**1. Introduction**

Near-inertial internal gravity waves (NIWs), with frequencies close to the local inertial frequency (*f*), are ubiquitous in stratified rotating oceans. The NIWs mainly originate from surface wind forcing, enhanced primarily within the surface mixed layer; in general, the waves propagate into the ocean interior below the mixed layer and towards the equator and ultimately dissipate, while enhancing turbulent mixing [1–4]. The rate of work done by surface wind on global mixed layer NIWs is known to range from 0.3 TW to 1.3 TW, which is comparable to the global energy derived from barotropic to baroclinic tides (1.0–1.2 TW) [5–7]. Both winds and tides play a key role in providing energy to induce turbulent mixing and redistribute energy and materials in the ocean [3,8–13]. Along with turbulent mixing enhanced by tides, NIW-enhanced mixing may sustain the meridional overturning circulation [13–15]; previous studies used numerical simulations to suggest that near-inertial variations in the meridional overturning circulation are caused by equatorward-propagating NIWs [16,17]. NIWs are also important as they significantly affect, via turbulent fluxes, primary production and marine ecosystems [18–23].

The generation, evolution, propagation, and decay of NIWs are affected by mesoscale flow fields and wind forcing [2,24–27]. The wind forcing excites NIWs in the mixed layer

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**Citation:** Noh, S.; Nam, S. Nonseasonal Variations in Near-Inertial Kinetic Energy Observed Far below the Surface Mixed Layer in the Southwestern East Sea (Japan Sea). *J. Mar. Sci. Eng.* **2022**, *10*, 9. https://doi.org/ 10.3390/jmse10010009

Academic Editors: Eugenio Fraile-Nuez and Christos Stefanakos

Received: 13 November 2021 Accepted: 20 December 2021 Published: 23 December 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

which generally propagate equatorward horizontally and downward vertically below the mixed layer. The amount of wind energy input into and below the mixed layer is modulated by interaction processes between the mesoscale flow fields and NIWs. One method of interaction is the trapping (reflection) of NIWs in a region of negative (positive) relative vorticity that decreases (increases) the effective Coriolis frequency (e.g., *fe f f* = *f* + <sup>1</sup> 2 *ζ* where *ζ* is the relative vorticity; *ζ* = *∂V*/*∂x* − *∂U*/*∂y*, and *U* and *V* are zonal and meridional components of horizontal mesoscale currents) acting as a waveguide in the northern hemisphere (opposite sign in the southern hemisphere). Although, in general, NIWs freely propagate in frequencies between *f* and buoyancy frequency (*N*), the relative vorticity shifts the lowest limit from *f* to *fe f f* (Figure 1) [24,28,29]. Thus, the NIWs entering into a region of negative relative vorticity (*ζ* < 0) or lowered *fe f f* can hardly propagate out of the region and can, thus, be trapped. Another way of interaction is a straining that stretches and rotates the wavenumber vectors of NIWs depending on differential advection of mesoscale flow fields (*U*, *V*). Under one kind of the straining processes called 'wave capture' (strain dominates vorticity), the NIWs can draw energy from mesoscale flow fields [30–33]. Staining causes exponential increase in the vertical and horizontal wavenumbers of NIWs, which results in growing wavenumbers and decreasing group velocities of NIWs, with NIWs captured within the region of high total strain and eventually dissipated through energy cascading (Figure 1) [30–33]. *J. Mar. Sci. Eng.* **2022**, *10*, x FOR PEER REVIEW 3 of 20

**Figure 1.** Schematics on interaction between mesoscale flow field (grey line) and wind-induced NIWs (red arrow), enhancing the near-inertial kinetic energy. Red spirals indicate dissipation of NIWs. **Figure 1.** Schematics on interaction between mesoscale flow field (grey line) and wind-induced NIWs (red arrow), enhancing the near-inertial kinetic energy. Red spirals indicate dissipation of NIWs.

**2. Data and Methods** *2.1. Data* Since 1996, long time-series data of zonal and meridional currents were collected using a subsurface mooring, named EC1 (37°19.13 N, 131°25.62 E), located between Ulleugdo and Dokdo, at a water depth of 2300 m (Figure 2). The EC1 was recovered and redeployed 24 times (as of December 2021) and equipped for most periods, with current meters at three nominal depths (400, 1400, and 2200 m). Rotary-type current meters (Aanderaa RCMs 7 and 8) and Doppler-type current meters (Aanderaa RCMs 9 and 11; Nortek Aquadopp) were attached to the mooring, and continuous time-series data were recorded with a sampling interval equal to or less than 1 h. An upward-looking acoustic Doppler current profiler (ADCP, 300 kHz) was mounted at 500 m with a depth interval (bin size) of 8 m, instead of a using single-type current meter at 400 m, from March 2011 to July 2012. All EC1 data collected from 1996 to 2020 were upgraded by quality control and quality Previous studies on NIWs interacting with mesoscale flow fields in the East Sea (Sea of Japan) have been reported from both observations and numerical models. The formation, presence, and decay of mesoscale eddies are frequently observed in the East Sea, particularly off the east coast of Korea, and are partly associated with the strong meandering of a western boundary current, the East Korea Warm Current. A semi-permanent anticyclonic eddy, the Ulleung Warm Eddy (UWE), is often found off the coast where the boundary current forms and separates [34,35]. Seasonal variation in NIWs (with winter intensification) was reported by Mori et al. [36] and Jeon et al. [37] in association with the East Asian Monsoon and mesoscale circulation. Additionally, studies have suggested annual variations in the deep NIW kinetic energy observed off the coast, related to mesoscale fields imposed by the UWE [38]. Upward reflection of downward-propagating NIWs by the UWE was also observed [39]. Noh and Nam [40] reported the importance of mesoscale strain fields in the enhancement of NIWs, focusing on specific cases of NIW events. Likewise, the effects of mesoscale circulation on the behaviour of NIWs off the coast have been examined previously. However, the effects of mesoscale flow fields on temporal variations in NIW kinetic energy beyond the seasonal cycle have not been presented in the region to date.

assurance and were made available by SEANOE [41]. In this study, the time-series data of currents collected at 400 m of EC1 for almost 21 years, from January 2000 to November 2020, were used. Thus, this study is the first to describe the intraseasonal, interannual, and decadal variations (nonseasonal variations) in NIW kinetic energy in southwestern East Sea, using moored observations over the duration of 21 years. The objective was to identify statistically significant factors, particularly in association with mesoscale flow fields, that control

**Figure 2.** Location of subsurface mooring EC1 (red square) with bathymetry (colour) in the southwestern East Sea, off the east coast of Korea. Green dotted line indicates meridional line where sea surface wind data were extracted. Black dashed lines indicate trajectories of typhoon Maemi in 2003, Megi in 2004, and Maysak in 2020. The yellow circles indicate radii of 30, 100 and 200 km centred at

EC1, respectively.

nonseasonal variations in NIW kinetic energy based on long-term continuous observations. The data used and the methods applied in this study are described in the next section. In Section 3, we have presented the results of moored observations and damped slab model. Additionally, results of nonseasonal variations in NIW kinetic energy, in terms of surface wind forcing and mesoscale field variability, are provided and discussed in Section 4, and Section 5 provides the conclusions of our study. **Figure 1.** Schematics on interaction between mesoscale flow field (grey line) and wind-induced NIWs (red arrow), enhancing the near-inertial kinetic energy. Red spirals indicate dissipation of NIWs.

*J. Mar. Sci. Eng.* **2022**, *10*, x FOR PEER REVIEW 3 of 20

## **2. Data and Methods 2. Data and Methods** *2.1. Data*
