The near-inertial waves observed east of the Philippines*

Shengming YUAN , Xiaomei YAN , Linlin ZHANG , Bing YANG ,Chongguang PANG , Dunxin HU

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 conf ined 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.

Keyword: near-inertial wave (NIW); generation mechanism; dynamic characteristic

1 INTRODUCTION

The wave frequencyωof internal waves in the ocean is between the inertial frequencyfand the buoyancy frequencyN(Garrett, 2001; Alford et al.,2016). Near-inertial waves (NIWs) have a frequency near the local Coriolis frequencyf, wheref=2 Ω sinθ,Ω is the angular speed of the Earth’s rotation, andθis 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 aff ect 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 nearinertial 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 (ω1andω2) waves is usually close to half the forcing frequency (ω0). It has been verif ied by in-situ observations that PSI is eff ective 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 aff ecting seabed topography (Nikurashin and Ferrari, 2010).NIWs can also be spontaneously generated by largescale stress instability (Hoskins and Bretherton, 1972)and radiation by time-dependent instabilities of lowfrequency 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 diff erent 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 diff erences in diff erent 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 Pacif ic, Hou et al. (2019) observed maximum nearinertial 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 Pacif ic 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 Pacif ic, intense TCs are frequently formed (Webster et al., 2005). The annualmean power input from the wind to near-inertial motions in the North Pacif ic 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 Pacif ic 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 Pacif ic 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 Pacif ic which could signif icantly aff ect 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 typhooninduced 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 diff erences between diff erent NIW events generated by various mechanisms remain unclear, especially in the Northwestern Pacif ic. 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 diff erent origins in the Northwestern Pacif ic. 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.

Fig.1 The six-hourly tracks of typhoon Lan (colored solid curves) and Nock-ten (colored dashed curves)

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 Prof iler (ACDP) were equipped on the main f loat at a depth of 400 m. The ADCP was conf igured 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 f irst 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.2c-e). Therefore, although the nearinertial 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.

The near-inertial horizontal velocity (ui,vi) were obtained by a band-pass f ilter 0.8f0-1.2f0(Liu et al.,2018; Hu et al., 2020), wheref0is the local Coriolis frequency. The NIKE was calculated by

whereρ0=1 024 kg/m3is 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 def ined as the depth where the temperature is 0.5 °C 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.

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 f ield (blue line) (b); time evolutions of the zonal component of the near-inertial velocities during three NIW events (c-e)

3 METHOD

3.1 Pollard-Millard slab model

The slab model developed by Pollard and Millard(1970) has been widely used to simulate the nearinertial 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:

whereuandvare the zonal and meridional components of the near-inertial velocity in the ML, respectively,τxandτyare the zonal and meridional components of the wind stress, respectively,f0is the local Coriolis frequency,ρ0=1 024 kg/m3is the water density,tis the time. The mixed layer depthHdef ined as the depth where the temperature is 0.5 °C lower than that at the surface, was calculated with the HYCOM reanalysis outputs. The damping coeffi cientrwas set to be 0.15f0according to Alford (2001). Correspondingly, the work done by the wind on the near-inertial wave f ield was calculated as

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 specif ic vertical structure with similar behaviors in the horizontal direction and in time to a homogeneous f luid with a free surface.The normal mode equation of the internal gravity waves is written as

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

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

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 def ined as i

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

4 RESULT

We f irst 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 f ive events exceeding one standard deviation from the mean. The three strongest ones I, Ⅱ, and Ⅲemerged 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.Therefore, the three events are representative with diff erent generation mechanisms and are examined in detail in this study.

Table 1 Basic characteristics of the NIWs in three events

Table 2 Basic characteristics of the typhoon

Fig.3 Thewindvelocity(arrows)and thelogarithmofwind-induced NIKE calculated with the slab model (color shading,unit: J/m3) inthestudy areafromOct.16-21,2017

4.1 NIW Event I

4.1.1 Generation mechanism

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/ f 0 (d) from Oct. 10 to Nov. 8, 2017

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 def ined 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 prof ile, 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 def ined by Eq.11, and the results are summarized in Table 1.

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 intensif ied in the mixed layer with a maximum value of 63.1 J/m3at 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/m3on Oct. 25, 2017, and then gradually decreased. On Oct. 30, 2017, it decreased to 1/eof the maximum NIKE. Thus, thee-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.5 Power spectra of the zonal (a) and meridional (b) current components

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 f low would modify the frequency of the NIWs:fe=f0+ζ/2, wherefeis the eff ective Coriolis frequency andζis the background vorticity. As shown in Fig.4d, during this NIW event, theζcalculated 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 frequencyfp(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 (ζgAVISO), HYCOM simulated sea surface height (ζgHYCOM), and velocity (ζHYCOM). It was found that in the vertical, the magnitude ofζHYCOMgenerally decreases with depth. In spite of that, the vertically averagedζHYCOMin the upper 0-400 m is consistent with theζgHYCOM(f igure not shown).Therefore, the surface geostrophic vorticityζcan well represent the mean vorticity in the upper ocean and the frequency blueshift phenomenon we noticed above can be attributed to the background vorticity.

4.1.3 Vertical structure

The empirical orthogonal function (EOF) analysis method can decompose the time series of a physical f ield 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 nearinertial current during Oct. 10 to Nov. 10, 2017 was also analyzed with this methodology, and the results are shown in Fig.6. The f irst two modes dominate the NIWs and contribute 59.9% and 16.6% of the variance, respectively. The f irst mode presents an antiphase feature in the vertical direction with a node at 90-m depth, meaning that it is the f irst baroclinic mode. Although the second mode is much weaker than that of the f irst 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 prof iles (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 f irst two EOF modes

4.2 NIW Event Ⅱ

The NIW Event Ⅱ occurred between December 2016 and January 2017. Figure 2c shows the nearinertial 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 nearinertial 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, diff erent from the surface-intensif ication of NIWs observed during typhoon Lan, the nearinertial 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 Ⅱwas 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 twoe-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 modelsimulated 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 typhoongenerated 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 nearinertial 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 conf irm 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/m 3) in the study area from Dec. 21, 2016 to Jan. 9, 2017

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

Fig.9 Time evolutions of the NIKE (a), the near-inertial shear (b), and the ζ/ f 0 (c) from Dec. 23, 2016 to Jan. 31, 2017

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.

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 f irst f ifteen baroclinic modes (n=1, 2, ···, and 15). The vertical distribution of the combination of these f ifteen 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 f itted. Furthermore, it can be seen that above 70 m, the f irst 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 4-8thmodes. Using the EOF decomposition method, similar results were obtained (f igure not shown). The contribution rate of the f irst EOF mode is only 48.3%, much smaller than that in the f irst 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.

Fig.10 The time-averaged NIKE for the f irst f ifteen baroclinic modes (a) and comparisons between the combination of these f ifteen modes (black line) and the observed NIKE (red line) averaged from Jan. 1-31, 2017 (b)

As indicated by Alford et al. (2016), for small vertical-wavelength motions with large wavenumberkz, the vertical group velocity becomes slow. The vertical wavenumberkzis proportional to the mode numbern, and hence a largernwill 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 eff ective Coriolis frequency, which increases the resistance for wave propagation. Hence, the existence of the cyclonic eddy during this event may also make it diffi cult for the NIKE to be transmitted downward. Furthermore,similar to the f irst 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.

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

Note that the upward NIW trajectories appear in the highRregion, 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 largerRassociated with smaller buoyancy frequencyNand stronger vertical shear of horizontal currents would lead to unusual upward propagating NIWs, in good agreement with Chen et al. (2013).

We also verif ied the NIW trajectories at diff erent 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.

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 above results indicate the NIWs in the surface and subsurface layers were generated by diff erent 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 conf irmed 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 D1internal tides. Moreover, there is no signif icant peak in the D1-ffrequency 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 diff erent characteristics from the NIW Events I and Ⅱas 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 -3×10-7to 3×10-7N/m3(Fig.12c). Therefore, the deep penetration of the near-inertial shear can be attributed to the positive SLA and weak wind stress curls.

The particular vertical structure of the NIWs in this case was further examined with the EOF method. As shown in Fig.14, the f irst and second EOF modes change four and three times of signs between depths of 50 and 400 m, respectively. Clearly, the f irst two dominant modes are high vertical baroclinic modes and contribute 45.6% and 31.6% of the variance,respectively. The amplitude of the f irst 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 f irst 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.13 Spatial distributions of the sea level anomalies and geostrophic currents at 3-day intervals during Apr. 13-22, 2017

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 D1-ffrequency. In addition, it shows that during Mar.2-31, 2017, the motion is dominated by the D2tides and the near-inertial signals are weaker. During Apr.1-30, 2017, the near-inertial motions were strengthened signif icantly and the (D2±f) wave currents occurred (Fig.15b). The vertical distributions of the band-pass f iltered motions in the frequency bands of ([0.8-1.2]f), ([0.9-1.1]D2), ([0.93-1.08]D2-f), and ([0.94-1.15]D2+f) are further shown in Fig.16.The kinetic energy of the D2±fwave increased sharply between depths of 100 and 200 m during Apr. 7-25,2017 (Fig.16c-d), consistent with the occurrence of strong NIKE in this event (Fig.16b). Moreover, the kinetic energy of D2internal tides was also evident at this time and depths (Fig.16a). The correlation coeffi cients between the near-inertialfand D2-f, D2and D2-f, near-inertialfand D2+f, D2and D2+f, and near-inertialfand D2kinetic energy are 0.69, 0.33,0.37, 0.23, and -0.01, respectively, all of which exceed the 95% signif icance level except for that betweenfand D2waves. The results indicate that D2±fwaves have a stronger dependence on near-inertial processes.In addition, during Apr. 1-30, 2017, the bicoherence values of the [f, D2-f] and [f, D2+f] frequencies are signif icant 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.15c-e).All the above results indicate that there was a nonlinear wave-wave interaction between NIWs and D2tides, which further induced strong D2±fwaves.

Fig.14 Vertical prof iles (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 f irst two EOF modes

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 diff erent mechanisms were captured at this single mooring station, which is of great signif icance for the study of the characteristic diff erences of the NIWs. Among the three events, the f irst 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 verif ied 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 diff erent 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 aff ecting 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.

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, D2- f] (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)

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 f irst two EOF modes of the near-inertial currents were dominated by high baroclinic modes, also diff erent 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 D2tides,which further induced strong D2±fwaves.

The three NIW events hade-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 Pacif ic. 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 f lux is much less than the downward energy f lux. 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

Fig.16 Kinetic energy of D 2 internal tides (a), near-inertial motions (b), D 2-f waves (c), and D 2+ f waves (d)

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 Pacif ic.

6 DATA AVAILABILITY STATEMENT

The mooring ADCP data were provided by the Northwestern Pacif ic 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/.