70f–1.12f frequency band (yellow shading in Figure 4b) as the cutoff frequency for NIWs. A fourth-order Butterworth bandpass filter was used to extract the near-inertial currents from the residual currents. The filter was carried out twice in the forward and backward directions to eliminate all phase shifts. Figure 5 displays the vertical profiles of the zonal and meridional components of the near-inertial currents over time. NIWs usually occur a few hours after the passage of a typhoon and dissipate within a few days [53]. Figure 5 clearly shows that strong near-inertial currents were generated at the mooring after typhoon Mitag passed. The maximum zonal (meridional) near-inertial velocity was approximately 0.21 m/s (0.19 m/s) at a depth of 100 m (120 m), which is larger than that excited by typhoon Nesat observed by Yang et al. [25] (the maximum value was 0.15 m/s). The zonal velocity was slightly higher than the meridional velocity, indicating that the elliptical particle motions of NIWs have different deflection angles and sizes at different depths. The near-inertial currents showed an obvious upward propagation of the phase. According to the slope of the 0.05 m/s contour of the velocities, it takes approximately 10.50 h for the phase to propagate upward for 150 m, so the upward phase velocity was estimated to be 14.28 m/h. This value was higher than the upward phase velocities of the NIWs observed near the East China Sea continental slope by Park et al. [52] and Yang et al. [25], which were 4.68 m/h and 11.84 m/h, respectively. Near-inertial currents mainly existed above 300 m depth and presented subsurface enhancement characteristics, consistent with previous studies [23,25,35].

3.3. Near-Inertial Kinetic Energy

To analyze the characteristics of near-inertial energy produced by typhoon Mitag, we used Equation (8) to calculate the Mitag-induced near-inertial kinetic energy (NIKE).

$$NIKE=\frac{1}{2}{\rho }_0(u_f^2+v_f^2)$$

(8)

where ${\rho }_0$ = 1024 kg/m³ is the reference water density and $u_f$ and $v_f$ are the zonal and meridional near-inertial currents, respectively.

Figure 6a displays the depth–time evolutions of the NIKE. After the passage of Typhoon Mitag, the NIKE reached 290 m, based on the maximum depth of the NIKE of 5 J/m³. There were two significant high-value kinetic energy regions, which were 70–160 m and 190–270 m. The maximum energies of the two NIKE high-value regions were 23.01 J/m³ at 12:30 on 2 October at depths of 100 m and 17.08 J/m³ at 9:00 on 2 October at a depth of 200 m. According to the propagation velocity of the energy core, the vertical group velocity of the NIWs was estimated to be 10.00 m/h, which is higher than the 3.60 m/h estimated by Zheng et al. [54] and the 9.71 m/h estimated by Yang et al. [11]. This result is consistent with the 10.00 m/h estimated by Yang et al. [34]. The dominant baroclinic modes of NIWs are one of the important reasons for the different vertical group velocities. High (low) baroclinic mode dominance corresponds to small (large) vertical group velocity. Therefore, the NIWs excited by typhoon Mitag were mainly dominated by the low baroclinic mode. The modal characteristics of Mitag-induced NIWs are examined later. Figure 6b shows the evolution of different depths of the low-pass filtered NIKE. The results indicate that the NIKE of the subsurface layer is stronger than that of the surface and deep layers. The NIKE at 50 m first reached its maximum value, which occurred before typhoon Mitag passed the mooring. The maximum NIKE at 120 m, 200 m, and 300 m appeared after the passage of typhoon Mitag. The time variation in the peaks of the NIKE at different depths suggests that the energy source that excited the NIWs was on the surface and that the NIKE propagated downward. It is worth noting that upward NIKE propagation occurred on approximately 5 October (Figure 6a).

To further study the propagation characteristics of the NIKE, we used the rotary vertical wavenumber spectra of the near-inertial currents. Figure 7a illustrates the time evolution of the difference between the clockwise rotary spectrum ($S_{-}$) and the counterclockwise rotary spectrum ($S_{+}$). A positive value (negative value) means that energy is propagated downward (upward). It is noteworthy that the color scale of the colormap is asymmetrical, thereby highlighting the upward propagation of energy. The results show that after typhoon Mitag passed, the NIKE was dominated by downward propagation, with the smaller wavenumber band (<0.007 cpm) being the most significant. Moreover, the phenomenon of the upward propagation of energy was present, but mainly in the larger wavenumber band (0.007–0.014 cpm), which occurred from 30 September to 2 October and from 10 October to 12 October. The upward NIKE propagation in the smaller wavenumber band (0.002–0.005 cpm) on approximately 5 October corresponds to that shown in Figure 6a. The time-averaged rotary vertical wavenumber spectra show that the clockwise component is always larger than the anticlockwise component in the whole wavenumber band, especially in the wavenumber band that is less than 0.036 cpm (Figure 7b).

To investigate the damping of Mitag-induced NIWs, the e-folding time of the NIWs was estimated through the depth-averaged NIKE temporal autocorrelation function [23,25,34]. As shown in Figure 8a, the decay timescale of the NIWs was approximately 9.5 days, which was smaller than the near-inertial motion event with an e-folding time of 11 days observed by Yang et al. [25]. The longer decay timescale was determined by two consecutive wind energy inputs [25]. Figure 8b shows the time variation of 10 m wind stress on the sea surface at the mooring calculated from the ERA5 dataset, indicating that there was only one wind energy input for this near-inertial motion event. However, the decay timescale of 9.5 days is larger than the decay timescale of the NIKE in the mixed layer, which is generally less than 5 days [53]. The study of Cao et al. [38] showed that the local long decay time of the NIKE was related to the propagation of NIWs from other locations. In Figure 6a, after 6 October, significant NIKE appeared at the mooring, with a maximum value of approximately 13.24 J/m³ occurring on 9 October. The NIKE time series at a depth of 120 m also showed that a new NIKE peak appeared on 9 October (Figure 6b). Therefore, it is reasonable to speculate that the NIWs from other locations propagate to the mooring, resulting in a longer decay timescale for this near-inertial motion event. Since the data are single-point observations, it is necessary to combine the model data to further study the three-dimensional propagation characteristics of the NIWs on the East China Sea continental slope.

3.4. Modal Content of Near-Inertial Waves

Modal content is an important characteristic of internal ocean waves [38,50]. Therefore, it is necessary to study the modal characteristics of NIWs excited by typhoon Mitag. Figure 5 shows that from 29 September to 5 October 2019 and from 6 October to 15 October 2019, the near-inertial currents had significantly different upward phase velocities of approximately 14.28 m/h and 4.56 m/h, respectively, indicating that the near-inertial currents were dominated by different modes in these two periods. The buoyancy frequency N at the mooring was calculated using HYCOM analysis data. The time evolution of the buoyancy frequency squared N² at the mooring is shown in Figure 9a. The results show that after typhoon Mitag passed, the depth layer with a high buoyancy frequency N was significantly lifted due to the pumping effect caused by typhoon Mitag, and the location corresponding to the maximum N became shallower. The time-averaged buoyancy frequency squared N² profile (Figure 3b) shows that the trend of the buoyancy frequency first increased and then decreased with depth, with a maximum value at 70 m and a maximum standard deviation.

The mean buoyancy frequency squared N² from 29 September 2019 to 15 October 2019 was used to calculate the normal modes because the time-varying buoyancy frequency has little effect on the normal mode decomposition [55]. In this study, it is appropriate to use the first five baroclinic modes for modal decomposition, as shown in Figure 9b,c, which can reflect the characteristics of the NIWs to a greater extent without causing overfitting. Figure 10a,b shows the time series of the NIKE and the NIKE of the baroclinic modes, respectively. The first and fourth baroclinic modes dominated the NIKE from 29 September to 15 October, accounting for 58.0% and 18.7% of the total NIKE, respectively, and the variation in the two baroclinic modes was nearly consistent with the NIKE. The NIKE proportions of the other baroclinic modes were all less than 10%. From 29 September to 5 October, the first baroclinic mode was dominant, indicating that locally generated NIKE was dominated by the first baroclinic mode. From 6 October to 15 October, the fourth baroclinic mode was the main mode, which further indicates that the NIWs recorded by the mooring during this time period were caused by near-inertial signal propagation from other locations. This is consistent with the findings of the study of Cao et al. [38], which showed that the transmitted near-inertial signals were dominated by higher baroclinic modes.

3.5. Frequency of Near-Inertial Waves

Previous studies have shown that the frequency of NIWs is generally inconsistent with the local inertial frequency due to the influence of background vorticity and background currents [20,56,57]. Figure 11a,b shows the vertical profiles of the power spectra of zonal and meridional residual currents from 25 September to 20 October, respectively. Clearly, the high spectral density of the near-inertial frequency band 0.70f–1.12f is concentrated at depths shallower than 400 m, especially 60–160 m, which corresponds to the most significant NIKE. Figure 11c displays the near-inertial spectral peak frequencies of zonal and meridional residual currents from 50 to 400 m. The results show that the near-inertial spectral peak frequencies are basically smaller than the local inertial frequency f, showing a red-shifted characteristic. However, the near-inertial peak frequency of the zonal residual currents shows the obvious characteristic of a blue-shift from 300–330 m depth, which may be related to the background stratification [58]. The depth averages of the near-inertial peak frequencies of the zonal and meridional residual currents were 0.918f and 0.929f, respectively. In addition, the time variation in the spectral peak frequencies of the near-inertial band 0.70f–1.12f obtained by continuous wavelet transformation is shown in Figure 12. The results indicate that from 30 September to 15 October, the near-inertial spectral peak frequencies of the zonal and meridional residual currents were both smaller than the local inertial frequency f, which is consistent with the above results. The time-averaged spectral peak frequencies were 0.934f and 0.946f, respectively. However, the spectral peak frequencies increased from 4 October to 11 October. The background vorticity could modify the near-inertial frequency through the effective Coriolis frequency f_e [20] such that:

$$f_e=f+\frac{\zeta }{2}$$

(9)

$$\zeta =\frac{\partial v_g}{\partial x}-\frac{\partial u_g}{\partial y}$$

(10)

where f is the local inertial frequency, ζ is the background vorticity, and $u_g$ and $v_g$ are the zonal and meridional sea surface geostrophic currents, respectively. From 4 October to 11 October, a cyclonic eddy existed on the west side of the mooring, as shown in Figure 13. At the same time, the background vorticity of the mooring increased significantly (Figure 14a), resulting in an increase in the frequency of the near-inertial spectral peak (Figure 12). The average background vorticity at the mooring from 30 September to 15 October was 0.427f. Positive background vorticity generally causes the effective Coriolis frequency f_e to be greater than the local inertial frequency f, resulting in a blue-shift of the near-inertial wave frequency, but the frequency of the NIWs induced by typhoon Mitag was red-shifted. Research by Yang et al. [25] showed that the Doppler shift caused by the Kuroshio would lead to a red-shift of the NIW frequency. The mooring was affected by the background currents of the Kuroshio, as shown in Figure 13. Therefore, the Doppler shift effect caused by the Kuroshio is examined next, which can be estimated by Equations (11) and (12):

$$\begin{array}{cc}\omega & ={\omega }_0+\overrightarrow{k}\cdot \overrightarrow{v}\\ & \approx {\omega }_0+\overrightarrow{k_h}\cdot \overrightarrow{v_h}\end{array}$$

(11)

$$\overrightarrow{k_h}\cdot \overrightarrow{v_h}=\left|\overrightarrow{k_h}\right|\left|\overrightarrow{v_h}\right|\cos \alpha$$

(12)

where ${\omega }_0\in \left[f,N\right]$ is the intrinsic frequency, $\omega$ and $\overrightarrow{k_h}$ are the Eulerian (absolute) frequency and horizontal wavenumber of NIWs, respectively.$\overrightarrow{v_h}$ is the background currents of the Kuroshio (here, it is 10-day low-pass filtered meridional raw currents at the mooring due to the northward-dominated Kuroshio, as shown in Figure 14b), and α is the angle between the horizontal phase velocity of NIWs and the horizontal background currents. For example, in the Northern Hemisphere, under the influence of northward (southward) background currents, when the NIWs propagate northward, the cosine value is positive (negative), so the Doppler shift term ($\overrightarrow{k}\cdot \overrightarrow{v}$) is greater than (less than) 0, increasing (decreasing) $\omega$. In this study, as shown in Figure 14b, after typhoon Mitag passed, the background currents of the Kuroshio were 0.10–0.60 m/s; typical NIWs have a horizontal wavenumber of 6.28 × 10⁻⁵ m⁻¹ [1,25]. The NIWs propagating southward (NIWs generated at low latitudes propagate predominantly toward the equator [59]) and the northward-dominated background currents of the Kuroshio are combined. In addition, we assume that the horizontal phase velocity of NIWs parallels the background currents of the Kuroshio. Therefore, the corresponding Doppler shift was $\overrightarrow{k_h}\cdot \overrightarrow{v_h}=$ −(0.10f–0.60f). According to Figure 14a, the effective Coriolis frequency during the period of the NIW event varied from 0.93f to 1.52f at the mooring. Hence, the above analysis shows that the Doppler shift induced by the background currents of the Kuroshio is able to cause the Mitag-induced NIWs to be red-shifted.

4. Discussion

Typhoon Mitag, with a translation speed of 8.44 m/s, passed over the southwestern continental slope of the ECS on 30 September 2019. Then, we observed a significant NIW event at the mooring. Previous observations have shown that the upper ocean response to typhoons is mainly NIWs, as a result of the typhoon imparting a large momentum into the mixed layer [23,31,32,34]. Combined with the above spectral analysis, the observed NIWs were excited by typhoon Mitag. To further confirm that the NIWs were generated by the passage of Mitag and to understand how typhoons excite NIWs, we used the damped slab model, which has been widely and successfully used to explain the near-inertial currents generated in the mixed layer via wind stress [10,27,61,62]. The model is governed by the following:

$$\begin{array}{l}\frac{\partial u_m}{\partial t}-f{v}_m=\frac{{\tau }_x}{{\rho }_{0}D}-r{u}_m\\ \frac{\partial v_m}{\partial t}+f{u}_m=\frac{{\tau }_y}{{\rho }_{0}D}-r{v}_m\end{array}$$

(13)

where $u_m$ and $v_m$ are the zonal and meridional mixed-layer currents, f is local inertial frequency, ${\tau }_x$ and ${\tau }_y$ are the zonal and meridional wind stress, ${\rho }_0$ = 1024 kg/m³ is reference water density, D is mixed layer depth, and r is the damping coefficient. The simulated near-inertial currents were obtained by bandpass filtering of the mixed-layer currents, referring to Yang et al. [25]. The results of the slab model included Ekman currents and near-inertial currents. The wind stress was calculated by Equation (4) based on the EAR5 dataset (shown in Figure 8b). The mixed-layer depth is defined as the depth at which the temperature is 0.5 °C lower than the sea surface temperature [63] and was estimated to be 45 m from the HYCOM analysis data. The damping coefficient was set to 0.25f.

Figure 15a denotes the time evolution of the wind power input into the mixed layer calculated by the slab model at the mooring. It clearly shows that typhoon Mitag imparted much energy at the mooring as it transited. Figure 15b,c displays the zonal and meridional simulated near-inertial currents in the mixed layer and the observed near-inertial currents (here, the zonal near-inertial currents at 100 m and the meridional near-inertial currents at 120 m were chosen, with the zonal and meridional near-inertial currents being maximum at the depth) during the passage of Mitag. Although the simulated NIWs in the mixed layer were slightly larger than the observed NIWs below the mixed layer, which is the result of the decay of near-inertial energy during propagation [64,65], the simulated and observed NIWs were generally consistent. The results of the slab model and the downward (upward) energy (phase) propagation (Figure 5 and Figure 7) verify that the observed NIWs were induced by the strong winds of Mitag. When typhoon Mitag passed through, time-varying strong wind stress was generated on the sea surface at the mooring, transferring a large amount of momentum and energy to the oceanic mixed layer and producing a resonant response in the mixed layer of water oscillating horizontally at a frequency close to the inertial frequency. After the typhoon passed, the mixed-layer near-inertial energy radiated to the thermocline and even the deep ocean in the form of NIWs [26,27,32,66]. In addition, Figure 15d indicates the time series of sea level anomalies (SLA) at the mooring. The results suggest that the time period of the cyclonic eddy affecting the mooring was from 4 October to 11 October (purple shading in Figure 15d), which lags the observed significant NIWs from September 30 (Figure 5). These results suggest that typhoon Mitag is the predominant cause of the intense NIWs that occurred on the southwestern continental slope of the ECS.

Energetic M₂ barotropic-to-baroclinic conversion occurs in the ECS [67,68]. The above spectral analysis shows that even the significant near-inertial internal waves were generated by the typhoon, the spectral density of which was much smaller than that of M₂ internal tide. Both internal tides and NIWs have important contributions to ocean mixing [69,70]. The shear values of currents can represent the strength of seawater mixing and the energy dissipation rate. Larger shear values indicate that the stronger the mixing is, the greater the energy dissipation rate. To study and compare the mixing effect caused by the Mitag-induced NIWs and the M₂ internal tide on the continental slope of the ECS, the vertical shear spectra of the residual currents were calculated. The depth-averaged vertical shear spectra of zonal and meridional residual currents are shown in Figure 16. The results show that there is strong shear at near-inertial and semidiurnal frequencies, and the strengths of both are equal. Therefore, although the NIWs excited by typhoon Mitag have much less energy than the M₂ internal tide, the ocean mixing caused by the NIWs was comparable to that of the strong M₂ internal tide. To further study the shear characteristics of the NIWs and M₂ internal tide, the shear is calculated as follows:

$$s=\sqrt{{\left(\frac{\partial u_b}{\partial z}\right)}^2+{\left(\frac{\partial v_b}{\partial z}\right)}^2}$$

(14)

where $u_b$ and $v_b$ are the zonal and meridional components of the NIWs or M₂ internal tide, respectively. According to the spectral analysis results (Figure 4b), the frequency band of (0.0705–0.0881) cph corresponding to 1.96f–2.45f was selected as the cutoff frequency for extracting M₂ internal tides. Figure 17a,b displays the depth–time plots of 24 h low-pass filtered shear caused by the NIWs and M₂ internal tide, respectively. Clearly, the strong shear generated by the NIWs and M₂ internal tide mainly occurred above 120 m, and the maximum shear values were 0.0117 s⁻¹ and 0.0182 s⁻¹, corresponding to the former and the latter, respectively. Strong near-inertial shear corresponds to weak near-inertial currents (Figure 5 and Figure 6a), while strong M₂ internal tidal shear is consistent with strong M₂ internal tide. In addition, compared with near-inertial shear, M₂ internal tidal shear was also significant below 300 m.

Spectral analysis results show that there was a spectral peak at the frequency of M₂−f (Figure 4b). It is speculated that M₂−f waves were generated by the nonlinear wave–wave interactions between the NIWs and M₂ internal tides. Because the two-wave coupling theory indicates that the two main waves are coupled into the third wave, the frequency relationship between them satisfies w₁ ± w₂ = w₃, and the wavenumber relationship satisfies k₁ ± k₂ = k₃ [71]. To estimate the occurrence of the nonlinear interaction process between internal waves, the bicoherence of the residual currents, which is the normalized version of the bispectrum, was calculated. This method can effectively estimate the phase-locking between waves with different frequencies. It has been widely used to distinguish between nonlinearly coupled waves and independent waves [12,13,72,73,74,75,76]. The bispectrum is expressed in the frequency domain as:

$$\begin{array}{cc}B({\omega }_1,{\omega }_2)\hfill & =E\left[X_{{\omega }_1}{Y}_{{\omega }_2}{Z}_{{\omega }_1+{\omega }_2}^{*}\right]\hfill \\ & =E\left[\left|X_{{\omega }_1}\right|\left|Y_{{\omega }_2}\right|\left|Z_{{\omega }_1+{\omega }_2}\right|e^{-i({\theta }_1+{\theta }_2+{\theta }_3)}\right]\hfill \end{array}$$

(15)

where E[] is the expected value; * denotes the conjugate; X_ω, Y_ω, and Z_ω are the Fourier coefficients of variables x, y, and z in frequency space. θ₁, θ₂, and θ₃ are the relative phases of the respective Fourier coefficients. The bicoherence can be expressed as follows:

$$b^2({\omega }_1,{\omega }_2)=\frac{{\left|B({\omega }_1,{\omega }_2)\right|}^2}{E\left[{\left|X_{{\omega }_1}\right|}^2\right]E\left[{\left|Y_{{\omega }_2}\right|}^2\right]E\left[{\left|Z_{{\omega }_1+{\omega }_2}\right|}^2\right]}$$

(16)

With the influence of the wave amplitude eliminated, bicoherence measures the phase-locking between the interacting triads.

Figure 18a gives the bicoherence values with depth for the frequency bins [f, M₂−f] and [f, M₂], which were calculated from the zonal residual currents. In the thinner depth layer near a depth of 130 m, the bicoherence values around the [f, M₂−f] and [f, M₂] frequencies exceed the 90% confidence interval or even the 95% confidence interval. At the same time, the bicoherence analysis at 130 m shows that significant bicoherence values occurred around the [f, M₂–f] and [f, M₂] frequencies (Figure 18b). Figure 19 shows the depth-averaged kinetic energy in the near-inertial, M₂ (0.0705–0.0881 cph) and M₂–f (0.0417–0.0543 cph) frequency bands at the mooring. Significant M₂–f kinetic energy occurred during the period when the kinetic energy of M₂ and near-inertial kinetics were both strong. The linear correlation coefficient between the near-inertial and M₂–f kinetic energy was 0.94 (p < 0.01). Through ideal experiments and simple derivation, Cao et al. [75] pointed out that when NIWs have a nonlinear interaction with M₂ internal tides, they have a significant bicoherence value around the frequencies of [f, M₂–f] and [f, M₂]. Therefore, this evidence indicates that M₂–f waves are the result of the nonlinear interaction of the NIWs and M₂, and the energy transfers from M₂ and f to M₂–f, reflecting a mechanism of energy dissipation of NIWs and semidiurnal internal waves.

5. Conclusions

On 30 September 2019, typhoon Mitag passed over the southwestern continental slope of the ECS, generating strong NIWs, which were fully captured by an ADCP deployed here. Based on in situ observations as well as analysis and satellite data, the horizontal velocity, energy, modal, and frequency characteristics of the NIWs are analyzed.

Analysis of the power spectra and continuous wavelet spectra shows that a significant spectral density appeared near the local inertial frequency f after the passage of typhoon Mitag, but the near-inertial spectral density peak was approximately 1/30 of that of semidiurnal internal M₂ tides. This value indicates that the high-frequency movement on the southwestern continental slope of the ECS was dominated by semidiurnal internal tides. The vertical shear spectra show that the shear spectrum energy of the near-inertial band is equivalent to that of semidiurnal internal M₂ tides, indicating that the NIWs had much less energy than semidiurnal internal M₂ tides, but the strong shear generated by the NIWs resulted in turbulent ocean mixing comparable to that of semidiurnal internal M₂ tides. In addition, spectral analysis shows that there was also a significant spectral peak at the frequency of M₂–f. The simultaneous enhancement of near-inertial currents and M₂–f currents as well as the significant bicoherence values of the [f, M₂–f] frequency indicate that this was the result of nonlinear interaction between the NIWs and M₂–f waves, which reflects a mechanism of energy dissipation of internal tides and NIWs. Moreover, Yang et al. [76] showed that the M₂ internal tide transmits energy on a smaller scale through the parametric subharmonic instability (PSI) mechanism, revealing a complex mechanism of energy dissipation of internal tides and NIWs on the southwestern continental slope of the ECS. It is also necessary to further study the contribution of ocean mixing caused by NIWs compared with internal tides.

The time–depth profile of the near-inertial currents shows that the maximum zonal (meridional) Mitag-induced near-inertial currents with a velocity of 0.21 m/s (0.19 m/s) occurred at a depth of 100 m (120 m). The zonal velocity is slightly greater than the meridional velocity, showing the motion characteristics of elliptical particles of NIWs. Based on the slope of the 0.05 m/s velocity contour, the upward phase velocity was estimated to be 14.28 m/h. The NIKE was mainly shallower than 290 m, two high-value areas of kinetic energy showed subsurface enhancement characteristics, and the maximum kinetic energy was 23.01 J/m³. According to the propagation velocity of the energy core, the vertical group velocity of the NIWs was estimated to be 10.00 m/h. The time variation in the NIKE at different depths showed that the NIKE of 50 m reached its maximum value before the center of typhoon Mitag passed the mooring, while the NIKE values of 120 m, 200 m, and 300 m reached their maximums after the center of typhoon Mitag passed the mooring. As the depth increases, the time delay to reach the maximum value indicates that the NIKE excited by typhoon Mitag propagated downward. The time-averaged rotary vertical wavenumber spectra showed that the NIKE propagates significantly downward in the wavenumber band (<0.036 cpm). The time variation in the rotary vertical wavenumber spectra shows that there was also a weak upward NIKE propagation phenomenon, mainly in the 0.007–0.014 cpm wavenumber band, and it occurred in different time periods. The time autocorrelation function of the deep-averaged NIKE shows that the e-folding time of the NIWs was 9.5 days; this value is larger than the decaying timescale of the NIKE in the mixed layer, which was generally less than 5 days [53]. The longer decaying time scale of the NIKE may be related to the propagation of near-inertial signals excited by typhoon Mitag at locations other than the mooring.

Normal mode analysis shows that the NIWs were dominated by the first baroclinic mode, followed by the fourth baroclinic mode. These two baroclinic modes account for 58.0% and 18.7% of the total NIKE, respectively. However, the NIKE of the first baroclinic mode was dominant from 29 September to 5 October, and the NIKE of the fourth baroclinic mode was dominant from 6 October to 15 October. The former corresponded to a large upward phase speed (14.28 m/h), and the latter corresponded to a small upward phase speed (4.56 m/h). The frequencies of the zonal and meridional near-inertial currents were 0.918f and 0.929f, respectively. Although the average background vorticity was 0.427f, the NIWs excited by typhoon Mitag exhibited a red-shift due to the Doppler shift effect of the Kuroshio. Interestingly, from 4 October to 11 October, affected by a cyclonic eddy, the positive background vorticity at the mooring increased significantly, but the frequency of the NIWs was still lower than the local inertial frequency f. This implies that the frequency of NIWs in the Kuroshio area of the ECS is mainly affected by the Kuroshio Doppler shift effect. Further research is needed to provide more evidence.