1. Introduction
Most of the power into the ocean’s general circulation arises from stress exerted by the wind at the surface (Fofonoff 1981; Oort et al. 1994; Wunsch 1998). Because of the ocean’s boundaries, wind patterns, density distribution, and Earth’s rotation, this energy organizes into 100–1000-km gyres and currents and fields of 10–100-km mesoscale eddies. This large-scale quasigeostrophic dynamics arrests transfer of energy to smaller scales where it could be dissipated, instead cascading energy to larger scales. But energy in the general circulation must be dissipated at the same 1-TW rate that it is forced by wind. Several dissipation mechanisms have been proposed involving interactions with bottom or lateral boundaries (Fig. 1) including 0.2 TW in internal lee-wave generation (Nikurashin and Ferrari 2011) and 0.1 TW of bottom drag (Wunsch and Ferrari 2004). However, these forces are negligible away from boundaries (Wunsch and Ferrari 2004) and fall short of the power input. Hence, there remains a gap in our understanding of how the interior ocean subinertial circulation dissipates.
Schematic of this study. Wind power input to the ocean general circulation is estimated to be O(1) TW (Wunsch 1998). This power input is balanced by energy dissipation processes such as bottom drag O(0.1) TW (Wunsch and Ferrari 2004) and lee-wave generation O(0.2 TW) (Nikurashin and Ferrari 2011) near the bottom boundary. The study described here suggests that an unforced front can lose power from balanced circulations to near-inertial waves of O(0.36) TW. However, most of this is reabsorbed into the balanced flows with relatively little lost to explicit model dissipation O(0.001–0.047) TW.
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
Several studies have pointed out that fronts can spontaneously generate inertia–gravity waves. Using a two-dimensional numerical model, Snyder et al. (1993) showed that atmospheric fronts forced out of balance by frontogenetic confluence can spontaneously radiate inertia–gravity waves as they undergo geostrophic adjustment (Rossby 1938). Plougonven and Snyder (2007) found that near-inertial waves are radiated from a meandering atmospheric front and stall near the front. Ford (1994) showed that barotropic shallow-water models with zonal bands of anomalous PV radiate inertia–gravity waves from evolving vortices. Similarly, Danioux et al. (2012) used a 2-km-resolution primitive equation ocean model to show that gravity waves are emitted from high-Rossby-number flow associated with density filaments near the surface. Shakespeare and Taylor (2014) showed analytically that a two-dimensional front undergoing frontogenesis can radiate inertia–gravity waves that remain trapped and amplified within the front by the confluent flow. In laboratory experiments, Williams et al. (2008) found that the amplitude of the emitted waves from balanced flow is linearly proportional to Rossby number, estimating that 1.5 TW could be transferred from the balanced flow to internal gravity waves in the ocean. Based on estimates of the mesoscale eddy/internal-wave momentum transfer coefficients in the Sargasso Sea (Polzin 2010), Ferrari and Wunsch (2009) inferred a global net transfer rate of 0.35 TW. From an analytic model for minimum-frequency near-inertial waves in a baroclinic front under the influence of confluent flow, Thomas (2012) suggested a 0.1-TW global loss of balanced energy to near-inertial waves.
Based on the order-of-magnitude spread in the above estimates, the energy that can be drained from the subinertial quasigeostrophic flows of the ocean general circulation by spontaneous generation of internal waves remains uncertain. Here, we explore this possible sink for quasigeostrophic energy numerically. We motivate this study with numerous recent measurements that show enhanced near-inertial shear in the Kuroshio Front and Gulf Stream (section 2). Unforced numerical simulations of the Kuroshio spontaneously generate near-inertial waves to reproduce the observed near-inertial shear and enhancement of turbulent dissipation under the front (section 3). Global internal-wave power gain, through spontaneous radiation from fronts forced out of balance by confluent flows followed by reabsorption and dissipation, is estimated in section 4, and conclusions are summarized in section 5.
2. Observations of near-inertial waves in the Kuroshio
a. Kuroshio surveys
To motivate our study, we first describe four transect surveys. Three transects were sampled across the Kuroshio Front along 143°E during 8–10 August 2008 and 8–10 August 2011 and along 142°E during 9–11 August 2012. In these field programs, expendable bathythermographs (XBT T-7s) were deployed every 3.7 km in 2008 and 2011 and 2.8 km in 2012 to measure temperature in the upper 750 m from 36°36′ to 35°N during 2008, 36°30′ to 34°30′N during 2011, and 35°44′ to 34°19′N during 2012. A freefall towyo CTD (Underway CTD) was used to measure upper-500-m temperature and salinity every 14.8 km in the 2012 survey. During 2008, five Falmouth CTD profiles of temperature and salinity to 500-m and TurboMAP-II microstructure profiles to 300-m depth were collected every 28 km (Nagai et al. 2009). During 17–24 October 2009, five north–south transects were sampled across the Kuroshio to measure CTD and microstructure at 5–8 stations with 9-km resolution in each section (Nagai et al. 2012). During 2011 and 2012, five CTD and four TurboMAP-L (Doubell et al. 2009) profiles were collected every 9.3 km and expendable CTDs (XCTD) were dropped at the north and south ends of the transect.
To obtain salinity with the same resolution as XBT temperature, an optimal interpolation was performed for the CTD data with monthly salinity climatology from the World Ocean Atlas 2005 using 20 km and 40 m as horizontal and vertical decorrelation scales. Buoyancy is defined as b = −g(ρ − ρo)ρo−1, where ρ is the potential density calculated from temperature and salinity using the equation of state of seawater (EOS-80), the reference density ρo = 1025 kg m−3, and g is the gravitational acceleration. Turbulent kinetic energy dissipation rates are computed by integrating microscale shear spectra over the wavenumber band where they agree with the Nasmyth (1970) model spectrum—that is, from approximately 1 m down to twice the Kolmogorov scale.
Currents were measured using a 38.4-kHz Teledyne RD ADCP (30° beam angle, 3.6° beamwidth) and 130-kHz Furuno ADCP. During 2008, the Teledyne measured flows to 1218-m depth in 16-m bins with 16-m transmitted pulse length while, during 2011, it measured to 1018-m depth in 10-m bins with 11.59-m transmitted pulse length. The vertical wavenumber spectra for zonal ADCP shear uz(z) near the Kuroshio Front suggest signal attenuation around 30-m vertical wavelength (not shown) so that vertical shear on larger wavelengths is resolved.
During August 2011, the Kuroshio flowed along a relatively stable path with a strong eastward flow exceeding 2 m s−1 at the observational line (Fig. 2). The high-pressure warm-core eddy north of the Kuroshio (Fig. 2) provided confluent flow near the observation sites. During 2008, the Kuroshio was relatively unstable, exhibiting 100-km-scale meanders upstream of the transect (Fig. 1 of Nagai et al. 2009).
Satellite sea surface height (absolute dynamic topography) (color) of the Kuroshio Front east of Japan around 8 Aug 2011 superimposed with (i) geostrophic currents inferred from absolute dynamic topography (white arrows), (ii) the ship track (meridional thick black line), and (iii) the horizontal dimensions of the numerical domain in Fig. 5 (thin black lines). Topography of Honshu Island is shown in green shading.
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
b. Near-inertial shear
To isolate the spatial structure of near-inertial shear across the Kuroshio Front, residual shear is extracted by subtracting alongfront geostrophic shear
Meridional sections of (a) back-rotated observed zonal residual vertical shear
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1



(a),(b) Depth hodographs of back-rotated ageostrophic shear (10−3 s−1) along the (a) black–white–black solid vertical bar in the bottom left and (b) white–black–white vertical bar in the top right of Fig. 3a with depths indicated. (c),(d) Meridional hodographs along the (c) black–white–black and (d) white–black–white horizontal bar in Fig. 3a, with distances from the front indicated. Spline interpolation was used for the residual vertical shear in the meridional hodographs (c),(d).
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
During 2011, a typhoon passed 500 km south of the region two weeks prior to the observations, but the time elapsed since the storm far exceeds the 2–4-day time scale expected for propagation |Δr|/|Cg|, where r is the distance and Cg the group speed, or dissipation E/ε, where E is the inertial wave energy and ε is the dissipation rate of the waves. The wind during the 2011 cruise was weak with speeds of 5–10 m s−1. Results from a slab model (Pollard and Millard 1970) for mixed-layer inertial motions forced with reanalyzed hourly winds from the week prior to the typhoon (GPV-MSM-S of the Japan Meteorological Agency; Saito et al. 2006) show weaker cumulative wind power input to inertial motions (~1000 J m−2) compared to the near-inertial horizontal kinetic energy integrated between 100- and 750-m depth near the Kuroshio Front (~5000 J m−2; not shown).
In summary, observed bands of near-inertial shear (i) appear to be stronger near the front (Fig. 3a), (ii) recur from year to year as well as being found in other western boundary current fronts (Winkel et al. 2002; Rainville and Pinkel 2004; Inoue et al. 2010), and (iii) appear to be unrelated to surface forcing, though this cannot be established unequivocally with our limited data. Near-inertial waves can be trapped and amplified by frontal shears (Kunze 1985; Whitt and Thomas 2013) and wind-generated waves may stall in fronts long after forcing. While these alternative possibilities cannot be discounted based on available data, here these observations motivate numerical investigation into the hypothesis that the observed near-inertial shear arises from internal dynamics associated with frontogenesis (frontal strengthening) and frontolysis (frontal weakening) of the Kuroshio Front.
3. Model simulation of the Kuroshio Front
a. Model setup
We use the three-dimensional nonhydrostatic equation process study ocean model (PSOM) (Mahadevan et al. 1996a,b) to investigate generation of near-inertial waves by frontal instability. The model horizontal resolution is 1 km and domain dimensions 192 and 384 km in zonal (x) and meridional (y) directions, respectively. There are 64 vertical levels in the model with a flat bottom at 750-m depth. The vertical resolution is a few meters in the upper 150 m and telescopes from ~5 to 30 m between 150- and 750-m depth. Zonal boundaries are periodic while meridional boundaries rigid walls. Sponge layers of 35-km width along the north and south boundaries suppress reflection of propagating waves. The bottommost layer is also a sponge layer. Horizontal diffusivities are 500 m2 s−1 within the sponge layers and 1 m2 s−1 elsewhere. Within the north and south sponge layers, there is additional Rayleigh damping −αou with decay rate αo = 2 days−1 and velocity vector u. Based on vertical internal-wave energy fluxes, bottom generation of internal waves was found to be negligible in all of the simulations. Vertical diffusivities are 10−5 m2 s−1 everywhere. No hyperviscosities or hyperdiffusivities are used.
To provide realistic initial conditions for the modeled Kuroshio, the 2008 grid-averaged meridional density section (Nagai et al. 2009) is used. To suppress initial unbalanced disturbances in the simulation, temperature and salinity at each vertical level across the front are fitted with high-order polynomial functions. Potential densities calculated from temperature and salinity are then sorted to be vertically monotonic so as to remove any gravitationally unstable density inversions; density inversions are present in 3% of the original unsorted 1-m data. The resulting density field is linearly interpolated onto the 1-km horizontal model grid.
To induce a frontal meander, a sinusoidal fluctuation is introduced in the initial condition by shifting the initial vertical section meridionally by δy = A sin(xπ/Lx), where δy is the meridional displacement, A = 3 km is the displacement amplitude, x is the zonal coordinate, and Lx = 96 km is half the zonal wavelength. The velocity is initialized to be everywhere in geostrophic balance. The initial quasigeostrophic imbalance is quantified by computing the magnitude of the frontogenetic Q vector (
b. Evolution of the model flow field
As the model solution evolves, baroclinic instability generates a ~100-km-scale meander and eddy on a time scale of weeks. At this O(weeks) time in the simulation, model mesoscale fields (Fig. 5) are similar to those often observed in the Kuroshio Front (e.g., Fig. 1a in Nagai et al. 2009; Kouketsu et al. 2007). The magnitude of the model 30-h average confluence
Plan views of normalized 30-h running average surface vorticity
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
Plan views at 100-m depth of normalized 30-h running average horizontal divergence
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
To filter out the subinertial flow, Eulerian high-pass quantities are obtained by subtracting 30-h averages from instantaneous data, where 30 h was chosen because the lowest internal-wave frequencies are modulated by geostrophic shears (Kunze 1985; Whitt and Thomas 2013) and Doppler shifting in the Eulerian frame. The high-pass fields include both internal waves and Doppler-shifted subinertial structures; Eulerian 30-h high-pass velocity is strongly correlated with Eulerian high-pass pressure gradient (not shown), suggesting a significant contribution from thermal wind.
Frequencies in an Eulerian frame can be difficult to interpret dynamically owing to Doppler shifting by subinertial front and eddy flows. To characterize the frequencies of the banded structure in a Lagrangian frame, we introduce 10 000 virtual massless particles (drifters) near the center of the model front at 50–150-m depth. These particles are advected passively by the three-dimensional flow without influencing the dynamics. Four Lagrangian particles are selected as examples to record high-pass flow fields for 20 days as they pass through the region of strong banded signals that mostly lie along the main stream (Fig. 7a). The resulting Lagrangian rotary spectra are clockwise in time for frequencies between f and 2f (Figs. 8a and 8b), confirming that the banding in the Eulerian high-pass quantities is near-inertial waves. The relatively broad peaks in the spectra are likely caused by modulation of the lowest allowed internal-wave frequency by geostrophic vorticity (Kunze 1985) and baroclinicity (Mooers 1975; Whitt and Thomas 2013).
(a) Trajectories of four sample floats out of 10 000 released in the numerical simulation. (b) Lagrangian frequency spectra of normalized horizontal divergence
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
(a) Lagrangian spectral ratios of clockwise
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
Hodographs of residual shear (
Depth-time series of WKB-normalized residual (a) zonal shear
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
Unlike geostrophic motions, internal waves are associated with horizontal divergence ux + υy (Fig. 6; Müller and Siedler 1976; Lien and Müller 1992; Lelong et al. 1999; Plougonven and Snyder 2007; appendix B). High-pass horizontal divergences are strongly intensified after passage of a meander or eddy during days 10–11 (Figs. 6c,d and 10a). Such wave-intensifying events recur as the front evolves and subinertial confluent regions pass a fixed location (diamonds in Figs. 5c,d; Figs. 9 and 10). Divergence recorded by the particles provides several Lagrangian time series that also exhibit spectral peaks between f and 2f (Fig. 7b). Eulerian divergence spectra (dashed curve in Fig. 7b) show a greater dominance of subinertial variance, indicating that the near-inertial waves’ Eulerian frequency is subinertial, like internal lee waves, so these waves might be expected to be confined within the frontal jet and would not be identified as near inertial in fixed mooring measurements.
Depth-time series of normalized fluctuating (a) horizontal divergence
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
For a single propagating near-inertial wave, vertical vorticity
c. Internal-wave energy fluxes and flux divergences










(a) Top 30-m-averaged semi-Lagrangian 30-h mean
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
To average internal-wave energy flux over a typical 20-km wavelength (Figs. 5 and 6), a 20-km two-dimensional Gaussian horizontal average is applied. The resulting internal-wave energy-flux divergence is not sensitive to small changes in spatial and temporal filtering scales.
Large depth-integrated fluxes
Snapshot at day 11 from the model showing quasigeostrophic vertical kinetic energy VKEQG [(8)] in color, evaluated using 30-h semi-Lagrangian running averaged fields (except for frontal depth Hf) with energy fluxes superimposed (black arrows). Arrows are centered on their grid. Energy fluxes less than 0.5 kW m−1 are not shown. Blue contours are energy-flux divergence
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
Time-meridian plots of zonally averaged depth-integrated internal-wave energy (a) source (red), (b) sink (blue), and (c) net difference, (a)+(b), where internal-wave energy sources and sinks have been zonally averaged separately. Gray contours demark surface density. (d) Zonally and temporally averaged depth-integrated northward (red), southward (blue), and net meridional energy fluxes (black). (e) Zonally and temporally averaged depth-integrated internal-wave energy source (red), sink (blue), and net source (black) based on 30-h semi-Lagrangian high-pass quantities.
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
Local recurrent events of internal-wave generation, or internal-wave power gain
Zonally averaged depth-integrated positive values of the wave–mean flow interaction terms on the right-hand side of (2) show similar time variability and magnitudes to the internal-wave energy source (Figs. 14a and 13a). This is confirmed by the positive correlation coefficient of 0.89 with a near-zero p value between internal-wave energy source and positive interaction terms (Fig. 14b), indicating dynamical consistency. Normal Reynolds-stress deformation terms
(a) Time evolution of positive zonally averaged depth-integrated interaction terms on the right-hand side of (2). Gray contours demark surface density. (b) Scatterplot of internal-wave energy source and positive zonally averaged depth-integrated interaction terms. Data exceeding 1.5 standard deviations are excluded from these. The black line represents bin-averaged interaction terms as a function of internal-wave energy source. Gray shading indicates one standard deviation. The bottom sponge layer is excluded in these calculations.
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
d. Model internal-wave energy sinks and dissipation rates
Similarly, negative values of the right-hand side of (2) agree with the internal-wave energy sinks (Figs. 15a and 13b) with the normal-stress terms once more dominating over the off-diagonal horizontal shear-stress terms and by an order of magnitude over other interaction terms. Thus, subinertial (QG) confluence both emits and absorbs near-inertial waves.
(a) Time evolution of negative zonally averaged depth-integrated interaction terms on the right-hand side of (2) similar to Fig. 14a. (b) Time evolution of zonally averaged depth-integrated internal-wave energy dissipation rate, the last term of (2). (c) Scatterplot of internal-wave energy sink and negative zonally averaged depth-integrated interaction terms. Data exceeding 1.5 standard deviations are excluded from these. Solid lines represent bin-averaged values as a function of internal-wave energy sink for (red) interaction terms, (black) internal-wave energy dissipation rates, (blue) downward internal-wave energy flux above the bottom sponge layer, and (green) total loss terms on the right-hand side of (2) including downward internal-wave energy flux. Gray shadings are 1 standard deviation. The bottom sponge layer is excluded in these analyses.
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1




These results suggest that, in our numerical simulations, spontaneous internal-wave energy is generated then reabsorbed by the submesoscale subinertial flow (Booker and Bretherton 1967; Polzin 2008, 2010) with only 5–10% dissipating. Both wave energy generation and loss are dominated by normal-stress interaction terms
e. Summary of modeling results
Motivated by in situ measurements of elevated near-inertial shear and turbulent kinetic energy dissipation in the Kuroshio, numerical experiments were conducted that spontaneously emit internal waves (Fig. 12) from an unforced model Kuroshio Front with properties consistent with near-inertial waves. The simulations find similar banded shear along frontal isopycnals (Figs. 3c and 3d) as the observations (Figs. 3a and 3b). Lagrangian frequencies of these banded features are (1–2)f. The estimated average internal-wave power gain within 200 km of the Kuroshio Front is O(0.01) W m−2 (Fig. 13e) with little energy escaping the front (Fig. 13d). The bulk of the internal-wave energy appears to be reabsorbed within 50–100 km north and south of the source regions (Fig. 13e) with little lost to explicit model dissipation. This implies that most of the subinertial (QG) energy lost to internal waves is redistributed rather than dissipating. Evidence that the model internal-wave energy, energy fluxes, and their divergences and convergences based on the high-pass fields are dominated by internal waves comes from (i) the Lagrangian spectra, (ii) the spatial and temporal rotary properties of the residual shears, (iii) absence of correlation between Lagrangian high-pass velocity and pressure gradient, and (iv) that geostrophically balanced flows have no energy-flux convergence associated with them (3).
4. Discussion
The previous laboratory study by Williams et al. (2008) estimated that 1.5 TW could be lost from the wind-driven circulation to spontaneous generation of near-inertial waves globally, while Ferrari and Wunsch (2009) suggested a more modest 0.35 TW based on Polzin’s (2010) momentum transfer coefficients, and Thomas (2012) extrapolated 0.1 TW from analytic theory. To quantify the global contribution of gross inertial-wave generation and reabsorption from our simulations, we now estimate the global power transferred to the internal-wave field from the subinertial flow and back again using a two-step process. First, a scaling relation between the internal-wave energy source
a. Scaling for the quasigeostrophic vertical kinetic energy (VKEQG)













b. Relation between VKEQG and 














List of parameters governing VKEQG, where
(a) Top 70 percentile 10-day average internal-wave energy sources (internal-wave power gain
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
c. Global estimation of internal-wave power gain
We next use the 0.1°-resolution global OFES simulation to estimate VKEQG [(8)] and thence
Global distribution of (a) the gross internal-wave power gain
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
List of the estimated global internal-wave power gain for OFES with lower and upper bound values of
5. Conclusions
Banded shear signals are observed in the Kuroshio Front under calm summer conditions (Fig. 3a). The residual shear has rotary properties in depth and time (Fig. 4), consistent with propagating near-inertial waves. Previous work (Williams et al. 2008; Polzin 2010; Thomas 2012) has suggested that frontal instabilities could transfer energy out of the quasigeostrophic flow field into near-inertial waves at rates of 0.1–1.5 TW, suggesting that this mechanism could represent a major sink for the large-scale balanced circulation.
These results motivated numerical simulations of an unforced meandering Kuroshio Front which spontaneously generates large-amplitude near-inertial internal waves associated with frontogenesis/frontolysis. Internal-wave energy is generated at a rate of O(10) mW m−2, about 10 times higher than estimated in the North Pacific Subtropical Front (Alford et al. 2013). Global estimates of the spontaneous internal-wave generation are 0.36 TW based on a scaling [(10)] between internal-wave power gain
Directly measured TKE dissipation rates during August 2008, October 2009, August 2011, and August 2012, averaged over 80–250-m depth and within 30 km of the Kuroshio Front, are over 10−8 W kg−1, which is an order of magnitude larger than the similarly averaged model subgridscale kinetic energy dissipation rates (Fig. 18). We emphasize that our model is unforced and contains no internal waves at the outset so that all waves originate from the initially geostrophically balanced flow through frontal instability. In the ocean, superposition of frontally generated waves with the background wave field from winds and tides may allow more of the spontaneously generated near-inertial wave energy to be dissipated before it can be reabsorbed as in the numerical model. But wind-forced near-inertial waves may also be trapped and dissipated in fronts so we cannot be certain whether dissipation rates are much larger in the ocean than in the model because of wind-forced or spontaneously generated near-inertial waves.
(a) Upper-300-m-depth-averaged σθ as a function of meridional distance y relative to the Kuroshio Front from 2008, 2009, 2011, and 2012 density measurements (solid) and model density (dashed), and (b) 80–250-m-depth-averaged dissipation rates ε as a function of meridional distance y relative to the Kuroshio Front from 2008, 2009, 2011, and 2012 fine- and microstructure measurements (solid) and model inferences of total kinetic energy dissipation rates,
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
Scalings from QG vertical kinetic energy VKEQG [(10)–(11)] provide an empirical parameterization that might be used for global models with sufficient resolution. However, more direct observations and modeling are needed to identify and understand spontaneous generation of the near-inertial internal waves, elucidate how much spontaneously generated wave energy dissipates through wave breaking versus being reabsorbed, and verify that (10) and (11) parameterize these mechanisms in climate models. The question of how the wind-induced large-scale circulation dissipates remains.
Acknowledgments
We thank Captain Noda and crews of R.T.V Umitaka-maru, Captain Ukekura and crews of R/V Natsushima, Dr. Sasaki at JAMSTEC for OFES outputs, JSPS (KAKENHI 24684036), “The Study of Kuroshio Ecosystem Dynamics for Sustainable Fisheries (SKED)” supported by MEXT, MIT-Hayashi Seed Fund, ONR (Awards N000140910196 and N000141210101), NSF (Award OCE 0928617, 0928138) for support, and two anonymous reviewers for their insights.
APPENDIX A
Sensitivity to Model Resolution
Previous work has shown that model resolution impacts the amplitude and frequency of internal-wave generation in atmospheric fronts (Plougonven and Snyder 2007). Divergences ux + υy at 100-m depth differ little between 1000-, 750-, and 500-m-resolution PSOM runs. Near-inertial convergence and divergence is most frequently observed in highly confluent regions of order ~10-km wide, regardless of resolution (Fig. A1).
Comparison of horizontal divergence of the full velocity
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
A histogram shows that divergence approaches ±0.8f at 1000-m resolution and ±f at 750- and 500-m resolution (Fig. A2). The extreme values occupy 0.02% and 0.04% of the model domain for 750- and 500-m-resolution runs, respectively. A quantile–quantile plot shows that the difference in the distribution of divergence between 500- and 1000-m-resolution runs only becomes noticeable for divergence magnitudes |ux + υy| > 0.5f. The Kolmogorov–Smirnov test shows that the null hypothesis of equal distribution between 1000- and 500-m-resolution cases is rejected with 95% confidence intervals (p value: 4.7 × 10−100) because of large extreme values at 500-m resolution (Fig. A2).
(a) Scatterplot of normalized horizontal divergence of the full velocity
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
The vertical velocity at 100-m depth shows more similarity among the three resolutions (Fig. A3), although the same null hypothesis is rejected (p value: 9.3 × 10−31) because w is skewed toward stronger downwelling (Mahadevan and Tandon 2006) in the 500-m-resolution run (Fig. A3). Stronger downwelling is associated with superinertial w′ mostly by internal waves in highly stratified simulations initialized with summer observation data. Here, 8.2% (1.6%) of the data points differ in flow divergence ux + υy (vertical velocity w) between 1000- and 500-m resolution by more than one standard deviation. Compared to the 1000-m run, the magnitude of the power gain increases by as much as 6% and 11% at 750- and 500-m runs. However, the timing and locations of the sources and sinks are indistinguishable among different resolutions. These results suggest that our 1-km model resolution is sufficient to simulate near-inertial wave generation by the unstable Kuroshio Front, though it may underestimate the power transfer from balanced flow to internal waves by up to 10%.
As in Fig. A2, but for vertical velocity (10−3 m s−1) at 100-m depth.
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
APPENDIX B
Sensitivity to Depth of the Model Domain
Our PSOM model domain is limited to 750 m vertically. The real Kuroshio region has a depth of about 4000 m. The depth of the domain may alter baroclinic instability and associated confluence fields, which are important for wave generation. Although the mesoscale meander takes several weeks longer to develop in a 2000-m-deep domain than the 750-m domain, the 2000-m simulations exhibit similar banded structures in horizontal divergence, signifying generation of internal waves (Fig. B1). Downward propagation of the waves below 1000-m depth and their reflection from the bottom are seen, because the bottom sponge layer is removed for simulations with 2000-m model depth. The results from the 2000-m-depth model scale identically to the 750-m domain for the internal-wave power gain [(6)], suggesting that the scaling law can be applied regardless of domain depth (Fig. 16) and results from the global OFES model are still valid.
Comparison of near-inertial horizontal divergence
Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0086.1
APPENDIX C
Hydrostatic versus Nonhydrostatic
We also ran the hydrostatic primitive equation ROMS model (Shchepetkin and McWilliams 2005) to examine internal-wave generation by meandering fronts. This model was initialized with the same August 2008 density section (section 3a). The model’s horizontal resolution is ~1000 m and uses 100 vertical levels. No explicit diffusion is included. Banding in horizontal divergence emerges at the meander trough and crest with similar magnitude and wavelengths as the PSOM simulations, suggesting that inertial-wave generation is hydrostatic.
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