**3. Results**

*3.1. Intraseasonal, Interannual, and Decadal Variations of Near-Inertial Kinetic Energy below and within the Surface Mixed Layer*

The VARNIW\_obs\_int values showed significant intraseasonal, interannual, and decadal variations, rather than seasonal variations, from 2000 to 2020 (Figure 5 and Tables 1 and 2). Notably, VARNIW\_obs\_int averaged over period high (red shaded box) was approximately 12 times higher than that of period neutral. During period low (blue shaded box), there was almost no VARNIW\_obs\_int variation at 400 m (<0.02 J2/m<sup>6</sup> ). The NIW kinetic energy (square root of VARNIW\_obs\_int) averaged over period high was ~1.1 <sup>×</sup> <sup>10</sup><sup>3</sup> J/m<sup>3</sup> , which is approximately 24 times higher than that over period low (~4.7 <sup>×</sup> <sup>10</sup> J/m<sup>3</sup> ). Relatively high (>5.8 <sup>×</sup> <sup>10</sup><sup>5</sup> J <sup>2</sup>/m<sup>6</sup> ) annual mean values of VARNIW\_obs\_int were found in 2003, 2012–2013, 2016, and 2020, with the maximum value being observed in 2016 (with the peak value of 9.5 <sup>×</sup> <sup>10</sup><sup>5</sup> J <sup>2</sup>/m<sup>6</sup> in 2016 corresponding to H5) (Figure 7b). In terms of decadal variations of VARNIW\_obs\_int, period high appeared more frequently in the 2010s than the 2000s, yielding a decadal mean of VARNIW\_obs\_int in the 2010s (~8.3 <sup>×</sup> <sup>10</sup><sup>4</sup> J <sup>2</sup>/m<sup>6</sup> ), significantly (95% confidence) higher than that in the 2000s (~3.1 <sup>×</sup> <sup>10</sup><sup>5</sup> J <sup>2</sup>/m<sup>6</sup> ). *J. Mar. Sci. Eng.* **2022**, *10*, x FOR PEER REVIEW 11 of 20

**Figure 7.** (**a**) Time series of normalised intraseasonal variations in KENIW at 400 m (VARNIW\_obs\_int) from 2000 to 2020. Red (blue) shaded boxes indicate period high (period low) and grey shaded area indicates period neutral. White area represents the data gap (no data available). Events 2–4 in Noh and Nam [40] are marked at the top of H2 (pink). (**b**) Annual (squares) and decadal mean (blue thick lines) of VARNIW\_obs\_int. In (**b**), grey and white squares indicate annual mean values of years in which the data acquisition rate was more and less than 50%. **Figure 7.** (**a**) Time series of normalised intraseasonal variations in KENIW at 400 m (VARNIW\_obs\_int) from 2000 to 2020. Red (blue) shaded boxes indicate period high (period low) and grey shaded area indicates period neutral. White area represents the data gap (no data available). Events 2–4 in Noh and Nam [40] are marked at the top of H2 (pink). (**b**) Annual (squares) and decadal mean (blue thick lines) of VARNIW\_obs\_int. In (**b**), grey and white squares indicate annual mean values of years in which the data acquisition rate was more and less than 50%.

Interestingly, the timing of the enhanced VARNIW\_model\_int did not match well with that of VARNIW\_obs\_int (Figures 7a and 8d,e). A VARNIW\_model\_int (or amplitude of NIWs) value greater than 1.0 <sup>×</sup> <sup>10</sup><sup>4</sup> J <sup>2</sup>/m<sup>6</sup> (~1 m/s) was found on 12 September 2003, 19 August 2004, and 3 September 2020 (green triangles in Figure 8d,e); notably, only the first date corresponded to period high (H2). H5 corresponded to the period when the value of VARNIW\_obs\_int was higher than that during H2; however, the wind energy input during H5 (~7 kJ/m<sup>2</sup> ) was smaller than that during H2 (~31 kJ/m<sup>2</sup> ) (Figures 7a and 8c). Except for H2 and H5, the amplitudes of the modelled NIWs and VARNIW\_model\_int were less than 0.2 m/s and 2.0 <sup>×</sup> <sup>10</sup><sup>3</sup> J <sup>2</sup>/m, respectively. It is also interesting that there was a statistically significant difference in VARNIW\_model\_int before and after 2010, yielding a higher decadal mean of 4.8 <sup>×</sup>10<sup>2</sup> J <sup>2</sup>/m<sup>6</sup> in the 2000s than the 4.5 <sup>×</sup> <sup>10</sup><sup>2</sup> J <sup>2</sup>/m<sup>6</sup> observed in the 2010s, in contrast to the observational results (higher decadal mean of VARNIW\_obs\_int in the 2010s; Figure 7b). *J. Mar. Sci. Eng.* **2022**, *10*, x FOR PEER REVIEW 12 of 20

**Figure 8.** Time series of (**a**) wind stress amplitude, (**b**) near-inertial band-passed zonal (red) and meridional (blue) wind stresses, (**c**) rate of wind work Π (left axis) and time integral of Π showing cumulative wind energy input to the mixed layer (green solid line, right axis), (**d**) mixed layer nearinertial current amplitude, ඥݑெ <sup>ଶ</sup> + ݒெ <sup>ଶ</sup>, calculated from the damped slab model, and (**e**) intraseasonal-band variance of (**d**) from local (black) and remote (pink) wind stresses where the latter denotes wind stress averaged over 38–40° N. Red (blue) shaded boxes indicate period high (period low). Grey shaded area indicates period neutral. Green triangles in (**c**–**e**) indicate the periods when the mixed layer near-inertial current amplitude was larger than 1 m/s. **Figure 8.** Time series of (**a**) wind stress amplitude, (**b**) near-inertial band-passed zonal (red) and meridional (blue) wind stresses, (**c**) rate of wind work Π (left axis) and time integral of Π showing cumulative wind energy input to the mixed layer (green solid line, right axis), (**d**) mixed layer near-inertial current amplitude, p *uML*<sup>2</sup> + *vML*2, calculated from the damped slab model, and (**e**) intraseasonal-band variance of (**d**) from local (black) and remote (pink) wind stresses where the latter denotes wind stress averaged over 38–40◦ N. Red (blue) shaded boxes indicate period high (period low). Grey shaded area indicates period neutral. Green triangles in (**c**–**e**) indicate the periods when the mixed layer near-inertial current amplitude was larger than 1 m/s.

#### *3.2. Composite Mean of Near-Inertial Kinetic Energy at 400 m Dependent on Mesoscale Condition 3.2. Composite Mean of Near-Inertial Kinetic Energy at 400 m Dependent on Mesoscale*

In our study, the magnitudes of Π and *S* 2 composited for period high (period low) were significantly larger (smaller) than those for period neutral, showing 1.54 <sup>×</sup> <sup>10</sup>−<sup>3</sup> W/m<sup>2</sup> (0.43×10−<sup>3</sup> W/m<sup>2</sup> ) and 0.08 *f*/s (0.06 *f*/s), respectively (Figures 8 and 9 and Tables 1 and 2). The Π during the period high events (except for H1 and H8) were significantly larger than the composite mean during period neutral, while those during period low events (except L6) were significantly smaller than those during period neutral. The *α* <sup>2</sup> and *ζ* composite mean values for period high (period low) had positive (negative) and negative (positive) signs, showing <sup>+</sup>2.80 <sup>×</sup> <sup>10</sup>−12/s<sup>2</sup> (−20.45 <sup>×</sup> <sup>10</sup>−12/s<sup>2</sup> ) and −0.04 *f*/s (0.10 *f*/s), indicating the dominance of strain to vorticity (vorticity to strain) and lower (higher) *fe f f* , respectively. At period high, it was shown that the *ζ* < 0 or strain fields were strengthened by mesoscale flow fields, while at period low, *ζ* > 0 by cyclonic circulation appeared (Figure 6). More than half of the period high and period low events could be identified by the signs of *ζ* and *α* 2 . The role of the *ζ* was identified by comparing Categories I and III for *S* <sup>2</sup> > *ζ* 2 (corresponding to *α* <sup>2</sup> > 0), and Categories II and VI for *S* <sup>2</sup> < *ζ* 2 (corresponding to *α* <sup>2</sup> < 0), commonly yielding more period high events for a negative *ζ* (Table 3). The role of *S* 2 was determined by comparisons between Categories I and II for *ζ* > 0 and between Categories III and IV for *ζ* < 0, commonly yielding more period high events for *S* <sup>2</sup> > *ζ* 2 (positive *α* 2 ). For each Category, the composite means of VARNIW\_obs\_int were 1.05 <sup>×</sup> <sup>10</sup><sup>5</sup> , 1.29 <sup>×</sup> <sup>10</sup><sup>5</sup> , 1.25 <sup>×</sup> <sup>10</sup><sup>5</sup> , and 1.43 <sup>×</sup> <sup>10</sup><sup>5</sup> J <sup>2</sup>/m<sup>6</sup> yielding that at Category I < Category II, Category III < Category < IV and Category II < Category IV with 95% significant level (*p*-value < 0.05). There was no significantly high correlation between Category II and Category III (*p*-value > 0.05). *Condition* In our study, the magnitudes of Π and ܵ ଶ composited for period high (period low) were significantly larger (smaller) than those for period neutral, showing 1.54 × 10ିଷ W/m<sup>2</sup> (0.43 × 10ିଷ W/m2) and 0.08 *f/*s (0.06 *f/*s), respectively (Figures 8 and 9 and Tables 1 and 2). The Π during the period high events (except for H1 and H8) were significantly larger than the composite mean during period neutral, while those during period low events (except L6) were significantly smaller than those during period neutral. The ߙ ଶ and ζ composite mean values for period high (period low) had positive (negative) and negative (positive) signs, showing +2.80 × 10ିଵଶ/s <sup>2</sup> (−20.45 × 10ିଵଶ/s <sup>2</sup>) and -0.04 *f/*s (0.10 *f/*s), indicating the dominance of strain to vorticity (vorticity to strain) and lower (higher) ݂ , respectively. At period high, it was shown that the ζ < 0 or strain fields were strengthened by mesoscale flow fields, while at period low, ζ > 0 by cyclonic circulation appeared (Figure 6). More than half of the period high and period low events could be identified by the signs of ζ and ߙ ଶ . The role of the ζ was identified by comparing Categories I and III for ܵ <sup>ଶ</sup> > ζ ଶ (corresponding to ߙ <sup>ଶ</sup> > 0), and Categories II and VI for ܵ <sup>ଶ</sup> < ζ ଶ (corresponding to ߙ <sup>ଶ</sup> < 0), commonly yielding more period high events for a negative ζ (Table 3). The role of ܵ <sup>ଶ</sup> was determined by comparisons between Categories I and II for ζ > 0 and between Categories III and IV for ζ < 0, commonly yielding more period high events for ܵ <sup>ଶ</sup> > ζ ଶ ߙ positive( ଶ ). For each Category, the composite means of VAR-NIW\_obs\_int were 1.05 × 10<sup>ହ</sup> , 1.29 × 10<sup>ହ</sup> , 1.25 × 10<sup>ହ</sup> , and 1.43 × 10<sup>ହ</sup> J 2 /m<sup>6</sup> yielding that at Category I < Category II, Category III < Category < IV and Category II < Category IV with 95% significant level (*p*-value < 0.05). There was no significantly high correlation between Category II and Category III (*p*-value > 0.05).

**Figure 9.** Time series of (**a**) *S* <sup>2</sup> normalised by *f*, (**b**) *ζ* normalised by *f*, and (**c**) *α* <sup>2</sup> normalised by *f* 2 . Red (blue) shaded boxes indicate period high (period low). Grey shaded area indicates period neutral.
