Journal of Oceanology and Limnology   2022, Vol. 40 issue(5): 1889-1908     PDF       
http://dx.doi.org/10.1007/s00343-021-1180-0
Institute of Oceanology, Chinese Academy of Sciences
0

Article Information

YUAN Shengming, YAN Xiaomei, ZHANG Linlin, YANG Bing, PANG Chongguang, HU Dunxin
The near-inertial waves observed east of the Philippines
Journal of Oceanology and Limnology, 40(5): 1889-1908
http://dx.doi.org/10.1007/s00343-021-1180-0

Article History

Received Jun. 10, 2021
accepted in principle Aug. 18, 2021
accepted for publication Nov. 15, 2021
The near-inertial waves observed east of the Philippines
Shengming YUAN1,4, Xiaomei YAN1,2,3, Linlin ZHANG1,2,3, Bing YANG1,2,3, Chongguang PANG1,2,3, Dunxin HU1,2,3     
1 Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China;
2 Pilot National Laboratory for Marine Science and Technology (Qingdao), Qingdao 266237, China;
3 Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao 266071, China;
4 College of Earth Science, University of Chinese Academy of Sciences, Beijing 100049, China
Abstract: Based on mooring observations from Aug. 1, 2016 to Dec. 14, 2017, the characteristics and underlying mechanisms of near-inertial waves (NIWs) observed east of the Philippines were studied. Three strong NIW events were investigated in detail. The NIWs in Event Ⅰ were induced by typhoon Lan and had the strongest magnitudes of 0.35 m/s. The maximum near-inertial kinetic energy (NIKE) was shown at the ocean surface. The NIW in Event Ⅱ was stimulated by a moderate cyclonic wind with the extreme NIKE located at about 110-m depth. The existence of a cyclonic eddy during Events Ⅰ and Ⅱ led to a blue shift of near-inertial frequencies. For Event Ⅲ, the surface near-inertial signals were also induced by local weak wind, whereas the real generation mechanisms for the subsurface NIWs remain unclear. In particular, during Event Ⅲ, there was a nonlinear wave-wave interaction between NIWs and semidiurnal (D2) tides, which further induced strong D2±f waves. Overall, the NIWs in the three events exhibited distinct vertical structures. The NIWs in Events Ⅰ and Ⅱ were dominated by lower modes with elevated NIKE well confined to the upper 250 m and 270 m, respectively. In contrast, the NIW Event Ⅲ was dominated by higher modes and the NIWs penetrated downward beyond 360 m. Such deep penetration of NIWs could be attributed to the weak wind stress curl and positive sea level anomalies associated with an anticyclonic eddy. In addition, the three NIW events had e-folding timescales of less than 7 days.
Keywords: near-inertial wave (NIW)    generation mechanism    dynamic characteristic    
1 INTRODUCTION

The wave frequency ω of internal waves in the ocean is between the inertial frequency f and the buoyancy frequency N (Garrett, 2001; Alford et al., 2016). Near-inertial waves (NIWs) have a frequency near the local Coriolis frequency f, where f=2Ωsinθ, Ω is the angular speed of the Earth's rotation, and θ is the local latitude (Pollard, 1980; Baines, 1986). They are ubiquitous in the global ocean, acting as an important way for wind to transfer energy to the ocean and providing energy for the ocean mixing process (Munk and Wunsch, 1998; MacKinnon and Gregg, 2003). NIWs are not only an important part of the ocean dynamic system, but also may affect the biogeochemical and atmospheric processes (Fu, 1981; Jochum et al., 2013).

The NIWs are primarily caused by transient strong wind systems, such as the passage of tropical cyclones (TCs) (Alford et al., 2016). When a TC passes over the sea surface, kinetic energy is injected into the ocean surface mixed layer (ML), causing the generation of NIWs. As the NIWs propagate downward into the thermocline, their associated near-inertial kinetic energy (NIKE) is transferred to the deep ocean (Brooks, 1983; Yang and Hou, 2014; Wang et al., 2019). Another important source of NIWs is the parametric subharmonic instability (PSI), which is a nonlinear resonant triad interaction that transferring the energy of one low-mode internal wave to two high-mode waves with opposite wavenumbers (Alford et al., 2007; Xie et al., 2008, 2011). In theory, the frequency of each of the two subharmonics (ω1 and ω2) waves is usually close to half the forcing frequency (ω0). It has been verified by in-situ observations that PSI is effective at generating the diurnal (D1) and semidiurnal (D2) internal tides near the critical latitudes of 14°N and 29°N, respectively (Hibiya et al., 2002; Carter and Gregg, 2006; Alford, 2008; Xie et al., 2008, 2009; MacKinnon et al., 2013). Moreover, Lee waves can induce NIWs by stabilizing and slowly evolving into low-frequency geostrophic currents through internal wave affecting seabed topography (Nikurashin and Ferrari, 2010). NIWs can also be spontaneously generated by large-scale stress instability (Hoskins and Bretherton, 1972) and radiation by time-dependent instabilities of low-frequency currents (Ford, 1994).

In general, NIWs triggered by TCs continue for a period of time after TCs pass through (Chen et al., 2013; Cao et al., 2018; Hou et al., 2019; Ma et al., 2019). They may have different characteristics due to various TC strengths, trajectories, moving speeds, and distances from the moorings (Sun et al., 2015; Cao et al., 2018; Hou et al., 2019). In addition, NIWs also show differences in different sea areas. In deep waters, the TC-induced near-inertial current in the South China Sea can reach up to 35 cm/s, and the NIWs are maintained for 7–10 days (Yang and Hou, 2014; Wang et al., 2019), while in the Northwestern Pacific, Hou et al. (2019) observed maximum near-inertial currents of about 50 cm/s that lasted for 7–16 days during typhoons. In shallow waters, such as on the continental shelf of the northwestern South China Sea, TC-induced near-inertial velocities are weaker than 30 cm/s, and the NIWs continue for about 10 days (Yang et al., 2015). Besides, the NIWs exhibit seasonal variations with the seasonality varying from place to place (Alford and Whitmont, 2007). In the South China Sea, Chen et al. (2013) found that the largest NIKE was in autumn. In the Northwestern Pacific along 130°E, Hu et al. (2020) showed that at 17.5°N, 15°N, and 12.6°N, the NIKE peaks occurred in autumn, while at 11°N and 8.5°N the NIKE in winter was strongest. In the western North Atlantic Ocean, the maximum NIKE was also observed in winter by Silverthorne and Toole (2009).

In the Northwestern Pacific, intense TCs are frequently formed (Webster et al., 2005). The annual-mean power input from the wind to near-inertial motions in the North Pacific was estimated to be 65±10 GW, accounting for 13% of the global total wind-energy inputs (Alford, 2003a). These NIKE plays an important role in maintaining the equilibrium state of the global ocean circulation. Alford et al. (2012) indicated that 12%–33% of the NIKE input into the ML could propagate downward to 800-m depth based on in-situ observations, implying that the near-inertial motions may contribute to the mixing in the deep ocean. Hu et al. (2020) statistically analyzed the observations from several moorings deployed in the Northwestern Pacific and showed that the magnitude of TC-induced NIWs varied from 20 to 60 cm/s and the decay timescales of the NIKE were 4–9 days with the penetration depth ranging 220– 580 m. Hou et al. (2019) found the vertical group velocity of the TC-induced NIWs in the Northwestern Pacific was relatively small with more high-mode NIWs generated compared with those in the South China Sea. In addition to the frequent TCs, there are also abundant mesoscale eddies in the Northwestern Pacific which could significantly affect the downward propagation of the NIWs (Byun et al., 2010; Chen et al., 2010; 2011; Jaimes and Shay, 2010; Chelton et al., 2011). The intensive interaction between typhoon-induced NIWs and meso-scale eddies thus plays an important role in providing energy for ocean mixing in this region (e.g. Kim et al., 2013).

Although the NIWs have been extensively studied, our knowledge about their characteristics and underlying dynamics is very limited. Similarities and differences between different NIW events generated by various mechanisms remain unclear, especially in the Northwestern Pacific. Fortunately, a mooring observation system was deployed east of the Philippines from August 2016 to December 2017. During the mooring period, three intense NIWs events were captured, of which one was induced by typhoon Lan and two by other mechanisms. The present study attempts at a comparative analysis of these three NIW events, which will enable us to better understand the dynamic features of NIWs of different origins in the Northwestern Pacific. This paper is organized as follows. In Section 2, we introduce some details of the data used in this study. In Section 3, data processing methods are described. In Section 4, the characteristics and associated mechanisms of the observed NIWs are comprehensively analyzed. Finally, the conclusion and discussion are presented in Section 5.

2 DATA

Velocity records used to examine the near-inertial currents were obtained from a subsurface mooring deployed east of the Philippines at 130°E, 11°N (the red star in Fig. 1) from Aug. 1, 2016 to Dec. 14, 2017. For the mooring system, an upward-looking and a downward-looking 75-kHz Acoustic Doppler Current Profiler (ACDP) were equipped on the main float at a depth of 400 m. The ADCP was configured to measure velocities hourly with a standard bin size of 8 m. The time interval is short enough to obtain the NIW information. The measured velocity data were first processed using a standard quality control program and then interpolated to the depth levels between 0 and 400 m at 10-m intervals. Current measurements in the upper 0–50 m were discarded because of the poor quality. It is well known that NIWs caused by wind are generally excited to be generated in the surface mixed layer. During the three strong NIW events that we mainly focus on in the present study, the mixed layer depth was generally deeper than 50 m with the average values being about 66.7, 61.5, and 53.6 m (Fig. 2ce). Therefore, although the near- inertial velocity at depths of 50–70 m may be weaker than that at the surface, its variation can be used to represent the time evolution of near-inertial current in the mixed layer to a certain extent.

Fig.1 The six-hourly tracks of typhoon Lan (colored solid curves) and Nock-ten (colored dashed curves) TD, TS, STS, and TY represent tropical depression, tropical storm, severe tropical storm, and typhoon, respectively. The red star denotes the location of the mooring station. The colors indicate the bathymetry (unit: m), and the black vectors are satellite altimeter-derived mean surface geostrophic current during the mooring period.
Fig.2 Time series of the 50–400-m depth-averaged hourly (gray line) and daily (black line) NIKE (a), and the wind stress (black line), wind stress curl (orange line), as well as the wind work on the near-inertial wave field (blue line) (b); time evolutions of the zonal component of the near-inertial velocities during three NIW events (c–e) In (a), the red solid line and blue dashed line represent the mean NIKE and the upper 1 standard deviation, respectively; the black dashed line denotes the time when the typhoon center is nearest to the mooring station; and the three NIW events Ⅰ, Ⅱ, and Ⅲ highlighted are examined in this study. In (c–e), the black contours mark the velocity of 5 cm/s, and the purple line denotes the mixed layer depth; the black circles indicate the time when the typhoon center was closest to the mooring station.

The near-inertial horizontal velocity (ui, vi) were obtained by a band-pass filter 0.8f0–1.2f0 (Liu et al., 2018; Hu et al., 2020), where f0 is the local Coriolis frequency. The NIKE was calculated by

    (1)

where ρ0=1 024 kg/m3 is the density of seawater.

The TCs that passed near the mooring location were tracked using the best track data from the Japan Meteorological Agency (http://www.jma.go.jp/jma/jma-eng/jma-center/rsmc-hp-pub-eg/besttrack.html) (Fig. 1). The positions of the TC centers were recorded at an interval of 6 h. Daily absolute dynamic topography (ADT) and sea level anomaly (SLA) data provided by the Archiving, Validation and Interpretation of Satellite Oceanographic (AVISO) (http://www.aviso.altimetry.fr/en/data.html) were adopted to examine mesoscale eddies. The SLA data have a spatial resolution of 1/4°. The 3-hourly HYCOM+NCODA global 1/12° reanalysis data (http://hycom.org/data/glbv0pt08) that assimilate satellite altimetry and available in-situ temperature and salinity observations were used to supplement missing hydrography information. Particularly, the model simulated temperature was adopted to estimate the mixed layer depth which is defined as the depth where the temperature is 0.5 ℃ lower than that at the surface. Wind velocity and wind stress data from NCEP Climate Forecast System Version 2 (CFSv2, https://rda.ucar.edu/datasets/ds094.1/) with a time resolution of 1h and a spatial resolution of 0.5°×0.5° (Saha et al., 2014) were also utilized.

3 METHOD 3.1 Pollard-Millard slab model

The slab model developed by Pollard and Millard (1970) has been widely used to simulate the near-inertial currents in the ML generated by wind stress (Pollard, 1980; Alford, 2003b; Guan et al., 2014; Yang et al., 2015; Cao et al., 2018). In this study, we also use the slab model to simulate the near-inertial currents in the ML during typhoon Lan and Nock-ten. The slab model equations are given as follows:

    (2)
    (3)

where u and v are the zonal and meridional components of the near-inertial velocity in the ML, respectively, τx and τy are the zonal and meridional components of the wind stress, respectively, f0 is the local Coriolis frequency, ρ0=1 024 kg/m3 is the water density, t is the time. The mixed layer depth H defined as the depth where the temperature is 0.5 ℃ lower than that at the surface, was calculated with the HYCOM reanalysis outputs. The damping coefficient r was set to be 0.15f0 according to Alford (2001). Correspondingly, the work done by the wind on the near-inertial wave field was calculated as

    (4)
3.2 Normal mode analysis

Gill (1982) indicated that the motion of the ocean could be expressed as a sum of the vertical normal modes. Each mode has a specific vertical structure with similar behaviors in the horizontal direction and in time to a homogeneous fluid with a free surface. The normal mode equation of the internal gravity waves is written as

    (5)

where ϕn and cn are the vertical displacement and phase speed of the nth mode, respectively. The buoyancy frequency was calculated with the HYCOM temperature and salinity outputs at the mooring location. The boundary conditions corresponding to a rigid surface and a flat seafloor are ϕ(0)=0 and ϕ(-H)=0. In this way, the horizontal near-inertial velocity components u and v can be given by (Danioux et al., 2008)

    (6)

In the present study, this normal mode decomposition method was used to analyze the vertical structure of the NIWs.

3.3 Near-inertial wave ray tracing

The ray-tracing model developed by Kunze (1985) can track the NIWs in flow field. Here it is also used to explore the propagation of NIWs and the underlying mechanisms. In this model, the wave position r=rxi+ryj+rzk and the wavenumber K=kxi+kyj+kzk are given by

    (7)
    (8)

where Cg=Cgxi+Cgyj+Cgzk is the group velocity, V=Ui+Vj is the subinertial current velocity. The vertical component of the group velocity is given by

    (9)

where ω0 is the intrinsic frequency of the NIW, N is the buoyancy frequency, and kH2 =kx2 +ky2. In addition, the dispersion relation is

    (10)

where ω is the Eulerian frequency, fe=f0+ζ/2, ζ is the background vorticity and K·V represents the Doppler shift.

Besides, from the basic dynamics of oceanic internal waves, in a stably stratified ocean, the dispersion relationship for internal waves can be written as

    (11)

and the horizontal component of the group velocity is given by

    (12)
3.4 Bicoherence analysis

The bicoherence analysis is frequently used to distinguish between nonlinearly coupled waves and waves that have been independently excited (Carter and Gregg, 2006; MacKinnon et al., 2013; Cao et al., 2018). The bicoherence is defined as

    (13)

where

    (14)

is the bispectrum, E[ ] is the expected value, X represents the complex Fourier transform of any variable of interest and X* is the conjugate. In this study, the bicoherence analysis is applied to examine the relationships between NIWs and other internal waves.

4 RESULT

We first examine the time series of the 50–400-m depth-averaged NIKE. As shown in Fig. 2, the NIKE is weaker than the mean value most of the time, and there are five events exceeding one standard deviation from the mean. The three strongest ones Ⅰ, Ⅱ, and Ⅲ emerged in October, January, and April 2017, respectively (Table 1). The Event Ⅰ was accompanied by typhoon Lan (Table 2). For Event Ⅱ, an interesting phenomenon is that although it seemed to occur after the typhoon Nock-ten, the intense NIWs were actually generated by the synchronous moderate wind which will be demonstrated later in this work. In Event Ⅲ, the wind was much weak and hence the elevated NIKE should be caused by other mechanisms.

Table 1 Basic characteristics of the NIWs in three events
Table 2 Basic characteristics of the typhoon

Therefore, the three events are representative with different generation mechanisms and are examined in detail in this study.

4.1 NIW Event Ⅰ 4.1.1 Generation mechanism

The NIW Event Ⅰ occurred between October and November 2017 when the typhoon Lan passed by the mooring site. Typhoon Lan was formed near 137.3°E, 8.8°N on Oct. 15, 2017, and dissipated near 155.4°E, 44.4°N on Oct. 23, 2017. On Oct.17, 2017 the typhoon center was nearest to the mooring station with a distance of 273.4 km, which was smaller than the radius of 50-kt wind speed 333.4 km (Fig. 3; Table 2). As a result, when the typhoon Lan passed by the mooring station on Oct. 17, 2017, near-inertial signals were immediately generated in the mixed layer and captured by the mooring observation, which then propagated downward with time (Figs. 2e & 3). The propagation depth range (D), hereafter defined as the maximum depth with a horizontal velocity of 5 cm/s (black solid line in Fig. 2e), was approximately 250 m. The magnitude of the NIWs reached up to 0.35 m/s with the maximum zonal and meridional velocity components being 0.28 and 0.32 m/s, respectively, both at 50-m depth. According to the slope of the near-inertial current profile, the vertical phase velocity of the NIW was estimated to be 6.5 m/h. The basic characteristics of the NIW can be obtained with the dispersion relation defined by Eq.11, and the results are summarized in Table 1.

Fig.3 The wind velocity (arrows) and the logarithm of wind-induced NIKE calculated with the slab model (color shading, unit: J/m3) in the study area from Oct. 16–21, 2017 The red star denotes the mooring station. The colored solid curve is the six-hourly track of the typhoon Lan as illustrated in Fig. 1. The black rectangle indicates the position of typhoon center on the day denoted in each panel.

The NIKE induced by a typhoon will spread from the ocean surface ML to the deep sea over time (Geisler, 1970; Brooks, 1983; Price, 1983; Gill, 1984; Shay and Elsberry, 1987). The vertical distribution of the NIKE is shown in Fig. 4a. As typhoon Lan passing by, the NIKE was intensified in the mixed layer with a maximum value of 63.1 J/m3 at 50 m, which decayed rapidly with time and depth. The vertical group velocity was estimated to be 0.17 m/h. From the time series of the 50–400-m depth-averaged NIKE (Fig. 4c), it is clear that the NIKE began to increase on Oct.16, 2017, reached the maximum value ~5.5 J/m3 on Oct. 25, 2017, and then gradually decreased. On Oct. 30, 2017, it decreased to 1/e of the maximum NIKE. Thus, the e-folding timescale is approximately 5 days. As illustrated in Fig. 4b, the depth of the mixed layer increased from ~50 m to ~65 m during typhoon Lan. Meanwhile, the near-inertial shear was enhanced at depths between 65 and 95 m, i.e., from the base of the mixed layer to the top of the thermocline (~80 m), with a maximum of 0.022/s. Yang and Hou (2014) and Wang et al. (2019) also observed such a phenomenon in the South China Sea. As they suggested, the strong vertical shear indicates active momentum transfer between the mixed layer and the thermocline. Besides, considering that the vertical shear instabilities induced by NIWs would trigger turbulent mixing (Brannigan et al., 2013; Jochum et al., 2013), therefore the consistency between the temporal variation of the mixed layer depth and the velocity shear suggests that the deepening of mixed layer can be attributed to the enhanced mixing during the typhoon period. Overall, typhoon Lan passed by the mooring station in a relatively short time and imparted energy to the ML, which was further transferred into the ocean interior in the form of NIWs.

Fig.4 Time evolutions of the NIKE (a), the near-inertial shear (b), the 50–400-m depth-averaged hourly (blue line) and daily (black line) NIKE (c), and the ζ/f0 (d) from Oct. 10 to Nov. 8, 2017 The solid and dashed contours in (a) indicate 1/e of the maximum NIKE and 3 J/m3, respectively. The purple line in (a–b) denotes the mixed layer depth. The black and red points in (c) represent the maximum value and its 1/e, respectively. The red and blue dots in (d) indicate negative and positive vorticities, respectively.
4.1.2 Frequency blueshift

Spectral analysis was applied to the time series from Oct. 10 to Nov. 8, 2017 at all levels from 50 to 400 m. As illustrated in Fig. 5, there was an obvious power concentration in the near-inertial frequency band, especially at 50–150 m. The mean of the peak frequency in the upper 400 m was 1.16f0; that is, the NIWs had a blueshift of 0.16f0. Kunze (1985) showed that the vorticity of the background flow would modify the frequency of the NIWs: fe=f0+ζ/2, where fe is the effective Coriolis frequency and ζ is the background vorticity. As shown in Fig. 4d, during this NIW event, the ζ calculated with the AVISO ADT was indeed positive with the time-mean value being about 0.31f0, in good agreement with the blueshift in the estimated frequency fp (Table 1). Note that the background vorticity in the ocean may vary with depth. To verify this, we further compared the vorticity calculated with the ADT (ζAVISOg), HYCOM simulated sea surface height (ζHYCOMg), and velocity (ζHYCOM). It was found that in the vertical, the magnitude of ζHYCOM generally decreases with depth. In spite of that, the vertically averaged ζHYCOM in the upper 0–400 m is consistent with the ζHYCOMg (figure not shown). Therefore, the surface geostrophic vorticity ζ can well represent the mean vorticity in the upper ocean and the frequency blueshift phenomenon we noticed above can be attributed to the background vorticity.

Fig.5 Power spectra of the zonal (a) and meridional (b) current components The white dashed lines from left to right represent 0.9f0, the local inertial frequency f0, and 1.3f0. The black solid line represents the peak near-inertial frequency.
4.1.3 Vertical structure

The empirical orthogonal function (EOF) analysis method can decompose the time series of a physical field into space patterns and corresponding time series. It has been frequently applied to examine the vertical structure of the NIWs (e.g., Yang et al., 2015; Hou et al., 2019; Wang et al., 2019). Here the near-inertial current during Oct. 10 to Nov. 10, 2017 was also analyzed with this methodology, and the results are shown in Fig. 6. The first two modes dominate the NIWs and contribute 59.9% and 16.6% of the variance, respectively. The first mode presents an antiphase feature in the vertical direction with a node at 90-m depth, meaning that it is the first baroclinic mode. Although the second mode is much weaker than that of the first mode, the amplitudes of the two modes both increase immediately after typhoon Lan and peak around Oct. 25, 2017 with the meridional component lagging behind the zonal component by about 15 h (Fig. 6a). It is clear that the strongest signals of the two modes came at the same time as the enhanced NIWs emerged (Fig. 4c).

Fig.6 Vertical profiles (a, c) of the zonal (solid red line) and meridional (dashed blue line) components of the near-inertial current and their associated time series (b, d) for the first two EOF modes
4.2 NIW Event Ⅱ

The NIW Event Ⅱ occurred between December 2016 and January 2017. Figure 2c shows the near-inertial velocities during this period. The amplitude of the near-inertial current is ~0.2 m/s, weaker than that generated by typhoon Lan. However, the intense near-inertial current is widely distributed in the upper 400 m of the water column. The vertical range is about 270 m, deeper than the 250 m in Event Ⅰ. Particularly, different from the surface-intensification of NIWs observed during typhoon Lan, the near-inertial velocity in this case peaks at the subsurface layer (~110 m). As a result, the depth-averaged NIKE during this event was stronger than that in Event Ⅰ as shown in Fig. 2a. The vertical phase velocity of the NIWs was estimated to be about 4.4 m/h.

4.2.1 Generation mechanism

The generation mechanism of the NIW Event Ⅱ was explored. As illustrated in Fig. 2c, around Dec. 23, 2016, the typhoon Nock-ten passed by the mooring, but did not stimulate strong NIWs. Instead, the much enhanced near-inertial signals emerged in January 2017, about two e-folding timescales after.

On Dec. 23, 2016, the typhoon center was nearest to the mooring station with a distance of 208.4 km, larger than the radius of 50-kt wind speed 166.7 km (Table 2). From the horizontal maps of the slab model-simulated NIKE, it can be further seen that the mooring station is located at the left side of the typhoon track, where the near-inertial velocity caused by the typhoon is weaker than on the right (Fig. 7). These are probably the main causes for the observed weak near-inertial signals associated with this typhoon. After the passage of typhoon Nock-ten, the NIKE around the mooring site has been much weakened on Dec. 27, 2016. Moreover, there was no obvious horizontal propagations for the typhoon-generated NIWs to reach the mooring station. During Jan. 6 to 8, 2017, another moderate cyclonic wind passed by the mooring station from the left side and the strong NIWs burst (Figs. 2c & 7). Therefore, instead of the typhoon Nock-ten, this moderate cyclone may be the main generation mechanism for the NIW Event Ⅱ. To verify this, the simulated near-inertial velocity in the mixed layer at the mooring station with the Pollard-Millard slab model was further compared with that observed. As demonstrated in Fig. 8, the model reproduces the mean near-inertial currents well at depths of 50–70 m during the NIW Event Ⅱ. The simulated near-inertial velocity corresponds well with that observed in terms of phase, and the amplitudes in the forced phase are also very similar. These results confirm that the intense NIWs in January 2017 were caused by the moderate cyclone instead of the typhoon Nock-ten.

Fig.7 The wind velocity (arrows) and the logarithm of wind-induced NIKE calculated with the slab model (color shading, unit: J/m3) in the study area from Dec. 21, 2016 to Jan. 9, 2017 The red star denotes the mooring station. The colored solid curve is the six hourly track of the typhoon Nock-ten as illustrated in Fig. 1. The black rectangle in (b–d) indicates the position of typhoon center on the day denoted in each panel.
Fig.8 Observed (50–70-m depth-averaged, red line) and modeled (blue line) zonal (a) and meridional (b) near-inertial velocity in the mixed layer

It is worth mentioning that at the mooring site, the wind stress during this event reached up to 0.4 N/m2, weaker than that during typhoon Lan but stronger than most of the rest time (Fig. 2b). Thus there were no more events like Event Ⅱ occurred during the mooring period.

4.2.2 Vertical structure

Similar to the situation during the typhoon Lan, the NIKE in this event was generated in the mixed layer and propagated downward with depth and time. In the vertical, the NIKE shows three peaks (Figs. 9a & 10b). The surface energy core is located in the upper 70 m. As the instrumental data above 50-m depth are not credible, this surface NIKE peak is not well represented. An enhanced subsurface core is shown at 80–130 m with the maximum value being about 32.3 J/m3. The energy transmission of this NIW package is not obvious with the estimated vertical group velocity being only 0.14 m/h. In addition, there was a third NIKE peak at ~250 m, which is much weaker with values less than 3 J/m3.

Fig.9 Time evolutions of the NIKE (a), the near-inertial shear (b), and the ζ/f0 (c) from Dec. 23, 2016 to Jan. 31, 2017 The solid and dashed contours in (a) indicate 1/e of the maximum NIKE and 3 J/m3, respectively. The purple line in (a–b) denotes the mixed layer depth. The purple line in (a–b) denotes the mixed layer depth. The red and blue dots in (c) represent the negative and positive vorticities, respectively.
Fig.10 The time-averaged NIKE for the first fifteen baroclinic modes (a) and comparisons between the combination of these fifteen modes (black line) and the observed NIKE (red line) averaged from Jan. 1–31, 2017 (b)

To understand the complicated vertical structure of the NIKE, the horizontal near-inertial velocity was analyzed with the normal mode decomposition method. Figure 10a shows the time-averaged NIKE for the first fifteen baroclinic modes (n=1, 2, …, and 15). The vertical distribution of the combination of these fifteen modes is generally consistent with that of the observed NIKE (Fig. 10b). All the three peaks shown in the surface mixed layer as well as at 110 m and 250 m are well fitted. Furthermore, it can be seen that above 70 m, the first vertical baroclinic mode is dominant, while at depths deeper than 80 m, the NIWs are determined by the higher modes. In particular, the subsurface NIKE peak at 110 m is captured mainly by the 4–8th modes. Using the EOF decomposition method, similar results were obtained (figure not shown). The contribution rate of the first EOF mode is only 48.3%, much smaller than that in the first event (~60%). Thus, higher EOF modes are more important in this case, especially for the subsurface elevated NIKE. All these results are consistent with Chen et al. (2013) who also found a subsurface NIKE maximum in the northwestern South China Sea that was dominated by higher modes.

As indicated by Alford et al. (2016), for small vertical-wavelength motions with large wavenumber kz, the vertical group velocity becomes slow. The vertical wavenumber kz is proportional to the mode number n, and hence a larger n will result in a smaller group velocity (Zervakis and Levine, 1995). Therefore, the dominant higher modes may be one of the causes for the slow downward propagation of the subsurface NIKE core as noticed in Fig. 9. Besides, the background vorticity shown in Fig. 9c further indicates that there was a cyclonic mesoscale eddy at the mooring site during the NIWs propagation. As argued by Kunze (1985), cyclonic eddies disperse the NIWs from the eddy region by increasing the effective Coriolis frequency, which increases the resistance for wave propagation. Hence, the existence of the cyclonic eddy during this event may also make it difficult for the NIKE to be transmitted downward. Furthermore, similar to the first NIW event, the positive background vorticity associated with the cyclonic eddy also led to a frequency blueshift of NIWs in this event (Table 1).

4.3 NIW Event Ⅲ 4.3.1 Generation mechanism

During the NIW Event Ⅲ, there were no typhoons. Although the wind stress was much weak throughout this period, there still existed an instantaneously increased wind work on near-inertial motions (~0.3 W/m2) during April 13–16 (Fig. 2b), generating strong NIWs in the upper 80 m of the water column. The amplitude of this surface near-inertial current was only 0.11 m/s at 50 m. In the subsurface layer around 150-m depth, on the other hand, there were also near-inertial oscillations with a larger amplitude of 0.16 m/s during Apr. 7–25, 2017, which thus did not seem to originate from the surface layer (Fig. 2d). Moreover, these NIWs penetrated to a deeper depth than the other two events with a vertical range of about 360 m. The vertical phase velocity of the NIWs was estimated to be 2.8 m/h.

Kunze (1985) proposed a ray-tracing model, which has been successfully applied to track NIW propagations (e.g., Byun et al., 2010; Jaimes and Shay, 2010; Chen et al., 2013). Here, we also adopted this model to track the propagation of NIWs and further explored the underlying mechanisms. Due to the constraints of a single mooring station, only the vertical component was used in the model. In the model, according to the basic characteristics calculated with the dispersion relation (Table 1), the initial values of the vertical wavelength (1/kz) and horizontal wavelengths (1/kx=1/ky) were set to 177 m and 152 km, respectively. Based on the HYCOM outputs, the buoyancy frequency N that varied vertically and temporally was calculated (Fig. 11b). The mooring observed raw currents U and V were low-pass filtered with a cutoff period of 95 hours as in Byun et al. (2010) and Chen et al. (2013). The ray-tracing began at 55 m, and the results are shown in Fig. 11a, where the white and black lines represent the trajectories of the tracking NIWs, and the color map is the reciprocal of the gradient Richardson number .Aspecial phenomenon was noted that there were unusual upward waves during Apr. 12–24, 2017. It suggested that the subsurface NIWs might not originate from the surface (Fig. 11a).

Fig.11 Calculated paths of the near-inertial waves from a ray-tracing model and time evolution of lg(R-1) (color) (a), the time evolution of buoyancy frequency (b), and total vertical shear (c) from Apr. 1–30, 2017 In (a), the white and black lines denote penetrating and reflecting ray trajectories, respectively.

Note that the upward NIW trajectories appear in the high R region, where the buoyancy frequency is relatively low and the velocity shear is relatively high (Fig. 11). Moreover, under the same parameters, no upward-propagating NIWs were derived when tracked starting from 100-m depth. All these results suggested that larger R associated with smaller buoyancy frequency N and stronger vertical shear of horizontal currents would lead to unusual upward propagating NIWs, in good agreement with Chen et al. (2013).

We also verified the NIW trajectories at different incident angles (theta=0°, 45°, 135°, 180°, 225°, 315°). It was found that there was an upward trend between 0° and 90°, and no upward waves could be obtained with angles larger than 90°. Therefore, the ray-tracing solutions only provide a qualitative description since the accurate value of parameters cannot be assigned based on a single mooring. However, the model gives an intuitive explanation for the separation of the surface and subsurface NIW packages.

The above results indicate the NIWs in the surface and subsurface layers were generated by different mechanisms. The surface NIWs were induced mainly by the local wind, while those in the subsurface layer may be due to other factors such as lateral propagation and PSI. For the horizontal advection, it cannot be confirmed from the single mooring data. On the other hand, the location of the mooring station is far away from the critical latitude of 14°N for the occurrence of PSI of diurnal D1 internal tides. Moreover, there is no significant peak in the D1f frequency band in the spectrum of the current as will be illustrated later in this work. Therefore, the PSI can also be ruled out from the causes of these NIWs. Although the actual underlying mechanism for the subsurface near-inertial signals remains unclear, the NIW Event Ⅲ shows different characteristics from the NIW Events Ⅰ and Ⅱ as demonstrated below.

4.3.2 Vertical structure

In this event, the maximum NIKE (15.0 J/m3) was located at 150 m (Fig. 12a), deeper than the position of the highest NIKE peak in the other two cases. With a vertical group velocity of about 0.12 m/h, the large near-inertial shear also showed a deepest penetration depth of 400 m (Figs. 4b, 9b, & 12b). Gao et al. (2019) suggested that the near-inertial downward shear was closely related to the wind stress curl and sea level anomaly. As they argued, moderate (even weak) cyclones contribute more to enhanced shear below the pycnocline than very strong cyclones, and positive and negative SLAs cause the accumulation of large shear in the lower and upper parts of the pycnocline by inducing downwelling and upwelling motions, respectively. From Apr. 1–30, 2017, the mooring station was in the area of an anticyclonic eddy with positive sea level anomalies (Fig. 13). Meanwhile, the wind stress curls were weak, ranging from -3×10-7 to 3×10-7 N/m3 (Fig. 12c). Therefore, the deep penetration of the near-inertial shear can be attributed to the positive SLA and weak wind stress curls.

Fig.12 Time evolutions of the NIKE (a), near-inertial shear (b), and background vorticity (dot), SLA (blue line) as well as wind stress curl (orange line) (c) from Apr. 1–30, 2017 The purple line in (a–b) denotes the mixed layer depth. The solid and dashed contours in (a) indicate 1/e of the maximum NIKE and 3 J/m3, respectively. The red and blue dots in (c) represent the negative and positive vorticities, respectively.
Fig.13 Spatial distributions of the sea level anomalies and geostrophic currents at 3-day intervals during Apr. 13–22, 2017Q The red star indicates the location of the mooring station.

The particular vertical structure of the NIWs in this case was further examined with the EOF method. As shown in Fig. 14, the first and second EOF modes change four and three times of signs between depths of 50 and 400 m, respectively. Clearly, the first two dominant modes are high vertical baroclinic modes and contribute 45.6% and 31.6% of the variance, respectively. The amplitude of the first mode started to increase on April 7 and peaked on April 17, with the meridional component lagging behind the zonal component by 15 h (Fig. 14b). The amplitude of the second mode is similar to that of the first mode, but the zonal component lags behind the meridional component by 18 h (Fig. 14d). Besides, according to Alford et al. (2016), the dominant higher modes lead to the slowest downward propagation of NIWs in this event (0.12 m/h) among the three events as summarized in Table 1.

Fig.14 Vertical profiles (a, c) of the zonal (red solid line) and meridional (blue dashed line) components of the near-inertial current and their associated time series (b, d) for the first two EOF modes
4.3.3 Nonlinear wave-wave interaction

The power spectra of currents during this event are shown in Fig. 15. Note that there is no obvious peak at D1f frequency. In addition, it shows that during Mar. 2–31, 2017, the motion is dominated by the D2 tides and the near-inertial signals are weaker. During Apr. 1–30, 2017, the near-inertial motions were strengthened significantly and the (D2±f) wave currents occurred (Fig. 15b). The vertical distributions of the band-pass filtered motions in the frequency bands of ([0.8-1.2]f), ([0.9-1.1]D2), ([0.93-1.08]D2f), and ([0.94-1.15]D2+f) are further shown in Fig. 16. The kinetic energy of the D2±f wave increased sharply between depths of 100 and 200 m during Apr. 7–25, 2017(Fig. 16cd), consistent with the occurrence of strong NIKE in this event (Fig. 16b). Moreover, the kinetic energy of D2 internal tides was also evident at this time and depths (Fig. 16a). The correlation coefficients between the near-inertial f and D2f, D2 and D2f, near-inertial f and D2 +f, D2 and D2 +f, and near-inertial f and D2 kinetic energy are 0.69, 0.33, 0.37, 0.23, and -0.01, respectively, all of which exceed the 95% significance level except for that between f and D2 waves. The results indicate that D2±f waves have a stronger dependence on near-inertial processes. In addition, during Apr. 1–30, 2017, the bicoherence values of the [f, D2f] and [f, D2+f] frequencies are significant at the 80% level between depths of 180 and 200 m and exceeding the 90% level at 190-m depth where the strong NIWs occurred (Fig. 15ce). All the above results indicate that there was a nonlinear wave-wave interaction between NIWs and D2 tides, which further induced strong D2±f waves.

Fig.15 Power spectra of meridional currents during Mar. 2–31, 2017 (a); Apr. 1–30, 2017 (b); bicoherence values of meridional currents around [f, D2f] (c) and [f, D2+f] (d) frequency plotted as a function of depth during Apr. 1–30, 2017; bicoherence values of meridional currents during Apr. 1–30, 2017 at 190-m depth (e) The three vertical dashed lines in (c, d) and three black lines over the color bar in (e) denote the 80%, 90%, and 95% significance level, respectively.
Fig.16 Kinetic energy of D2 internal tides (a), near-inertial motions (b), D2f waves (c), and D2+f waves (d) The black solid line represents the period-smoothed and depth-averaged (100-250 m) kinetic energy and the scales are indicated at the right axis.
5 CONCLUSION AND DISCUSSION

Based on the mooring observational data east of the Philippines (130°E, 11°N) from Aug. 1, 2016 to Dec. 14, 2017, the characteristics and underlying mechanisms of three NIW events were examined. The near-inertial internal waves generated by different mechanisms were captured at this single mooring station, which is of great significance for the study of the characteristic differences of the NIWs. Among the three events, the first one was caused by typhoon Lan, and the second one was stimulated by a moderate cyclonic-like wind that passed by the mooring station from the left. For the third NIW event, it seemed to have two separate NIW packages located in the upper 80 m and around 150-m depth, respectively. The surface near-inertial signals were induced by the local weak wind. Regarding the generation of strong NIWs in the subsurface layer, the PSI mechanism was ruled out. It may be due to lateral advection which, however, could not be verified on the base of the single mooring observation. Although the actual generation mechanisms for the subsurface strong NIWs remain unknown, the NIWs in Event Ⅲ exhibited different dynamic features from those in the other two events.

Both excited by transient strong or moderate cyclonic wind, the NIW Events Ⅰ and Ⅱ have similar characteristics with strong NIKE propagating downward with depth and time after generated in the mixed layer. The maximum NIKE induced by typhoon Lan was in the surface layer. However, the NIKE in Event Ⅱ peaked in the subsurface layer and generally stalled at 110 m without obvious downward propagation. According to previous studies, there are two possible factors affecting the downward propagation of NIWs. First, as stated by Kunze (1985), anticyclonic (cyclonic) eddies would enhance (prevent) the downward radiation of NIWs. Second, Alford et al. (2016) and Zervakis and Levine (1995) suggested that a higher vertical mode number corresponds to a larger vertical wavenumber and a slower group velocity. During the two events, the intensities of the background cyclonic eddy were found to be comparable. However, high vertical modes are more dominant in the NIWs of Event Ⅱ (Fig. 10). Therefore, the second cause may play a more important role in the much slower downward propagation of the NIKE during Event Ⅱ than during typhoon Lan. Besides, during the periods of the two events, the positive background vorticity also, lead to the blueshift of the near-inertial peak frequency.

Compared to the two wind-generated events, the NIWs in Ⅲ have larger vertical wavenumbers, smaller wavelengths, and weaker NIKE. There are two separated NIW packages observed in the surface and subsurface layers. The results of the ray-tracing model suggested that the smaller buoyancy frequency and stronger vertical shear of horizontal currents could cause the NIWs in the mixed layer to propagate upward instead of downward. Overall, the strong NIWs and near-inertial shear showed a deeper penetration depth of ~400 m, which can be attributed to the weak wind stress curl and positive SLA associated with an anticyclonic eddy. In addition, the first two EOF modes of the near-inertial currents were dominated by high baroclinic modes, also different from the other two events. As a result, in the third case, the NIWs showed the lowest downward propagation. More importantly, there was a nonlinear wave-wave interaction between NIWs and D2 tides, which further induced strong D2±f waves.

The three NIW events had e-folding timescales of less than 7 days, much smaller than that observed by Chen et al. (2013) in the South China Sea and Hou et al. (2019) in the Northwestern Pacific. In addition to vertical transmission, lateral propagation and local turbulent dissipation can also contribute to the decay of NIKE in the mixed layer (e.g., D'Asaro, 1989; Jonhnston and Rudnick, 2009; Brannigan et al., 2013). Based on a three-dimensional model, however, Zhai et al. (2009) demonstrated that the horizontal near-inertial energy flux is much less than the downward energy flux. Therefore, the contribution of horizontal propagation to the decay of local NIKE could be neglected. Here, according to Eq.12, we also evaluated the horizontal speed of the NIWs in the three cases (Table 1). The results showed that the NIWs generated by typhoon Lan propagate fastest in the horizontal direction with a speed of ~0.95 m/s, and that of NIWs in Event Ⅱ is the slowest with a speed of only ~0.12 m/s. However, based on the single mooring observation, the detailed horizontal propagation characteristics of NIWs cannot be well resolved. Therefore, more observational and numerical studies about the dynamic features of NIWs are needed in the future. All these results in the present study provide a benchmark for further studies of NIWs in the Northwestern Pacific.

6 DATA AVAILABILITY STATEMENT

The mooring ADCP data were provided by the Northwestern Pacific Ocean Circulation & Climate Experiment (NPOCE, http://npoce.org.cn/). Data of tropical cyclones are available online at (http://www.jma.go.jp/jma/jma-eng/jma-center/rsmc-hp-pub-eg/besttrack.html). The daily ADT and SLA of AVISO datasets are produced and distributed by the Archiving, Validation and Interpretation of Satellite Oceanographic (AVISO, http://www.aviso.altimetry.fr/en/data.html). The HYCOM+NCODA global 1/12° reanalysis outputs were downloaded from http://hycom.org/data/glbv0pt08 and the NCEP/CFSv2 wind velocity and wind stress data were obtained from https://rda.ucar.edu/datasets/ds094.1/.

References
Alford M H, Cronin M F, Klymak J M. 2012. Annual cycle and depth penetration of wind-generated near-inertial internal waves at Ocean Station Papa in the Northeast Pacific. Journal of Physical Oceanography, 42(6): 889-909. DOI:10.1175/JPO-D-11-092.1
Alford M H, MacKinnon J A, Simmons H L, Nash J D. 2016. Near-inertial internal gravity waves in the ocean. Annual Review of Marine Science, 8: 95-123. DOI:10.1146/annurev-marine-010814-015746
Alford M H, MacKinnon J A, Zhao Z X, Pinkel R, Klymak J, Peacock T. 2007. Internal waves across the pacific. Geophysical Research Letters, 34(24): L24601. DOI:10.1029/2007GL031566
Alford M H, Whitmont M. 2007. Seasonal and spatial variability of near-inertial kinetic energy from historical moored velocity records. Journal of Physical Oceanography, 37(8): 2022-2037. DOI:10.1175/JPO3106.1
Alford M H. 2001. Internal swell generation: the spatial distribution of energy flux from the wind to mixed layer near-inertial motions. Journal of Physical Oceanography, 31(8): 2359-2368. DOI:10.1175/1520-0485(2001)031<2359:ISGTSD>2.0.CO;2
Alford M H. 2003a. Redistribution of energy available for ocean mixing by long-range propagation of internal waves. Nature, 423(6936): 159-162. DOI:10.1038/nature01628
Alford M H. 2003b. Improved global maps and 54-year history of wind-work on ocean inertial motions. Geophysical Research Letters, 30(8): 1424. DOI:10.1029/2002GL016614
Alford M H. 2008. Observations of parametric subharmonic instability of the diurnal internal tide in the South China Sea. Geophysical Research Letters, 35(15): L15602. DOI:10.1029/2008GL034720
Baines P G. 1986. Internal tides, internal waves and nearinertial motions. In: Mooers C N K ed. Baroclinic Processes on Continental Shelves, Volume 3. American Geophysical Union, Washington. p. 19–31, https://doi.org/10.1029/CO003p0019.
Brannigan L, Lenn Y D, Rippeth T P, McDonagh E, Chereskin T K, Sprintall J. 2013. Shear at the base of the oceanic mixed layer generated by wind shear alignment. Journal of Physical Oceanography, 43(8): 1798-1810. DOI:10.1175/JPO-D-12-0104.1
Brooks D A. 1983. The wake of hurricane Allen in the western Gulf of Mexico. Journal of Physical Oceanography, 13(1): 117-129. DOI:10.1175/1520-0485(1983)013<0117:TWOHAI>2.0.CO;2
Byun S S, Park J J, Chang K I, Schmitt R W. 2010. Observation of near-inertial wave reflections within the thermostad layer of an anticyclonic mesoscale eddy. Geophysical Research Letters, 37(1): L01606. DOI:10.1029/2009GL041601
Cao A Z, Guo Z, Song J B, Lv X Q, He H L, Fan W. 2018. Near-inertial waves and their underlying mechanisms based on the South China Sea Internal Wave Experiment (2010-2011). Journal of Geophysical Research: Oceans, 123(7): 5026-5040. DOI:10.1029/2018JC013753
Carter G S, Gregg M C. 2006. Persistent near-diurnal internal waves observed above a site of M2 barotropic-to-baroclinic conversion. Journal of Physical Oceanography, 36(6): 1136-1147. DOI:10.1175/JPO2884.1
Chelton D B, Schlax M G, Samelson R M. 2011. Global observations of nonlinear mesoscale eddies. Progress in Oceanography, 91(2): 167-216. DOI:10.1016/j.pocean.2011.01.002
Chen G X, Hou Y J, Chu X Q. 2011. Mesoscale eddies in the South China Sea: mean properties, spatiotemporal variability, and impact on thermohaline structure. Journal of Geophysical Research: Oceans, 116(C6): C06018. DOI:10.1029/2010JC006716
Chen G X, Hou Y J, Zhang Q L, Chu X Q. 2010. The eddy pair off eastern Vietnam: interannual variability and impact on thermohaline structure. Continental Shelf Research, 30(7): 715-723. DOI:10.1016/j.csr.2009.11.013
Chen G X, Xue H J, Wang D X, Xie Q. 2013. Observed nearinertial kinetic energy in the northwestern South China Sea. Journal of Geophysical Research: Oceans, 118(10): 4965-4977. DOI:10.1002/jgrc.20371
D'Asaro E A. 1989. The decay of wind-forced mixed layer inertial oscillations due to the β effect. Journal of Geophysical Research: Oceans, 94(C2): 2045-2056. DOI:10.1029/JC094iC02p02045
Danioux E, Klein P, Rivière P. 2008. Propagation of wind energy into the deep ocean through a fully turbulent mesoscale eddy field. Journal of Physical Oceanography, 38(10): 2224-2241. DOI:10.1175/2008JPO3821.1
Ford R. 1994. Gravity wave radiation from vortex trains in rotating shallow water. Journal of Fluid Mechanics, 281: 81-118. DOI:10.1017/S0022112094003046
Fu L L. 1981. Observations and models of inertial waves in the deep ocean. Reviews of Geophysics, 19(1): 141-170. DOI:10.1029/RG019i001p00141
Gao J, Wang J N, Wang F. 2019. Response of near-inertial shear to wind stress curl and sea level. Scientific Reports, 9(1): 20417. DOI:10.1038/s41598-019-56822-z
Garrett C. 2001. What is the "near-inertial" band and why is it different from the rest of the internal wave spectrum?. Journal of Physical Oceanography, 31(4): 962-971. DOI:10.1175/1520-0485(2001)031<0962:WITNIB>2.0.CO;2
Geisler J E. 1970. Linear theory of the response of a two layer ocean to a moving hurricane. Geophysical Fluid Dynamics, 1(1-2): 249-272. DOI:10.1080/03091927009365774
Gill A E. 1982. Atmosphere-Ocean Dynamics. Academic Press, New York.
Gill A E. 1984. On the behavior of internal waves in the wakes of storms. Journal of Physical Oceanography, 14(7): 1129-1151. DOI:10.1175/1520-0485(1984)014<1129:OTBOIW>2.0.CO;2
Guan S D, Zhao W, Huthnance J, Tian J W, Wang J H. 2014. Observed upper ocean response to typhoon Megi (2010) in the northern South China Sea. Journal of Geophysical Research: Oceans, 119(5): 3134-3157. DOI:10.1002/2013JC009661
Hibiya T, Nagasawa M, Niwa Y. 2002. Nonlinear energy transfer within the oceanic internal wave spectrum at mid and high latitudes. Journal of Geophysical Research: Oceans, 107(C11): 3207. DOI:10.1029/2001JC001210
Hoskins B J, Bretherton F P. 1972. Atmospheric frontogenesis models: mathematical formulation and solution. Journal of the Atmospheric Sciences, 29(1): 11-37. DOI:10.1175/1520-0469(1972)029<0011:AFMMFA>2.0.CO;2
Hou H Q, Yu F, Nan F, Yang B, Guan S D, Zhang Y Z. 2019. Observation of near-inertial oscillations induced by energy transformation during typhoons. Energies, 12(1): 99. DOI:10.3390/en12010099
Hu S J, Liu L L, Guan C, Zhang L L, Wang J N, Wang Q Y, Ma J, Wang F J, Jia F, Feng J Q, Lu X, Wang F, Hu D X. 2020. Dynamic features of near-inertial oscillations in the Northwestern Pacific derived from mooring observations from 2015 to 2018. Journal of Oceanology and Limnology, 38(4): 1092-1107. DOI:10.1007/s00343-020-9332-1
Jaimes B, Shay L K. 2010. Near-inertial wave wake of hurricanes Katrina and Rita over mesoscale oceanic eddies. Journal of Physical Oceanography, 40(6): 1320-1337. DOI:10.1175/2010JPO4309.1
Jochum M, Briegleb B P, Danabasoglu G, Large W G, Norton N J, Jayne S R, Alford M H, Bryan F O. 2013. The impact of oceanic near-inertial waves on climate. Journal of Climate, 26(9): 2833-2844. DOI:10.1175/JCLI-D-12-00181.1
Johnston T M S, Rudnick D L. 2009. Observations of the transition layer. Journal of Physical Oceanography, 39(3): 780-797. DOI:10.1175/2008JPO3824.1
Kim E, Jeon D, Jang C J, Park J H. 2013. Typhoon rammasun-induced near-inertial oscillations observed in the tropical northwestern Pacific Ocean. Terrestrial, Atmospheric and Oceanic Sciences, 24(4): 761-772. DOI:10.3319/TAO.2013.03.28.01(Oc)
Kunze E. 1985. Near-inertial wave propagation in geostrophic shear. Journal of Physical Oceanography, 15(5): 544-565. DOI:10.1175/1520-0485(1985)015<0544:NIWPIG>2.0.CO;2
Liu J L, He Y H, Li J, Cai S Q, Wang D X, Huang Y D. 2018. Cases study of nonlinear interaction between near-inertial waves induced by typhoon and diurnal tides near the Xisha islands. Journal of Geophysical Research: Oceans, 123(4): 2768-2784. DOI:10.1029/2017JC013555
Ma Y G, Zhang S W, Qi Y Q, Jing Z Y. 2019. Upper ocean near-inertial response to the passage of two sequential typhoons in the northwestern South China Sea. Science China Earth Sciences, 62(5): 863-871. DOI:10.1007/s11430-018-9292-3
MacKinnon J A, Alford M H, Sun O, Pinkel R, Zhao Z X, Klymak J. 2013. Parametric subharmonic instability of the internal tide at 29°N. Journal of Physical Oceanography, 43(1): 17-28. DOI:10.1175/JPO-D-11-0108.1
MacKinnon J A, Gregg M C. 2003. Shear and baroclinic energy flux on the summer new England shelf. Journal of Physical Oceanography, 33(7): 1462-1475. DOI:10.1175/1520-0485(2003)033<1462:SABEFO>2.0.CO;2
Munk W, Wunsch C. 1998. Abyssal recipes Ⅱ: energetics of tidal and wind mixing. Deep Sea Research Part Ⅰ Oceanographic Research Papers, 45(12): 1977-2010. DOI:10.1016/S0967-0637(98)00070-3
Nikurashin M, Ferrari R. 2010. Radiation and dissipation of internal waves generated by geostrophic motions impinging on small-scale topography: theory. Journal of Physical Oceanography, 40(5): 1055-1074. DOI:10.1175/2009JPO4199.1
Pollard R T, Millard R CJr. 1970. Comparison between observed and simulated wind-generated inertial oscillations. Deep Sea Research and Oceanographic Abstracts, 17(4): 813–816, IN5, 817–821, https://doi.org/10.1016/0011-7471(70)90043-4.
Pollard R T. 1980. Properties of near-surface inertial oscillations. Journal of Physical Oceanography, 10(3): 385-398. DOI:10.1175/1520-0485(1980)010<0385:PONSIO>2.0.CO;2
Price J F. 1983. Internal wave wake of a moving storm. Part I. scales, energy budget and observations. Journal of Physical Oceanography, 13(6): 949-965. DOI:10.1175/1520-0485(1983)013<0949:IWWOAM>2.0.CO;2
Saha S, Moorthi S, Wu X R, Wang J D, Nadiga S, Tripp P, Behringer D, Hou Y T, Chuang H Y, Iredell M, Ek M, Meng J, Yang R Q, Mendez M P, van den Dool H, Zhang Q, Wang W Q, Chen M Y, Becker E. 2014. The NCEP climate forecast system version 2. Journal of Climate, 27(6): 2185-2208. DOI:10.1175/JCLI-D-12-00823.1
Shay L K, Elsberry R L. 1987. Near-inertial ocean current response to hurricane Frederic. Journal of Physical Oceanography, 17(8): 1249-1269. DOI:10.1175/1520-0485(1987)017<1249:NIOCRT>2.0.CO;2
Silverthorne K E, Toole J M. 2009. Seasonal kinetic energy variability of near-inertial motions. Journal of Physical Oceanography, 39(4): 1035-1049. DOI:10.1175/2008JPO3920.1
Sun Z Y, Hu J Y, Zheng Q A, Gan J P. 2015. Comparison of typhoon-induced near-inertial oscillations in shear flow in the northern South China Sea. Acta Oceanologica Sinica, 34(11): 38-45. DOI:10.1007/s13131-015-0746-0
Wang G L, Li D W, Wei Z X, Li S J, Wang Y G, Xu T F. 2019. Observed near inertial waves in the wake of typhoon Linfa (2015) in the northern South China Sea. Journal of Ocean University of China, 18(5): 1013-1021. DOI:10.1007/s11802-019-4081-5
Webster P J, Holland G J, Curry J A, Chang H R. 2005. Changes in tropical cyclone number, duration, and intensity in a warming environment. Science, 309(5742): 1844-1846. DOI:10.1126/science.1116448
Xie X H, Chen G Y, Shang X D, Fang W D. 2008. Evolution of the semidiurnal (M2) internal tide on the continental slope of the northern South China Sea. Geophysical Research Letters, 35(13): L13604. DOI:10.1029/2008GL034179
Xie X H, Shang X D, Chen G Y, Sun L. 2009. Variations of diurnal and inertial spectral peaks near the bi-diurnal critical latitude. Geophysical Research Letters, 36(2): L02606. DOI:10.1029/2008GL036383
Xie X H, Shang X D, van Haren H, Chen G Y, Zhang Y Z. 2011. Observations of parametric subharmonic instability, induced near-inertial waves equatorward of the critical diurnal latitude. Geophysical Research Letters, 38(5): L05603. DOI:10.1029/2010GL046521
Yang B, Hou Y J. 2014. Near-inertial waves in the wake of 2011 Typhoon Nesat in the northern South China Sea. Acta Oceanologica Sinica, 33(11): 102-111. DOI:10.1007/s13131-014-0559-6
Yang B, Hou Y J, Hu P, Liu Z, Liu Y H. 2015. Shallow ocean response to tropical cyclones observed on the continental shelf of the northwestern South China Sea. Journal of Geophysical Research: Oceans, 120(5): 3817-3836. DOI:10.1002/2015JC010783
Zervakis V, Levine M D. 1995. Near-inertial energy propagation from the mixed layer: theoretical considerations. Journal of Physical Oceanography, 25(11): 2872-2889. DOI:10.1175/1520-0485(1995)025<2872:NIEPFT>2.0.CO;2
Zhai X M, Greatbatch R J, Eden C, Hibiya T. 2009. On the loss of wind-induced near-inertial energy to turbulent mixing in the upper ocean. Journal of Physical Oceanography, 39(11): 3040-3045. DOI:10.1175/2009JPO4259.1