Two subsurface moorings were deployed in the Northwest Pacific east of Taiwan from August 2019 to December 2020 ( Figure 1 ), and each mooring was equipped with two 75 kHz Teledyne RDI acoustic Doppler current profilers (ADCPs). The details of the mooring deployments are listed in Table 1 . After pre-processing (including depth correction, quality control, etc.), the velocity data are interpolated onto standard layers with intervals of 5 m. Depending on the depth of propagation of the near-inertial events of interest in this paper, data from 50 to 800 m were used primarily for the follow-up study.

Typhoon MITAG formed as a tropical depression near 13.0°N, 138.9°E in the morning of 27 September 2019 and then moved northwest with a maximum wind speed of ~13 m/s. Then, MITAG entered the sea area east of Taiwan at 08:00 on 30 September while changing its direction to the north, and strong winds (wind speed exceeding 15 m/s) began to affect the observation points. On 30 September, MITAG passed between the two moorings, and the path of the typhoon center was closer to C06 ( Figure 1 ). After passing the moorings, MITAG made landfall in mainland China on 1 October. The typhoon best track data were downloaded from The Regional Specialized Meteorological Center (RSMC) Tokyo-Typhoon center (http://www.jma.go.jp/jma/jma-eng/jmacenter/rsmc-hp-pub-eg/RSMC_HP.htm).

A Butterworth bandpass filter was applied to obtain the near-inertial horizontal velocity (u,v). The frequency band of 0.9–1.12f (f is the local Coriolis parameter) was selected according to the results of power spectrum analysis ( Figure S1 ). Then, NIKE was calculated as:

where ρ ₀ is the average density of seawater (1.025×10³ kg/m³). Estimates of background flow are derived by applying a low-pass filter of 10 days to the original velocity records to remove the influences of tides and mesoscale eddies.

The altimeter product used in this paper is the sea level anomaly (SLA) and geostrophic velocity anomaly data provided by Ssalto/Duacs, which is distributed in real time through the Copernicus Marine and Environment Monitoring Service (CMEMS). These data are utilized to resolve the range of anticyclonic eddies and to calculate sea surface vorticity. The dataset has a spatial resolution of 0.25°×0.25° and a temporal resolution of 1 d and is widely used in NIWs and mesoscale eddy-related studies.

To calculate the wind energy flux input to the mixed layer during the transit of MITAG, the slab model (Pollard and Millard, 1970) and 10 m wind were adopted in this study. The wind data were derived from the European center for Medium-Range Weather Forecasts (ECMWF) global reanalysis ERA5 product, and its temporal and spatial resolutions are 1 h and 0.25°×0.25° (https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels?tab=form). The 10 m wind was first converted into wind stress. Then, the corresponding flow velocity in the mixed layer can be calculated as follows:

where Z are the velocities of the meridional and zonal flows in the mixed layer, τ is wind stress, f is the local Coriolis parameter, H is the mixed layer depth and r is the damping coefficient of inertial motions. The flow in the mixed layer can be expressed as the sum of the Ekman component and the near-inertial component. Alford (Alford, 2003) refined the model by applying a Fourier transform to the wind stress, resulting in the solution of Equation (2) as:

The Ekman component is:

Then, the inertial component is R_I = R + R_E , and finally, the wind-generated near-inertial energy flux is obtained by inversion of the Fourier transform.

NIWs can be represented by the superposition of multiple discrete baroclinic modes in the ocean interior (Gill, 1982; D’Asaro et al., 1995). The vertical structure of each mode is governed by (Gill, 1982; Thorpe and Jiang, 1998):

where n is the mode number, c_n is the separation constant (eigenvalue), H is the water depth, and Φ _n denotes the eigenfunction and represents the baroclinic mode structure of vertical undulations and vertical flow. The buoyancy frequency N can be expressed as follows:

where g is the acceleration of gravity. The baroclinic mode structure of the horizontal flow can be obtained according to two equations:

Thus, the baroclinic flow for each mode can be expressed in terms of the vertical structure and time variation:

where u(z,t) is the near-inertial velocity and u_n (t) is the velocity of mode n. In this paper, mode decomposition of near-inertial velocities from moorings and Hybrid Coordinate Ocean Model (HYCOM) data was carried out separately to investigate the dynamic structure. The version of the HYCOM data was GLBy0.08 with a temporal resolution of 3 h and a spatial resolution of 0.08° lon × 0.04° lat and was divided vertically into 40 layers, which clearly reveal the energy propagation characteristics of NIWs (https://www.hycom.org/dataserver/gofs-3pt1/analysis). Considering the lack of temperature and salinity observations at the mooring sites and to facilitate calculations, the averages of HYCOM temperature and salinity during the duration of NIWs generated by MITAG were used to compute N ²(z).

First, the input of wind energy is explored. The near-inertial energy flux in the mixed layer calculated from the slab model is shown in Figure 4 . Before and after the passage of MITAG, the wind field east of Taiwan was relatively stable, bringing no significant near-inertial energy flux. Between 6:00 and 18:00 on 29 September, the near-inertial energy flux was mainly caused by winds from the northwest of the typhoon center. Then, MITAG fed a large amount of near-inertial energy into the Kuroshio on the west side of its path and into the area near mooring C08 on the east side. After 6:00 pm on 30 September, MITAG gradually weakened along with the reduction in energy flux and then left the sea area east of Taiwan. As the main source of this near-inertial event, MITAG generates a strong energy flux mainly in the region west of 126°E, which corresponds well with the spatial distribution of NIKE in Section 4.2.

Mooring C06 is located on the path of the typhoon center, while C08 is on the right side. In the Northern Hemisphere, the wind stress above the mooring on the right side of the TC’s path was deflected clockwise due to the movement of the TC, leading to strong NIWs (Kim et al., 2013; Chen et al., 2015). The results of the slab model illustrate that there was more energy input to the near-inertial band at C08 with a flux maximum of 0.98 W/m² compared to 0.47 W/m² at C06. This could explain the difference in the amount of NIKE contained in the upper layer at the two moorings. However, sea surface winds cannot directly affect the propagation of NIWs in the ocean interior, and it was not the fundamental cause of the disparity in propagation.

The near-inertial flow was extracted by bandpass filtering of the original HYCOM velocity data, and then the time evolution of NIKE at different depths was obtained, as shown in Figures 5 , 6 . The 50/100/200 m, 400 m and 800 m were chosen to represent the distribution of NIKE in the upper, middle and deep layers, respectively. Additionally, the edge of the anticyclonic eddy was represented by the closed SLA contour of the outermost circle of the eddy center (Chelton et al., 2011). Before the arrival of MITAG ( Figure 5 , 26 September), NIKE east of Taiwan was very weak, existing only at the south edge of the eddy. As MITAG approached, powerful NIKE was quickly excited along the typhoon’s path in the upper layer. NIKE reached the maximum value and was most widespread at 50 m on 4 October. At this time, the NIWs had propagated to 400 m. Then, NIKE at 50 m faded away due to dissipation and downwards propagation. NIKE at 100 m and 200 m split into two parts: one at the west edge of the eddy and limited within the eddy, and the other rapidly dissipating near mooring C06, which completely disappeared by 12 October ( Figure 6 ).

Influenced by anticyclone eddies, NIWs may be horizontally trapped and thus confined in the eddy, or may propagate outwards after encountering seawater with a higher f_eff than the intrinsic frequency (Kunze, 1985). As NIWs enter the anticyclone eddy, a portion of the energy is reflected and then propagates westward. Therefore, NIKE at 400 m gradually accumulated and intensified on the west edge of the eddy before October 9. The other part of the energy is captured and propagated downward, but remains biased towards the west periphery of the eddy at 400 m and 800 m. This is related to the location of the near-inertial energy source and the vertical structure of the anticyclone eddy. The vertical structure of the eddy may be asymmetric, with the center gradually shifting westwards with increasing depth, like a lens-shaped eddy (Lin et al., 2015). In the deep layer, NIKE was only enhanced two weeks after the passage of MITAG and initially only occurred inside the eddy. The NIKE at 800 m was not fully dissipated until 24 October. This near-inertial event lasted for more than 3 weeks.

These results suggest that Typhoon MITAG can rapidly generate widespread NIWs near its path in the upper layer and that these NIWs tend to propagate downwards and accumulate in areas of negative vorticity. The time taken for NIWs to propagate to 200 m was approximately 3 days and to 400 m was 6 days. Under the mixed layer, the NIWs outside the anticyclonic eddy did not cross the thermocline and dissipated within a week, while NIWs inside the eddy gradually moved towards the center of the eddy and reached 800 m 12 days after the typhoon’s passage. The anticyclonic eddy significantly prolonged the duration of NIWs and facilitated the propagation of NIWs to the deep sea. This was also the main reason for the large disparity between the observations of the two moorings.

In addition, the near-inertial energy flux ( Figure 4 ) showed strong energy input to the Kuroshio east of Taiwan, but there was no significant enhancement of NIKE under 50 m west of 122.5°E. According to Jeon (Jeon et al., 2019), after the typhoon’s passage, strong NIKE existed upstream of the Kuroshio east of Taiwan at 4 m, but at 100 m, NIKE began to appear only north of 25°N. Therefore, this phenomenon may be due to advection of the upstream Kuroshio, with NIWs being carried poleward before propagating downwards.

Figure 7 illustrates the e-folding time of depth-integrated NIKE to better understand the damping of MITAG-generated NIWs. Except for the Kuroshio on the northeast side of Taiwan, the e-folding scale along MITAG’s path was below 5 days. High e-folding time areas were located inside the anticyclonic eddy and along its southwestern edge. The latter was largely distributed along the SLA contours and ranged from 2 to 3 weeks. With reference to the spatial distribution of NIKE ( Figures 5 , 6 ), it is clear that the high values south of 21°N may be due to the persistence of weak near-inertial energy (less than 0.2×10^-8 J/m²).

Moorings C06 and C08 can represent different situations in and outside the eddy, and their time series are shown in Figure 7B . To the right side of MITAG’s path, the NIKE peaked more quickly and gained more energy at C08, leading to an earlier start of e-fording time. At the same time, the dissipation at C08 was slower with a smaller rate of the time series in the eddy, and there was a small increase in energy from 8 October, which then started to decay again, leading to a later end of the e-folding time. As a result, the e-folding scales at the two moorings differed significantly, with time at C06 outside the eddy less than 1 week and time at C08 in the eddy more than 2 weeks. The time series at C06 first decayed close to zero and then reached a second peak on approximately 18 October, which corresponds to the deeper weaker NIKE in Figure 2B . The reasons for this phenomenon are explored in detail in Section 5.2.

To investigate the characteristics of the vertical propagation of this near-inertial event, the near-inertial vertical energy flux (F_E) was calculated for the main area where MITAG generated NIKE. The calculation of F_E can be obtained by (Nash et al., 2005):

where C_gz is the vertical group velocity and E is the near-inertial energy. To simplify the calculation, the mean value of C_gz of moorings C06 and C08 was substituted into Equation (10). C_gz can be estimated by identifying the downwards progression of kinetic energy maxima over time (Yu et al., 2022), resulting in 7.53 m/d at C06 and 38.82 m/d at C08. The time-averaged (from 30 September to 24 October) SLA was used to determine the edge of the eddy ( Figure 8 black solid line) and then the F_E outside and in the eddy was calculated, as shown in Figures 8A, B . The F_E in the eddy is an order of magnitude higher than that outside the eddy. Before October 10, the F_E in and outside the eddy both gradually extended deeper, but the speed was faster in the eddy. The F_E outside the eddy was on the order of 10^-4 under 500 m, which was essentially negligible. The downwards transmission of these NIWs was very weak, probably due to the viscous effect of seawater, and less efficient than that occurring in the anticyclonic eddy. After 10 October, the F_E outside the eddy had completely decayed, while the F_E in the eddy formed two high value areas bounded by 300 m.

As shown in Figure 8C , the mean near-inertial F_E generated by Typhoon MITAG decayed rapidly in the mixed layer, and the rate of damping decreased below the thermocline. Thirty-five percent of the energy crossed the thermocline, but at 800 m, only 12.8% of the F_E remains. The time-averaged F_E in the anticyclonic eddy after 10 October is shown in Figure 8D . There were two significant peaks in the changing curve of F_E, with the shallower one at 140 m. This corresponds to the peak in time-averaged buoyancy frequency (N²) at approximately 140 m ( Figure 8E ). The amplitude, energy and vertical wavenumber of NIWs were constantly adjusted due to the refraction of different stratifications. Therefore, the effect of N² on NIWs may be largely responsible for the shallow peak of F_E. Theory, models and observations all suggest that NIWs encounter a critical layer in the vertical direction when captured by anticyclonic eddies (Kunze, 1985; Lee and Niiler, 1998; Zhai et al., 2005; Lelong et al., 2020). The F_E curve weakens from the first peak to 300 m and then begins to strengthen again, reaching the second peak at 500 m. This reveals that the critical layer is approximately 500 m and that the F_E near the critical layer is significantly higher than the regional averaged results in Figure 8C .

For results averaged over the main area, most of the NIKE remains above the thermocline, and the anticyclonic eddy does not observably increase the proportion of NIKE propagating from the thermocline to the deeper layers. Nevertheless, NIKE propagating through the thermocline is found to occur predominantly in the anticyclonic eddy, leading to enhancement of F_E from 400 to 600 m. The transfer of NIWs from outside the eddy to the deep layer is minimal. Therefore, anticyclonic eddies play a crucial role in the transfer of more near-inertial energy to the deep ocean.

Theoretical analysis and numerical models indicate that the mean flow absorbs most of the wave energy in the critical layer (Thorpe, 1981; Altman, 1988). To investigate the process of energy release in the anticyclonic eddy, we calculated the background flow kinetic energy (KE) outside and in the eddy ( Figure 9 ). Before the passage of typhoon MITAG, the KE in the eddy was significantly lower than that outside the eddy, but they both showed a tendency to decrease. The decay rate of KE outside the eddy decreased after the typhoon’s passage, and KE remained largely unchanged from October 5. While KE in the eddy was converted from decay to increase, the background flow KE was enhanced from 50 m to 800 m. It does not take long for the KE in the anticyclonic eddy to exceed that before the arrival of MITAG, and it was even higher than the KE outside the eddy after 10 October. The biggest difference in these two regions, in and outside the eddy, after the passage of MITAG is the near-inertial energy flux. Combined with the results in Section 4.4, it can be illustrated that the downwards propagation of NIWs leads to the enhancement of the background flow KE. Osborn states that although 80% of the internal wave energy will be dissipated by turbulence, some of them will modulate the background flow (Osborn, 1980). Because of the low vertical resolution of the HYCOM data, we were unable to explore in detail the turbulent dissipation and could not obtain the proportion of energy transferred from NIWs to the background flow. However, this result is sufficient to confirm the existence of an inverse energy cascade between NIWs and background flow energy in the anticyclonic eddy, which has important implications for the study of the energy source of deep-sea mixing. At present, various models simulate results for deep sea circulation that are smaller than those actually observed. The propagation of NIWs to the deep sea and the increase in background flow kinetic energy in anticyclonic eddies are worthy of attention.

Decompose the near-inertial currents of HYCOM into vertical modes from 0 to 800 m, and perform a depth integration for different modes ( Figures 10 , 11 ). Examples of applying this method to the range from the surface to the maximum depth that NIWs can reach were common in previous work (Chen et al., 2013; Hou et al., 2019; Huang et al., 2021), so the range of 0-800 m selected for this study is fairly reasonable.

Calculations show that the initial widespread distribution of NIKE generated by MITAG was dominated by the first two modes. They fully dissipated after 12 October and existed for two weeks. The energy of the third mode mainly gathered to the south of mooring C06 until 12 October, and as the first two modes dissipated, the third mode formed more energy near mooring C08. Both the third mode and the sum of the higher modes (modes from 4 to 20, ∑4-20) split into two parts inside and outside the eddy. The energy south of C06 rapidly dissipated, while the energy inside the eddy was gradually enhanced. Eventually, the energy of ∑4-20 disappeared completely on 24 October. The mode structure indicates that the energy captured by the anticyclonic eddy is composed mainly of higher modes. In the absence of the anticyclonic eddy, referring to NIWs near C06, energy is rapidly transferred to the third mode and ∑4-20 and is completely dissipated in the case that the third mode contains the most energy. However, under the influence of the eddy, the energy of the higher modes continues to increase and exceeds that of the first three modes. This phenomenon can be maintained for more than one week.

The vertical distribution of energy for each mode was also explored ( Figures S3 - S6 ). NIKE of the third mode is stronger at 50 m, 200 m and 800 m and is concentrated on the western edge of the mesoscale eddy. The NIKE of ∑4-20 started to appear at 800 m on 3 October and then gradually intensified. Therefore, NIKE at 800 m consists mainly of the third mode and ∑4-20. Compared to mode 3 at 800 m, the core of ∑4-20 is closer to the center of the eddy and is composed of NIWs captured by the eddy (Buhler and McIntyre, 2005). Several previous investigations have recognized that the evolution of a eddy consists of three different stages. In the second stage, the eddy loses energy through the excitation of internal waves (Liao et al., 2019). Thus the high value of the third mode at 800 m may be related to the energy dissipation of the mesoscale eddies during their evolution.

The NIKE from both mooring and HYCOM data at C06 consists of two parts: one is directly generated by typhoon MITAG and dissipates above 400 m, and the other below 400 m only starts to strengthen after 12 October. To find the source of the second part, Figure 12A illustrates the depth-integrated NIKE along the zonal section of moorings (22.4°N). The NIKE east of 123.5°E is coherent over time and appeared before the energy at C06. This is because typhoon MITAG initially formed east of 123.5°E, and this region was always located to the right side of the typhoon center. This part of the NIKE showed a tendency to propagate westwards from 10 October. The typhoon-generated NIKE at C06 was weaker and decayed on approximately 10 October. Subsequently, the westwards propagating NIKE east of 123.5°E reached and formed the second part of the NIKE at C06.

The results of the dynamic mode decomposition ( Figure 12B ) indicate that the first part of the energy at C06 from October 6 to October 10 was dominated by ∑4-20. At C08, NIKE before 10 October consisted mainly of the first two modes, then mode 3 and ∑4-20 gradually account for the major contribution. The main component of the westwards propagating energy is ∑4-20, revealed a westwards transfer of mixing and dissipation. It is estimated that the duration of propagation along 22.4°N was from 10 October to 20 October, with a distance of approximately 92.63 km. Therefore, the zonal energy movement speed on average is u_NIW = -0.107 m/s (negative sign represents westwards flow). The zonal component of depth-averaged background flow at the eddy’s edge is u = -0.104m/s, almost the same speed as u_NIW . Thus, the energy source for the second part at C06 was the typhoon-generated NIKE east of 123.5°E, which advected westwards by the background flow.