*4.2. Effects of Surface Wind Forcing on Near-Inertial Energy within and below the Mixed Layer*

The NIWs within the mixed layer can be easily amplified by the changes in the local wind stress; however, the wind-induced NIWs within or just below the mixed layer may dissipate mostly (up to 70–85%) in the upper 200 m [61–63], and hardly penetrate far below the MLD to 400 m depth, accounting for significantly different nonseasonal variations in the *KENIW\_obs* at 400 m of the EC1 (VARNIW\_obs\_int) compared to those in *KENIW\_model*, within the mixed layer simulated by the damped slab model using local wind stress (VARNIW\_model\_int). Positive anomalies of VARNIW\_model\_int exceeding <sup>σ</sup> <sup>+</sup> <sup>µ</sup> ( <sup>∼</sup> 2.5 <sup>×</sup> <sup>10</sup><sup>3</sup> J <sup>2</sup>/m<sup>6</sup> ) were not found during the events of period high, although they were clearly accompanied by relatively high Π values during H2 and H5 (Figures 7 and 8). Indeed, periods of very high VARNIW\_model\_int (19 August 2004 and 3 September 2020) exceeding 1.0 <sup>×</sup> <sup>10</sup><sup>4</sup> J <sup>2</sup>/m<sup>6</sup> in association with the passage of typhoons (Figure 2) corresponded to period neutral events indicative of only moderate VARNIW\_obs\_int. In general, VARNIW\_model\_int was low (less than 2.0 <sup>×</sup> <sup>10</sup><sup>3</sup> J <sup>2</sup>/m<sup>6</sup> ) when Π decreased during period low. Significant dissipation of wind-induced NIWs may be confirmed around August 2004 (period neutral, green triangle in Figure 8); for example, the case when the *KENIW\_obs* of 1.12 <sup>×</sup> <sup>10</sup><sup>2</sup> J/m<sup>3</sup> observed at 400 m (corresponding to the square root of peak VARNIW\_obs\_int of 1.26 <sup>×</sup> <sup>10</sup><sup>4</sup> J <sup>2</sup>/m<sup>6</sup> ) explained only 9.6% of the *KENIW\_model* of ~11.68 <sup>×</sup> <sup>10</sup><sup>2</sup> J/m<sup>3</sup> within the mixed layer, supporting the deduction or strong dissipation of NIWs in the upper 200 m [62,63].

Because the surface wind stress is not uniform, equatorward- and downward-propagating NIWs generated by strong wind forcing in the north of EC1, despite the weak local wind forcing, may propagate down to 400 m of EC1, accounting for the high VARNIW\_obs\_int without a significant VARNIW\_model\_int (except H2 and H5). However, this possibility can be ruled out, as the intraseasonal variance in the kinetic energy of NIWs originating from higher latitudes (forced by wind stress at 38–40◦ N along the 131◦ E), propagating below the mixed layer to 400 m (of EC1; Figure 10), was not markedly different from VARNIW\_model\_int, nor did it correlate with VARNIW\_obs\_int (Figure 8e). deduction or strong dissipation of NIWs in the upper 200 m [62,63]. Because the surface wind stress is not uniform, equatorward- and downward-propagating NIWs generated by strong wind forcing in the north of EC1, despite the weak local wind forcing, may propagate down to 400 m of EC1, accounting for the high VAR-NIW\_obs\_int without a significant VARNIW\_model\_int (except H2 and H5). However, this possibility can be ruled out, as the intraseasonal variance in the kinetic energy of NIWs originating from higher latitudes (forced by wind stress at 38–40° N along the 131° E), propagating below the mixed layer to 400 m (of EC1; Figure 10), was not markedly different from VAR-NIW\_model\_int, nor did it correlate with VARNIW\_obs\_int (Figure 8e).

induced NIWs may be confirmed around August 2004 (period neutral, green triangle in

J/m<sup>3</sup> observed at 400 m

<sup>2</sup>/m6) explained

J

J/m<sup>3</sup> within the mixed layer, supporting the

*J. Mar. Sci. Eng.* **2022**, *10*, x FOR PEER REVIEW 15 of 20

only 9.6% of the KENIW\_model of ~11.68 × 10<sup>ଶ</sup>

Figure 8); for example, the case when the KENIW\_obs of 1.12 × 10<sup>ଶ</sup>

(corresponding to the square root of peak VARNIW\_obs\_int of 1.26 × 10<sup>ସ</sup>

**Figure 10.** Ray path of near-inertial internal waves (NIWs) (thick, white, solid line) in the spatially varying stratification observed in March 2018 (H8). Yellow solid line indicates ray path that could reach the depth of 400 m at EC1 (yellow star). Background colour indicates potential temperature, and dashed line indicates isopycnals of 27, 28, and 29 kg/m<sup>3</sup> . *4.3. Effects of Mesoscale Flow Fields on Near-Inertial Energy Far Below the Mixed Layer* **Figure 10.** Ray path of near-inertial internal waves (NIWs) (thick, white, solid line) in the spatially varying stratification observed in March 2018 (H8). Yellow solid line indicates ray path that could reach the depth of 400 m at EC1 (yellow star). Background colour indicates potential temperature, and dashed line indicates isopycnals of 27, 28, and 29 kg/m<sup>3</sup> .

#### The condition parameters of ζ and ܵ ଶ that represent the mesoscale flow field ex-*4.3. Effects of Mesoscale Flow Fields on Near-Inertial Energy Far below the Mixed Layer*

plained VARNIW\_obs\_int better than surface wind forcing, because a negative ζ (Categories III and IV) lowers ݂ (permitting the trapping and rapid deep propagation of NIWs) (Figure 6) [24,28] and increases ܵ ଶ , leading to a positive anomaly of ߙ ଶ (Categories I and III), which stretches and rotates the wavevector (resulting in exponentially growing wavenumber and decreasing group velocity), representing an enhancement of NIWs [30]. For example, the lowered ݂ (ζ < 0) associated with the anticyclonic circulation around the EC1 supports the high VARNIW\_obs\_int during the H6, contrasting to the low VARNIW\_obs\_int during the L4 when ζ > 0, associated with the cyclonic circulation around the EC1 (Figure 6). During the two events (N1 and N2) of the neutral period, we observed low VAR-NIW\_obs\_int values despite high VARNIW\_model\_int values, in association with the typhoon passage, which may be explained by unfavourable conditions (ζ > 0 and ܵ <sup>ଶ</sup> < ζ ଶ ; Category II) for NIW enhancement imposed by mesoscale conditions (Table 3). In contrast, more The condition parameters of *ζ* and *S* 2 that represent the mesoscale flow field explained VARNIW\_obs\_int better than surface wind forcing, because a negative ζ (Categories III and IV) lowers *fe f f* (permitting the trapping and rapid deep propagation of NIWs) (Figure 6) [24,28] and increases *S* 2 , leading to a positive anomaly of *α* 2 (Categories I and III), which stretches and rotates the wavevector (resulting in exponentially growing wavenumber and decreasing group velocity), representing an enhancement of NIWs [30]. For example, the lowered *fe f f* (*ζ* < 0) associated with the anticyclonic circulation around the EC1 supports the high VARNIW\_obs\_int during the H6, contrasting to the low VARNIW\_obs\_int during the L4 when *ζ* > 0, associated with the cyclonic circulation around the EC1 (Figure 6). During the two events (N1 and N2) of the neutral period, we observed low VARNIW\_obs\_int values despite high VARNIW\_model\_int values, in association with the typhoon passage, which may be explained by unfavourable conditions (*ζ* > 0 and *S* <sup>2</sup> < *ζ* 2 ; Category II) for NIW enhancement imposed by mesoscale conditions (Table 3). In contrast, more period high events were observed under favourable conditions (*ζ* < 0 and *S* <sup>2</sup> > *ζ* 2 ; Category III) for NIW enhancement imposed by mesoscale conditions (Table 3), mainly regardless of wind forcing.

The results of more frequent events of period high in the 2010s (compared to those in the 2000s) were also accounted for by the mesoscale field condition, and not by the surface-wind-induced NIWs within the mixed layer. The anticyclonic UWE anomalously lasted longer (nearly two years from October 2014 to August 2016) in the region [64], and a newly formed UWE appeared again in September 2016, providing mesoscale conditions of *ζ* < 0 that were favourable for NIW enhancement at 400 m of EC1 during H5, H6, and H7. Changes in mesoscale flow conditions due to the UWE in the 2010s accompanied the

strengthening of density stratification in the region, yielding significantly higher *N* and lower WKB scaling factor values at 400 m of EC1 during the 2010s, compared to those observed in the 2000s, due to a strong stratification linked to mesoscale conditions in 2003, 2006, 2011, 2013, and 2015–2018 (Figure 4). Interestingly, the 14% decrease in the WKB scaling factor or the increase in the NIW potential energy in the 2010s (compared to that observed in the 2000s), however, could not explain the increased frequency of period high events in the 2010s. Note that the events of period high and period low were not significantly dependent on whether WKB scaling was applied (now shown), indicating that the nonseasonal variation of NIW energy was more affected by the mesoscale flow field (vorticity and strain) than the stratification. The WKB scaling factor at 400 m was variable depending on the varying stratification, but always higher than the unity at the depth (Figures 3c–e and 4b,d).
