Observations of enhanced internal waves in an area of strong mesoscale variability in the southwestern East Sea (Japan Sea)

Oceanic internal waves near the local inertial frequency or near-inertial internal waves and internal waves of tidal origin or internal tides are two types of low-frequency internal waves. Their interactions, interaction with background field, and resulting internal waves at higher frequencies beyond the near-inertial and tidal frequencies have rarely been reported despite its importance on ocean mixing and circulation of energy and materials. Here, we present five episodic enhancements of the high-frequency or continuum frequency waves (CFWs) observed in the southwestern East Sea (Japan Sea) and discuss causes for the enhanced CFWs in relation to near-inertial waves (NIWs), semidiurnal internal tides (SDITs), mesoscale flow fields, and their interactions. The NIWs were amplified due to local surface wind forcing, significantly interacting with mesoscale strain via wave capture. The SDITs were generated in a remote place and propagated into the observational site, largely depending on the mesoscale fields. The observational results suggest that the five episodes of CFWs are results of enhanced NIWs or SDITs, or their wave-wave interaction, rather than locally generated lee-waves. Our study suggests the significant impact of mesoscale circulation on the variability of internal waves from near-inertial to buoyancy frequencies through multiple pathways.

bottom slope, propagate via interaction with background mesoscale conditions, and ultimately dissipate [30][31][32][33] . In spite of the tremendous progress on SDITs and diurnal ITs, including global time averaged maps of barotropic to baroclinic conversion and internal tidal beams [34][35][36] , spatio-temporal variability of local generation, propagation, refraction, and dissipation (or damping) of SDITs and diurnal ITs in many seas, and their interactions are still poorly understood.
Internal waves at higher frequencies (0.09-0.50 cph), defined here as continuum frequency waves (CFWs), have long been described by the classical Garrett-Munk (GM) spectrum 37 and believed to arise from nonlinear wave-wave interactions transferring energy out of the NIWs and ITs into the broadband continuum 3,38,39 . As the level of the continuum or CFW energy is closely related to small-scale turbulent mixing, many works have been dedicated to better understand the processes underlying the variations of CFW energy and spectral departure from the GM spectrum. Recent studies suggested the relationship between observed mixing rates and internal wave generations along with lee-waves over rough topography, hypothesising that the CFW energy comes only from the wind, tides, and mesoscale turbulence [40][41][42] . However, our understanding on processes underlying the CFW energy variations in space and time are largely limited due to rare relevant observations.
In the southwestern East Sea (also referred as Japan Sea) off the east coast of Korea, episodic events of NIWs and SDITs have been reported 19,31,[43][44][45][46][47][48][49][50][51][52][53][54][55][56][57] . The NIWs generated by local surface wind forcing have widely been observed in the region 49,51,53,54 , yet their interactions with mesoscale field were examined in only few studies 19,44,50,53,56 . A semi-permanent anticyclonic eddy named Ulleung Warm Eddy (UWE) was found to affect the distribution of NIW energy in the region as discussed by Jeon et al. 57 . In addition, upward propagating NIWs due to the reflection of downward propagating NIWs back to the surface from the UWE thermostad were observed 19 . However, the role of mesoscale strain in exchanging energy between NIWs and the mesoscale field has not been investigated thus far. Moreover, the mechanism of NIWs interacting with ITs and enhancing CFWs remained unanswered. Although diurnal ITs are mostly trapped in the southern Ulleung Basin near the generation area, northern slope of the Korea Strait (red hatched area in Fig. 1a), SDITs generated in the same area easily propagate poleward as located in the north of diurnal and south of SD critical latitudes 34,58,59 , interacting with mesoscale circulation 31,[45][46][47] . Thus, this study aims at (1) characterising the time and location of the enhancement of three kinds of internal waves (NIWs, SDITs, and CFWs) in the region, and (2) addressing possible mechanisms to explain the enhanced CFWs in relation to those of NIWs, SDITs, their interactions, and interactions with the mesoscale field.

Results temporal variations of enhanced internal wave energy over the vertical. Five episodic CFW
enhancements (Events 1-5) were observed along with those of NIWs or SDITs between 53 and 360 m at a subsurface mooring named EC1 located in the northern Ulleung Basin from July to December 2003 ( Fig. 1a-f, and Table 1). NIW horizontal kinetic energy (KE NIW ) varies drastically with depth and time after removing stratification effects (Fig. 1b,c) and yields different temporal and vertical structures during the events with the highest KE NIW found during Event 2 (Fig. 1d). In contrast to the NIWs intensified between 53 and 360 m during Events 1, 2, and 5, high KE NIW was rarely observed between 100 and 200 m during Events 3 and 4. Temporal variations of SDIT kinetic energy (KE SDIT ) basically followed a noticeable fortnightly spring-neap tidal cycle (Fig. 1e). However, vertical KE SDIT structures significantly vary with time, yielding surface intensified features during Events 1 and 5 in contrast to spreading features during Events 2-4 and early Event 5. High KE SDIT was rarely found below 153 m during Event 1 and between 53 and 360 m in August between Events 1 and 2. Not surprisingly, the time-depth pattern of CFW energy (KE CFW ) was generally similar to those of NIWs, SDITs, their summations (KE NIW + KE SDIT ), and their interactions (KE NIW+SDIT ), including the energies at higher tidal harmonics as well as interaction frequencies (Fig. 1d-h).
High KE CFW in Event 1 was found between 53 and 100 m, and 200 m where high KE NIW or KE SDIT were observed with significantly (p < 0.05) high correlation coefficients between KE CFW and KE NIW + KE SDIT and between KE CFW and KE NIW+SDIT ( Fig. 1d-g, Table 2). The time-depth pattern of KE CFW during Event 2 was generally more similar to those of KE NIW than KE SDIT , but it was complicated by the periods and depths where KE CFW was high without enhanced NIWs or SDITs (green boxes in Fig. 1f-h). Conversely, CFWs at a depth between 53 and 100 m during the early part of Event 2 were not enhanced in spite of high KE NIW (purple box in Fig. 1f- Fig. 1f-h). Since KE NIW + KE SDIT is highly correlated with KE CFW at all selected depths, there are events and depths where correlations between KE NIW + KE SDIT and KE NIW+SDIT were also significant ( Fig. 1g-h, Table 2). changes in horizontal kinetic energy spectra. The frequency spectra of horizontal kinetic energy at four depths consistently demonstrate temporal variations over the verticals of NIWs, SDITs, and CFWs during the five events ( Fig. 2a-e). Spectral peaks at near-inertial (f) and SD (M 2 ) frequencies and their interaction frequencies (e.g., M 2 + f, see Table 3) were significant. The spectral energy of the broad near-inertial peak decreased with depth during Event 1, whereas narrower near-inertial peaks had nearly the same spectral energy over depths during Event 2 (Fig. 2a,b). During Events 3 and 4, much broader near-inertial peaks were found with maximum spectral energy at 360 m (Fig. 2c,d). Two spectral peaks at near-inertial and SD frequencies with higher spectral energy at the upper depths found during Event 5 are similar to those during Event 1 (Fig. 2a,e).
In these spectra, higher energies at the continuum frequency band were found at deeper depths during Events 3 and 4 but at shallower depths during Events 1, 2, and 5, which is consistent with the time-depth patterns of  Table 3) of NIWs and SDITs, respectively, whereas KE NIW , KE SDIT , and KE CFW are directly estimated from NIWs, SDITs, and CFWs, respectively. Five events are denoted by grey boxes. Each colour box in (d-h) represents enhanced NIWs only with no enhancements of SDITs or CFWs (purple), enhanced CFWs only with no enhancements of NIWs or SDITs (green), enhanced NIWs and CFWs with no SDIT enhancement (black), enhanced SDITs and CFWs with no NIW enhancement (red), and enhanced NIWs, SDITs, and CFWs (blue). Timings of spring tide at the nearby tide-gauge station (Busan) are denoted by triangles in (e). The figure was generated by S. Noh using MATLAB R2019b, http://www.mathworks.com. www.nature.com/scientificreports www.nature.com/scientificreports/ Discussion niW generation by local wind forcing. Although a simple wind-forced, damped slab model cannot guarantee reproduction of all observed NIWs of surface wind origin, it is useful to identify the episodes of enhanced mixed layer NIWs, e.g., NIWs observed at 53 m (Fig. 3c). Here, the model was not used to reproduce realistic kinetic energy nor its temporal structure but only to identify the events. In particular, it is obvious that the NIWs observed at the upper depths during early Event 2 were triggered by strong wind stress fluctuations (peaked to 1.15 N m −2 ) due to the passage of Typhoon Maemi nearby the observation site (Figs. 1a and 3a). At that time, rate of wind work significantly fluctuated regardless of using local or regional (averaged over the area denoted with the blue rectangle) wind stress (Fig. 3b). The NIWs generated during this particular event were reported by Nam et al. 55 , and most (88%) of mixed layer NIWs observed in the region from 1999 to 2004 were suggested to be of wind origin as well reproduced by the wind-forced slab model although the amplitude was systematically over-estimated 54 . Our model applications with four different cases of input parameters along with the rate of wind work confirmed the surface wind-generated NIWs, at least, during Events 1, 2, and 5 ( Fig. 3a-d). Note that the vertical direction of NIW energy propagation was downward (or upward phase propagation) based on the time-depth pattern of zonal components of near-inertial currents (not shown) during the Events, consistently indicative of surface energy source.
Since the mixed layer NIWs can be amplified by surface background flow field during the generation stage, as recently suggested by Whitt and Thomas 25 and Jing et al. 26 , a modified slab model incorporating the effect of background mesoscale flow into the simple model was used to identify the time at which this effect becomes significant. The advection terms in the modified slab model representing nonlinear interaction terms between NIWs and mesoscale flow at the observation site (EC1) were two orders of magnitude lower than the other terms for all events except Event 4. During Event 4, the total strain of surface mesoscale flow consistently increased at EC1 (Fig. 4a) as anticyclonic UWE which existed during Event 3 moved westward and EC1 was located between two cyclonic circulations ( Fig. 3f-i). Consistently, the efficiency of energy transfer from mesoscale field to NIWs increased during Event 4 ( Fig. 3e), supporting the possibility of mesoscale flow amplifying NIWs in spite of surface wind forcing similar to or weaker than those during Events 1, 2, and 5 ( Fig. 3a-d).
Interaction between mesoscale flow field and NIWs. The KE NIW observed at 360 m of EC1 during Events 3-4 exhibited significantly higher near-inertial spectral energy with a broader peak, implying a source of energy other than the local wind forcing (Figs. 1d, 2c,d, 3d,e, 4a). A Doppler shift by lateral mesoscale flow fields may cause the broadening of the inertial spectral peak 60 . During Events 3-4, mesoscale (subinertial) energy www.nature.com/scientificreports www.nature.com/scientificreports/ averaged over the depth abruptly decreased from 90 to ~5 J m −2 , and the total strain of mesoscale flow increased from 0.55 × 10 −5 to 1.75 × 10 −5 s −1 (Fig. 4a,b). These changes are mainly due to changes of the mesoscale fields ( Fig. 3f-i), e.g., the EC1 was located in the western side of the UWE at early Event 3 (October 22) yielding strong geostrophic flow at the location (Fig. 3f) whereas it became located in the middle of mesoscale circulations raising the total strain (Fig. 3g,i). The enhanced total strain supports the possibility of efficiently transferring mesoscale or subinertial energy into NIWs as further evidenced below. Based on the wave capture process suggested previously 16,17,27 , the NIWs undergo the Doppler shift with wavenumber changing exponentially (~ e ±αt where α 2 is an Okubo-Weiss parameter defined as the difference between total strain and relative vorticity of mesoscale flow field), and extract energy from the mesoscale field when and where the strain exceeds vorticity, e.g., α 2 > 0. Events 3 and 4 correspond to the period favouring wave capture at EC1 according to the definition of Jing et al. 27 , yielding a positive Okubo-Weiss parameter with positive rates of energy transfer of 3.2 × 10 −9 and 1.1 × 10 −9 m 2 s −3 , respectively (Fig. 4a,c). Therefore, the NIWs enhanced at 360 m of EC1 during Events 3 and 4 can be explained by the wave capture, indicative of significant energy transfer from the mesoscale field to internal waves.
SDit generation at the Korea Strait. Although EC1 is far (~200 km) from the generation area of ITs in the north of the Korea Strait (red hatched area in Fig. 1a), and diurnal ITs (D 1 ) rarely propagate into the interior of the East Sea as f > D 1 , SDITs often propagate poleward freely as f < M 2 . The poleward propagating SDITs can account for high KE SDIT and spectral peaks at M 2 , as well as tidal subharmonic frequencies (Figs. 1e and 2a-e). Favourable periods for SDIT generation were found considering the bottom slope and buoyancy frequency at the shelf break in the generation region (corresponding depth of ~200 m) 31 . The internal wave characteristics slope is well matched to the bottom slope in August (between Events 1 and 2) and October (between Events 2 and 3), with buoyancy frequencies of 0.62 and 0.33 cph. On the other hand, the SDITs were weakly generated in June (before Event 1) and December (late Event 5) as the characteristic slope of 0.34-0.90 did not match well to the bottom www.nature.com/scientificreports www.nature.com/scientificreports/ slope with buoyancy frequencies of 0.04 and 0.20 cph. The summer-fall maximum and spring minimum of the barotropic-to-baroclinic conversion rate of SDITs in the area were consistent with recent numerical results presented by Jeon et al. 46 . The generated SDITs reached the EC1 within ~2.5 days, assuming the horizontal speed of mode-1 SDIT (~1 m s −1 ) 31 in September-November, but not in June, August, and December (as further discussed below). It is reasonable to account for the enhanced KE SDIT and spectral peaks at M 2 and the tidal subharmonic frequencies, particularly below 153 m with poleward propagating SDITs. Although there were general enhancements of KE SDIT following the spring-neap tidal cycle and enhancements of KE SDIT above 153 m, regardless of conditions, for the generation and refraction of SDITs, the KE SDIT below 153 m is affected by the generation of SDITs modulated by the stratification conditions in the northern Korea Strait.
Interaction between mesoscale field and SDITs. Although SDITs were favourably generated in the northern Korea Strait both in August and October, those in August could not reach the EC1 except in October. The SDITs are refracted westward or eastward and are propagated poleward, or are trapped in the generation area, as the mesoscale fields act as a wave-guide 31,45 . The eastward refraction of poleward propagating SDITs from the generation area into the EC1 is possible only when warmer water with higher sea surface height (SSH) occupies more of the western side than the eastern side of the Korea Strait, yielding faster propagation in the western than the eastern side. This condition was not satisfied before September when the observed SSH in the area was low, indicating that the cold water prevailed in the area to prohibit SDITs from propagating poleward out of the area, i.e., they were trapped in the area (Fig. 4f). During Events 2-4 and early Event 5 (September-November), the SSH in the western side became sufficiently high due to warmer water that allowed the eastward refraction of SDITs towards EC1 (Fig. 4f). Thus, high KE SDIT and spectral peaks at M 2 and tidal subharmonic frequencies below 153 m during Events 2-4 and early Event 5 could be explained by remote SDITs (Figs. 1e, 2b-e and 4e). In particular, SDITs generated at the northern Korea Strait are appropriate to explain the vertically spreading, beam-like KE SDIT well. In contrast, the SDITs generated during August rarely propagate into the EC1 but are trapped within the generation area as relatively cold water (having low SSH) prevails, accounting for the low KE SDIT observed below 153 m of EC1 during Event 1 and between Events 1 and 2 (Figs. 1e and 4f). Nevertheless, the KE SDIT observed www.nature.com/scientificreports www.nature.com/scientificreports/ above 153 m during same periods was still high, possibly due to long-range propagating low-mode baroclinic (rather than beam-like) SDITs.

cfW enhancement by interaction between niWs and SDits.
There are three possible mechanisms for enhanced CFWs: one is forward cascading occurring directly from either one of the enhanced NIWs or SDITs; the second is from nonlinear interaction between NIWs and SDITs; and the third is local generation from the interaction between currents and bottom topography, e.g., Lee-waves. The Froude number, F r = Uk H /ω (U: flow speed, k H : horizontally dominant wavenumber of bottom topography, and ω: CFW frequency) was considered to examine the third possibility of Lee-wave generation. For a given weak tidal flow and a dominant bottom wavelength of ~7 km (k H = ~9.0 × 10 −4 cpm) in the vicinity of EC1 (within a degree), located in a relatively flat area (Fig. 1a), F r was much smaller than unity. For this reason, we ruled out the third possibility. It is reasonable, considering the correlated time-depth patterns of KE NIW , KE SDIT , and KE CFW , that the wave energy was forward cascaded into the CFWs when and where either NIWs or SDITs or both were enhanced (high KE NIW + KE SDIT and KE NIW+SDIT ), supporting the first and second possibilities (Fig. 1d-h).
The two mechanisms are not simple, particularly considering the periods and depths where only NIWs were enhanced without enhancements of SDITs or CFWs (purple box in Fig. 1d-h) or where high KE CFW was observed without enhanced NIWs or SDITs (green boxes in Fig. 1f-h). During Event 2, extreme high KE NIW generated by the typhoon passage early on may propagate downward vertically, and presumably equatorward horizontally, as low-mode NIWs with a minimum energy loss into CFWs. A few days later, the CFWs enhanced via remote (rather than local) wave-wave interaction from high-mode NIWs were likely observed in the single mooring without locally enhanced NIWs or SDITs. Note that KE NIW+SDIT at 200 m remained high following high KE CFW during the period when both KE NIW and KE SDIT (thus KE NIW + KE SDIT ) were low (Fig. 1d-h), implying that wave-wave interaction processes were in action despite there being no local energy source (only remote).
The noticeable time-depth variations of the frequency spectrum of horizontal kinetic energy support different roles of multiple processes in facilitating energy transfer from NIWs and SDITs to CFWs, and potentially to turbulent mixing via forward energy cascading. Time series of energy level E fit and slope S fit of the frequency spectra over 20-day-segmented period demonstrates significant deviations from the conventional GM internal wave spectral slope (S fit = −2.0), as previously recognized 37,61 . E fit was remarkably high (>7 × 10 −5 m 2 s −2 cph −1 ) at 360 m during late Event 2, Events 3-4, and early Event 5 presumably due to 1) downward propagating NIWs enhanced by local and regional wind forcing and interaction between NIWs and the mesoscale field, 2) eastward refraction of poleward propagation SDITs into EC1 from the generation area, and 3) enhanced CFWs by interaction between NIWs and SDITs. Significant interactions between NIWs and SDITs and among CFWs are also supported by low S fit (less than −2.0, indicative of gentler spectral slope that deviates from the GM slope) during the entire observation period, except for Event 1 when KE SDIT was low below 153 m (Figs. 1e and 4d,e).

Summary and conclusion
In summary, we identified five episodic enhancements of CFWs observed from July to December 2003 in the southwestern East Sea, first time in the region, and discussed causes for the enhanced CFWs in relation to NIWs, SDITs, mesoscale fields, and their interactions. The schematics in Fig. 5 depict the impact of the mesoscale circulation on enhanced internal waves from near-inertial to buoyancy frequencies in several different ways. Our findings are summarised as follows: (1) The local wind-forced, damped slab model well reproduced most of mixed layer NIWs supporting www.nature.com/scientificreports www.nature.com/scientificreports/ well-known mechanisms of surface generation and downward propagation of NIWs, particularly during typhoon passage (Event 2); (2) Modified slab model explained mixed layer NIWs even with weak wind forcing by considering the amplification due to interaction with the surface background flow field during the generation stage (Event 4); (3) Potentially evident and efficient energy transfer from mesoscale field to internal waves via wave capture accounted for enhanced NIWs at 360 m when the total strain exceeds relative vorticity and rates of energy transfer is positive (Events 3 and 4); (4) Remarkable time-depth variations of SDITs in addition to noticeable spring-neap tide cycles were found largely following mesoscale conditions favourable for generating the SDITs at the shelf break in the north of the Korea Strait and eastward refracting of the poleward propagating SDITs toward the observation site in the northern Ulleung Basin (Events 2-4 and early Event 5); (5) Importance of local and remote wave-wave interaction processes and forward energy cascading from NIWs and SDITs into CFWs was emphasised to account for time-depth patterns of KE CFW and the frequency spectrum of horizontal kinetic energy, ruling out the possibility of bottom generation of local CFWs under the condition of small Froude number.
Our observations reveal that CFWs and forward energy cascading from low-to high-frequency internal waves are enhanced not only by direct local and remote wind forcing or by remote tidal forcing, but also through remarkable interactions among the internal waves, and with the mesoscale field via wave capture (Doppler shift of NIWs) and wave guide (refraction of SDITs). The results support previous works, which consistently show that (1) the NIWs are affected by mesoscale strain and vorticity [15][16][17][18][19][20][25][26][27]44,57 , (2) ITs are either refracted or trapped by the background fields 31,[45][46][47][48] , and (3) NIWs and SDITs significantly interact to shape the CFWs via forward energy cascading 4-6,37-39 . More and better observations are required to further deepen our understanding on how the internal waves extract energy from the mesoscale field and transfer the energy into a smaller scale and turbulence in the ocean. To extract three frequency bands, fourth-order Butterworth filters were applied to the hourly time series of the observed horizontal currents (u, v) at each depth. To preserve the phase, the filter was applied forward and backward, and the defined bands were not overlapped. The CFW, representing the high-frequency band of internal waves towards the buoyancy frequency, includes interaction frequencies between NIWs and SDITs and among higher tidal harmonics (Table 3).

Rate of wind work.
To examine wind and current resonance at near-inertial frequency, the rate of wind work was calculated as 57 . 53 53 where τ τ ( , ) x y NIW NIW and (u v ,

NIW
N IW m m 53 53 ) were near-inertial band-passed, zonal and meridional wind stresses at location nearest to the EC1 and averaged over the area shown in Fig. 1a, and zonal and meridional current observed at 53 m, respectively.
Damped slab model with and without background geostrophic current. To examine the inertial response of the mixed layer to surface wind forcing, a damped slab model was used 67,68 : where H ML , r and (u ML , v ML ) are the MLD, inverse damping time scale, and zonal and meridional currents in the mixed layer, respectively. To test the sensitivity of the slab model results to H ML and r, applications with four different cases were compared (Cases 1-4). The MLD was fixed to 20 and 60 m for Cases 1 and 2 (e.g., H ML = 20, 60), respectively, whereas time-varying MLD was used for Cases 3 and 4 based on the observations 65 . The damping time scale r −1 was set to 3 days for Cases 1, 2, and 4, and 6 days for Case 3 based on previous works 49,53,54,57 . Among the modelled results, the modelled amplitudes of NIWs with time-varying H ML (Cases 3 and 4) were more similar to the observed amplitudes at 53 m than those with constant H ML (Cases 1 and 2). While the modelled amplitudes of NIWs are sensitive to both MLD and damping time scale, the timing of enhanced NIWs is consistent among the cases, as described in previous section.
Since the mixed layer NIWs can be amplified by the energy transfer from mesoscale flow fields 25,26 , a modified slab model as below incorporating background geostrophic currents, → = U U V ( , ) was used to compare the order of magnitude of the advection terms (second and third terms in the left-hand-side) with other terms: Strain and vorticity of mesoscale field and Okubo-Weiss parameter. Horizontal velocity gradient tensors were calculated from the satellite altimetry-derived surface geostrophic currents → = U U V ( , ) where the normal and shear components of the rate of strain tensor, S n and S s , and vertical component of the relative vorticity, ζ were defined as: where the subscripts of U and V represented partial derivatives. Then, the relative importance of total strain and relative vorticity was diagnosed with the Okubo-Weiss parameter 69  www.nature.com/scientificreports www.nature.com/scientificreports/ mesoscale field to NIWs was estimated following Jing et al. 27 , uu vv S uv S P 05( ) n s = − . − − , where the angle brackets 〈〉 represent the running mean over three inertial periods.
internal wave characteristic slope. The characteristic slope of internal waves was calculated as 70 : where wave frequency ω is set to M 2 to compare the characteristic slope of SDITs with the bottom slope at the shelf break in the north of the Korea Strait. Herein, the hydrographic data collected in the northern Korea Strait are used to estimate the time-varying buoyancy frequency. estimation of energy level and slope of frequency spectrum. The frequency spectrum of horizontal kinetic energy was fitted to ω E fit S fit considering the conventional GM internal wave spectrum, where E fit , S fit , and ω are fitted energy level, slope, and frequencies 29,61 . To estimate temporal variations of the energy level E fit and slope S fit , a least-square fit of the spectrum for ranging from 0.09 cph and the Nyquist frequency (~0.5 cph) was applied to 20-day-long segment time series of horizontal kinetic energy at given depth. Deviations from the conventional GM internal wave spectrum (S fit = −2.0) were used to quantify time-depth variations of CFWs.