1. Introduction
The global hotspot for near-inertial wind power is located at 40°N (Alford 2003) just east of Japan and the Kuroshio–Oyashio confluence. During fall and winter, a dozen tropical cyclones, typhoons, and cold-weather outbreaks pass over the region, generating the bulk of global near-inertial power (D’Asaro 1985). A 15%–25% fraction of this wind power radiates equatorward as low-vertical-mode near-inertial waves, implying that the larger fraction dissipates locally (e.g., Furuichi et al. 2008). How and where this fraction is dissipated remains unknown, but the two most likely locales are the surface layer and upper pycnocline.
Storm-forcing generates surface-layer inertial oscillations of large horizontal scale that will not propagate into the pycnocline since the vertical group velocity
Since eddies focus or eject near-inertial waves, they will impact the distribution of wave breaking and turbulence. Previous microstructure measurements in anticyclones have found turbulence to be reduced in the upper core and enhanced near the core base and edges (Lueck and Osborn 1986; Kunze et al. 1995; Sheen et al. 2015, Qi et al. 2021). Whalen et al. (2018) inferred higher dissipation rates in anticyclones than in cyclones based on a finescale strain parameterization for turbulence to the Argo float dataset. Sanford et al. (2021) examined the evolution of near-inertial waves near the velocity maximum of a Sargasso Sea anticyclone where eddy confluence is strong and may influence wave trapping (Bühler and McIntyre 2005; Polzin 2008). However, microstructure measurements in eddies have tended to focus on strong signals at the base of the core while the eddy perimeter near the radius of maximum velocity is underobserved.
The paper layout is as follows: section 2 describes the float dataset, the Kuroshio–Oyashio confluence, and analysis methods. Section 3 describes the mesoscale anticyclonic eddy and typhoon forcing. Storm-forced generation of surface-layer near-inertial oscillations is described in section 4 and near-inertial wave packet propagation into the pycnocline and interaction with the eddy in section 5. Ray-tracing simulations in a model anticyclonic eddy are performed in section 6. Section 7 describes four distinct layers of turbulence variability and relates these to the near-inertial shear measurements and ray-tracing results. Results are summarized in section 8.
2. Experiment and analysis methods
a. Kuroshio–Oyashio confluence experiment
Three pairs of Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats were deployed in the Kuroshio–Oyashio confluence off the east coast of Japan during August 2016 to measure the upper-ocean response to storm forcing through subsequent fall and winter (Fig. 1a). The region lies just west of the global inertial wind power maximum at 40°N, 160°E–180° (Alford 2003) and is bound by the warm Kuroshio to the south and cold Oyashio to the north. It contains coherent anticyclonic eddies spun off from the Kuroshio and is subject to multiple storms, especially during fall and winter.
(a) Trajectories of six EM-APEX floats deployed east of Japan during late 2016. Floats 7788 (red) and 7787 (yellow) were trapped on the perimeter of an anticyclone near the radius of maximum and are subject of analysis here. (b) Photograph of an EM-APEX profiling float with Seabird Electronics SBE-41 CTD (T, S, P), two pairs of electromagnetic velocity sensors (u, υ), and a pair of FP07 microstructure temperature probes (χ) mounted on top.
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
The float sampling strategy was a compromise between saving battery power to prolong the mission and profiling fast enough to resolve near-inertial wave evolution during and after storms. By monitoring near-real-time weather forecasts from the Japan Meteorological Agency, profiling rates were adjusted before the arrival of storms to profile continuously between surface and target depth, collecting a ∼500-m roundtrip every ∼1.5 h at ∼0.14 m s−1 ascent and descent speeds, fully resolving near-inertial waves. During weak wind forcing, floats were programmed to only profile twice per inertial period to capture inertial wave signals, parking between 600 and 1200 m to save power when not profiling. This approach is effective if the velocity is dominated by balanced and near-inertial motions as here where internal tides are weak.
This analysis will focus on measurements taken by two floats deployed within an anticyclonic eddy (floats 7787 and 7788 in Fig. 1). Float 7788 was trapped in the eddy during its entire 3-month mission while float 7787 escaped after 1 month. Additional shipboard acoustic Doppler current profiler (ADCP), conductivity–temperature–density (CTD), and microstructure measurements aboard R/V Shinsei-maru provide further context of ocean conditions in the vicinity of float trajectories during the deployment cruise.
b. EM-APEX floats
EM-APEX floats (Fig. 1b) measure finescale horizontal velocity (u, υ) with ∼5-m resolution, temperature T, and salinity S with 2–3-m resolution, and microscale temperature-variance dissipation rate χ with 1-m resolution as a function of depth in a semi-Lagrangian frame following the average water movement over the 0–500-m profiling depth range in this experiment. Velocity is inferred from voltage difference across an insulating body due to the electric field induced by ocean currents moving through Earth’s magnetic field (Sanford et al. 2005, 2011). FP07 (https://rocklandscientific.com/) thermistors on each float, as well as deployment of float pairs, allow cross comparison of microstructure measurements to ensure quality of turbulence estimates. While at the sea surface, floats obtain their GPS positions, transmit data, and receive new mission instructions via Iridium satellites. All EM-APEX measurements were quality controlled and compared with neighboring floats and shipboard measurements when possible.
c. EM-APEX float velocity measurements
1) Correction for magnetic declination and unknown
Magnetic declination is corrected to transform measured float velocity from geomagnetic to geographic coordinates. Float velocity measurements u are relative to an unknown depth-independent velocity offset
2) Near-inertial filtering
The ∼1.5-h profiling period allows measured total horizontal velocity utot to be decomposed into subinertial usub and near-inertial uNI components. Irregular sampling in time is resampled to a 2-h target sampling interval using a piecewise cubic interpolating polynomial. To retrieve the near-inertial component, velocities are bandpass-filtered using a fifth-order Butterworth filter with cutoff frequencies 0.8f and 1.2f centered around the Coriolis frequency
d. Thermal diffusivity and turbulent dissipation rate
FP07s were deployed in pairs, yielding two estimates per float. Data were omitted when probes failed. Several tests were used to only retain well-behaved vertical wavenumber spectra following in Lien et al. (2016). Bad values were removed using χ, background
e. Available potential energy
f. Near-inertial wave energy flux
Horizontal and vertical energy fluxes on resolved vertical wavelengths were computed using floats’ synchronous profiles of density and velocity following Kunze et al. (2002). Near-inertial energy fluxes are covariances of near-inertial velocity uNI and near-inertial baroclinic reduced pressure anomaly
Near-inertial vertical velocities are estimated as
Based on normal vertical modes calculated from historical deep CTD casts (Gill 1984; Eriksen 1988), modes n ≥ 5 are expected to be resolved with the 500-m float profiles while lower-mode variability is not captured. Removal of the linear fits will remove more than 80% of variance of the unresolved modes, n < 5. HYCOM simulations suggest that more than half of the wind-forced near-inertial energy and energy flux will be in modes higher than 5 (Raja et al. 2022). The depth-invariant
g. Reanalysis wind stress
Wind speed, direction, and wind stress from the reanalysis forecasting model NCEP CFSv2 (Saha et al. 2010; Saha et al. 2014) are used to quantify surface forcing during storms. Reanalysis wind stress and wind speed have 0.25° horizontal and 1-h temporal resolution. Wind-work τ ⋅ u is computed using reanalysis wind stress τ interpolated onto the float trajectories and float-measured near-surface currents u.
3. Background conditions
a. Eddy characteristics
Two EM-APEX floats were deployed in a strong anticyclonic mesoscale eddy on 26 August 2016 (Fig. 2a). Satellite altimetry from AVISO (www.aviso.altimetry.fr) (Le Traon et al. 1998) reveals a ∼120-km-diameter eddy with a minimum sea surface vorticity of −0.3f at eddy center and −0.2f to −0.1f near the float trajectories at the eddy perimeter. Floats circle the eddy center at about 90% of the radius of maximum azimuthal velocity. Vertical profiles of area-averaged vorticity estimated from float velocity measurements using the circulation theorem along float trajectories’ (Fig. 2b) find a nearly homogeneous vorticity layer of −0.25f at 50–200-m depth, below which it weakens rapidly over a depth scale of
Eddy structure from (a) AVISO sea level anomaly (SLA) derived vertical vorticity with superimposed ship track of the R/V Shinsei-maru (red) and the two float trajectories, 28 Aug–3 Sep 2016 (black and gray dotted). (b) Vertical profiles of time-averaged shear squared S2 and stratification N2 measured by the two floats (left), and area-averaged vorticity (right) computed from floats’ velocity using the circulation on multiple float orbits and from ADCP by averaging vorticity over the longitude range of the eddy. (c) Zonal and (d) meridional velocity sections from shipboard ADCP. (e) One-component vorticity approximation
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
Shipboard ADCP measurements along a zonal section through the eddy are consistent with AVISO and float measurements (Figs. 2c–e). Section-averaged shipboard ADCP-derived vorticity agrees with area-averaged float vorticity (Fig. 2b). There are subsurface velocity maximum and one-component vorticity extremum at 100 m depth with decay below. However, due to the ∼1-day time lag between shipboard ADCP measurements and the nearest float measurements, the exact float position within the eddy relative to the ADCP section is uncertain.
b. Storm forcing
Typhoons Mindulle (category 1) and Lionrock (category 4) with wind speeds exceeding 30 m s−1 and lateral extents of several hundred kilometers, passed over the eddy with the eye of the storms skirting its western edge (Fig. 3). Mindulle traveled on a southwest–northeast trajectory and came within 50 km of the eddy on 22 August, four days prior to the floats’ deployment. Lionrock traveled on a south-southeast–north-northwest trajectory and came closest to the floats on 30 August.
Weather maps of Typhoons (a) Mindulle on 22 Aug and (b) Lionrock on 30 Aug 2016 east of Japan from 6-hourly CFSv2 reanalysis. Wind speed and direction shown with colored shading and wind barbs (one barb denotes 10 m s−1 winds), respectively. Red dots mark the positions of the typhoons’ eyes at 6-h intervals and red lines show their approximate tracks. Overlaid in blue are the trajectories of the two floats, 28 Aug–3 Sep 2016.
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
As propagating low pressure systems, Mindulle and Lionrock generate a near-inertial upper-ocean response due to resonant wind-work on ocean surface currents on the right side of their propagating tracks (e.g., Price 1981, D’Asaro 1985), that is, directly over the eddy. At the time of eddy encounter, Lionrock had higher wind speed (∼30 m s−1), and a more clearly defined maximum velocity core than Mindulle (∼22 m s−1), which had weakened along the Japanese coast (Fig. 3).
4. Near-inertial wave generation
a. Local and remote waves
Profile time series of near-inertial velocity uNI suggest the presence of two near-inertial wave packets (Figs. 4d,e), (i) one at 150–200-m depth, remotely generated by northward-moving Mindulle, and (ii) one in the mixed layer and upper pycnocline, locally generated by Lionrock. Figures 4b and 4c show that the floats circled the eddy in 5 days per cycle. Near-inertial velocity is 5 times smaller than the background eddy velocity.
(a) Time series of wind stress τ and wind-work τ ⋅ u from CFSv2 reanalysis and the shallowest float velocity u. (b),(c) Profile time series of total zonal utot and meridional υtot velocity. (d),(e) Profile time series of near-inertial zonal uNI and meridional υNI velocity. (f) Profile time series of near-inertial horizontal kinetic energy HKENI. Red arrows in (f) delineate the approximate downward-propagating wave packets generated by Mindulle and Lionrock.
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
Generation of the Mindulle wave packet was not directly measured. Its generation time is estimated to be 4–5 days prior to the float deployments by assuming a constant downward-propagating speed based on the wave packet’s change in depth with time (Fig. 4f) in agreement with Mindulle’s passage by the eddy’s western perimeter. Generation by the later northward Lionrock was captured by the floats. On 30 August (Fig. 4a), reanalysis wind stress exceeded 1 N m−2 and wind-work 1 W m−2. Near-inertial energy increased rapidly in the ∼80-m-thick surface mixed layer during the first few days after Lionrock’s passage due to resonant generation of inertial oscillations. In contrast to the Mindulle wave packet, this packet is mostly confined to the surface layer and only weakly energizes the upper pycnocline.
While both storm eyes skirt the western side of the eddy, their inertially resonant right-hand sides lie directly over the eddy (Fig. 3). Because Typhoons Mindulle and Lionrock propagate in different directions, near-inertial wave trains generated by these two typhoons should initially also have different propagation directions, i.e., the Mindulle-generated wave train toward the north-northeast and the Lionrock-generated wave train toward the north-northwest. Advection by the eddy and interactions with its vorticity and Doppler shifting are expected to change their propagation directions and properties. Wave propagation in the direction of the flow will tend to reduce the trapping tendency by the vorticity, i.e., expanding the trapping radius or allowing escape (Kunze 1985). This will be further investigated with ray-tracing simulation in section 6.
5. Propagation and interaction
a. Vertical propagation
The descending subsurface Mindulle-generated wave packet is the most prominent signal in near-inertial velocity, with its maximum HKENI propagating from shallower than 200-m depth on 29 August to deeper than 210 m on 1 September (Figs. 4d–f). It is dominated by upward phase propagation, consistent with downward energy propagation. Isotachs of the downward-propagating packet are almost vertical at the beginning but become slanted with time (Figs. 4d,e), consistent with an increasing vertical wavenumber.
Inertially back-rotated (a) velocity phase θu and (b) vertical wavenumber m based on velocity phase. The line plots in (a) are example profiles taken at marked times and depths (black horizontal and vertical lines) in the contour plots. Trending positive in time (blue–white–red) implies subinertial frequencies while trending negative with depth (red–white–blue) implies downward energy propagation. The line plot in (b) is the near-inertial kinetic energy-weighted vertical wavenumber mHKE.
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
We estimate vertical wavenumber as
The observed enhancement of near-inertial velocity, shear, and vertical wavenumber at 200–300 m depth implies wave amplification which might arise from radial caustics or vertical critical layers due to slowing group velocities or superposition of incident and reflected waves. Group velocities pass through zero at caustics while they approach zero at critical layers. Critical layers have been observed and simulated at the base of eddy cores (Kunze 1986; Kunze et al. 1995; Lelong et al. 2020; Sanford et al. 2021), whereas the turning-point caustics expected on the lateral peripheries of anticyclonic cores have rarely been studied. Ray-tracing simulations in section 6 aim to unravel wave physics near the eddy’s velocity maximum, differentiate critical layers from caustics and compare with float-measured properties.
b. Kinetic and potential energy conversion
To understand the relative roles of radiation and dissipation as the two wave packets transit the floats, we examine the time rate change of horizontal kinetic energy HKE and available potential energy APE.
In the surface mixed layer, HKE increases at rates of
Profile time series of inertially smoothed (a) near-inertial horizontal kinetic energy HKE, (b) available potential energy APE, and (c) time rates of change
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
At 200–300-m depth in the pycnocline, the descending HKE packet appears on 29 August and disappears on 1–2 September (Fig. 6c) at rates of
The time rate of change of APE is one order of magnitude weaker than that of horizontal kinetic energy, as expected for near-inertial waves. It is largest in the mixed layer, has larger vertical scales, and exhibits a similar descent slope and downward-propagating phase as the envelope of near-inertial HKE (Fig. 4f) but is too weak a signal to interpret reliably. Between 200- and 300-m depth,
c. Inward and downward NI energy fluxes
High-mode horizontal and vertical energy fluxes are computed following the method discussed in section 2. In the upper 200 m, radial energy fluxes are inward toward eddy center (Fig. 8). Azimuthal fluxes are slightly biased cyclonic against the flow and vertical fluxes primarily downward (Figs. 7, 8). Below 200 m, radial fluxes are still predominantly inward, though again are outward in the southwest while vertical fluxes are mostly upward, and azimuthal energy fluxes mostly cyclonic, though both azimuthal directions are seen.
Inertially smoothed (a) azimuthal, (b) radial, and (c) vertical energy fluxes. Center panels show profiles of the associated time-averaged energy fluxes. Right panels show histograms of all data (blue) and above 200-m depth (yellow). Positive azimuthal fluxes are cyclonic, positive radial fluxes are outward away from the eddy center.
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
Vectors of inertially smoothed horizontal energy fluxes (〈u′p′〉, 〈υ ′p′〉) averaged over (a) 0–50 m (mixed layer), (b) 50–250 m, and (c) 250–500 m. The scale in each panel is shown by a black quiver and color denotes time. Approximate storm track directions of Typhoons Lionrock and Mindulle (Fig. 3) are shown in green.
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
Azimuthal and radial energy fluxes of
Between 200 and 250 m, azimuthal and inward radial energy fluxes increase with depth, while vertical energy fluxes change sign. The strongest vertical gradient in vertical and radial energy fluxes occurs at about 200 m, coinciding with the depth of increasing vertical wavenumber (Fig. 5), shear squared, and turbulent dissipation rate (Fig. 12). Interpretation of this variability will be presented in section 6. Horizontal gradients of energy fluxes are unknown so energy flux divergence cannot be evaluated.
Horizontal energy fluxes are averaged in the surface mixed layer, upper pycnocline, and lower pycnocline (Fig. 8). In all three layers, energy fluxes are southward at the northwestern edge, opposite to the storms’ propagation directions and inward to the eddy center, outward in the southwest. These waves could be trapped by anticyclonic vorticity. Turning-point reflection or refraction inward is expected by the large radial vorticity and velocity gradients (Doppler-shifting) on the eddy perimeter (Kunze 1985; Asselin et al. 2020) and will be explored with ray-tracing simulations in the next section.
6. Ray-tracing simulations
To gain insight into how storm-forced near-inertial wave packets interact with an anticyclone near the eddy’s radius of maximum velocity, ray-tracing simulations of surface-generated near-inertial waves propagating in a model anticyclone were performed. The eddy is modeled as steady Gaussian reduced pressure anomaly
Map of surface vorticity (color) and ray paths (black) with the radius of maximum velocity rVmx, eddy radial length scale r0, and maximum vorticity rZmx marked by the three green dotted circles. Rays escaping the eddy are not displayed. Rays are advected azimuthally around the anticyclone by the flow but with little dynamical impact other than filling the anticyclonic core.
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
In baroclinic geostrophic shear flow, the wavevector k evolves following (6.1) due to gradients in the
-
flow (i.e., Doppler shifting k ⋅ V) (Olbers 1981),
-
vorticity ζ through fe (Mooers 1975; Kunze 1985; van Meurs 1998; Asselin et al. 2020),
-
buoyancy frequency N2 (Munk 1981), and
-
horizontal buoyancy gradients Bx and By (Mooers 1975; Kunze 1985; Whitt and Thomas 2013).
Changes in the wavevector k lead to changes in Eulerian group velocity CgE = ∇kωE = ∇kωL + V and hence wave amplitude and ray path r orientation.
Test waves are initiated on a horizontal grid at the sea surface spanning the model eddy. Initial meridional and vertical wavelengths are 300 km and 50 m, corresponding to passing storms and mixed layer thickness, respectively. Initial Lagrangian frequencies are ∼1.05fe and maximum Doppler shifts ∼±0.2f. Initial propagation is northward, set by the storms’ propagation direction, but strong interactions with the axisymmetric anticyclone eradicate this information as the waves radiate into the pycnocline and are advected around the eddy (Fig. 9). Ray-tracing equations (6.1) and (6.2) are integrated for one year to explore wave evolution in the eddy with a focus on behavior near the velocity maximum and time scales similar to those of the float measurements. Since measured near-inertial wave packets appear to have length scales smaller than the eddy (Figs. 4, 6), modeling them as radial/azimuthal modes (e.g., Kunze and Boss 1998; Llewellyn Smith 1999) is not appropriate, so wavenumbers and ray paths are integrated in Cartesian coordinates. Eulerian frequencies ωE are invariant as expected in a steady background field. Lagrangian frequencies ωL are largely above the effective Coriolis frequency and asymptote to fe with time, while horizontal wavenumbers kh tend to decrease, vertical wavenumbers m increase and group velocities Cg decrease (not shown). Lagrangian frequencies ωmin < ωL < fe are only found near radial turning-point cusps (<1%).
Some waves escape the anticyclone, usually those propagating with the mean flow, so are not considered further. Waves trapped in the negative vorticity core are advected azimuthally by eddy velocities (Fig. 9). Azimuthal advection has little dynamical impact because the eddy gradients affecting wave evolution are only nonzero with radius r and depth z. Thus, results will be presented with all azimuths collapsed onto the radial-depth plane, i.e., cylindrical coordinates.
Near-surface interactions with eddy vorticity and flow gradients preferentially turn radial wavenumbers inward so that trapped waves propagate downward and toward the eddy core’s center (Fig. 10), consistent with float-measured inward energy fluxes (Fig. 8). In contrast to Asselin et al. (2020) and Thomas et al. (2020), Doppler-shifting’s influence is comparable to vorticity in this evolution because the storms have imprinted finite initial horizontal wavenumber.
Depth–radius sections of vorticity (colored shading as in Fig. 9), isopycnals (green dotted), isotachs (red dotted), and ray paths (black solid). Waves escaping the anticyclone are not displayed. (a) Starting at the surface, rays propagate inward and downward, pass through the eddy center (r = 0, note that they are not reflected at the eddy center but pass through it) to propagate outward until reflected inward at turning-point caustics where ωL = ωmin inside r0. Near the radius of maximum velocity rVmx, interaction geometry results in a turning-point shadow zone in the upper half of the eddy (blue box) and turning points in the lower half [red box inset blown up in (b)]. (b) Turning-point cusps are tilted upward by sloping isopycnals so that radial reflection is parallel to isopycnals [green box inset blown up in (c)]. (c) Outward-radiating waves encounter two caustics. The first (a) lies just inside the upturned turning-point cusp (b), corresponding to radial wavenumber and vertical group velocity passing through zero (changing sign) and ωL passing through fe. The second (b) is the more prominent turning-point cusp at slightly larger radii associated with ωL grazing the minimum frequency ωmin, as well as radial and vertical group velocities changing sign as the wave is reflected inward toward the eddy center.
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
The rays pass through the center of the eddy (apparent “reflection” at r = 0 in Fig. 10a) to radiate outward until they are reflected inward by turning points (cusps) near the radius of maximum velocity (Fig. 10a). In the upper half of the eddy near its perimeter, propagation and trapping geometry produce a turning-point shadow zone because of initial inward radiation due to vorticity refraction (Fig. 10a). This is consistent with weak near-inertial shear and turbulence at shallower depths found in the float measurements (section 7, Fig. 11). In the lower half of the eddy near the perimeter, the interaction geometry produces turning points (Fig. 10c) where measured turbulence is elevated (section 7, Fig. 11). Turning points at greater depths occur at larger radii because these waves originate at the surface at larger radii, and hence larger fe and ωL (Fig. 10a).
Schematic of observed turbulence distribution in the anticyclonic eddy. (a) Storm-generated turbulence in the mixed layer. (b) Layer of reduced turbulence. (c) Patches of intense inertial-period turbulence. (d) Turbulence due to near-inertial wave amplification at turning-point caustics. (e) Enhanced turbulence layer at the base of the eddy (not sampled).
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
Trapped outward-propagating rays encounter two caustics where group velocities transiently pass through zero (Figs. 10b,c). The first (A, Fig. 10c) is associated with the radial wavenumber and vertical group velocity passing through zero (changing sign) and ωL passing through fe. Radial propagation continues outward, and the vertical wavenumber remains positive. The second is at slightly larger radii associated with the more visible upturned turning-point cusps (B, Fig. 10c) where the ray path reflects radially inward parallel to isopycnals. Here, the Lagrangian frequency grazes the minimum frequency, and both radial and vertical group velocities change sign (Fig. 10). The vertical wavenumber m remains positive and diapycnal group velocity negative (toward decreasing buoyancy) throughout. The two caustics are in such close proximity compared to horizontal wavelengths as to be indistinguishable.
At both caustics, vorticity gradients are the primary agents of radial wavenumber evolution with Doppler shifting, stratification and isopycnal slopes playing secondary roles (not shown). Based on 10 000 test waves seeded at different positions on the surface and with different initial horizontal and vertical wavenumbers, trapped-wave caustic behavior near the radius of maximum velocity is relatively insensitive to initial wave conditions, including setting the initial zonal and meridional wavenumber to zero to eliminate Doppler shifting. This is because, by the time waves encounter turning points at depth, strong interactions with the axisymmetric eddy have eradicated their initial conditions.
Wave amplification is expected at turning-point caustics both because of (i) transiently diminished group velocities and (ii) superposition of outward incident and inward reflected waves (Bender and Orszag 1978). Therefore, if incident waves are marginally stable, superposition will tend to create unstable shears and turbulent dissipation as measured by the floats in the lower half of the eddy (section 7).
In summary, the geometry of trapping in ray-tracing simulations is consistent with (i) measured inward energy flux (Fig. 8), (ii) a turning-point shadow zone in the upper half of the eddy perimeter (Fig. 10) compatible with weak measured near-inertial shear and turbulence in the upper pycnocline (Figs. 12, 13), and (iii) turning points in the lower half of the eddy perimeter where wave amplification due to superposition of radially incident and reflected waves could lead to elevated wave breaking and turbulence production as observed (section 7). Gradients in vorticity are the primary agents for wavenumber evolution near the radius of velocity maximum, with gradients in Doppler shifting, stratification and isopycnal slopes playing secondary roles. Near-inertial critical-layer stalling [defined as where m → ∞, Cg → 0 with time, as occurs at the base of the ring’s core (Kunze 1986; Kunze et al. 1995)] does not arise near the radius of maximum velocity or over the
Profile time series of (a) zonal near-inertial vertical shear uz, (b) total near-inertial shear squared S2, (c) buoyancy frequency squared N2, (d) gradient Froude number
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
Time-averaged vertical profiles of total (blue) and high turbulence patches bracketed by red vertical lines in Fig. 12 (orange) of (a) turbulent kinetic energy dissipation rate ε, (b) shear squared S2, (c) buoyancy frequency squared N2, (d) gradient Froude number δN = S/N, (e) vertical wavenumber m, (f) normalized vertical vorticity
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
7. Turbulence production
Turbulent kinetic energy dissipation rates ε inferred from float microstructure temperature measurements (section 2d) reveal four distinct turbulent layers near the anticyclone’s perimeter (Figs. 11–13) modulated by near-inertial wave propagation, amplification, and breaking of the two recently generated near-inertial wave packets and eddy vertical shear.
a. Mixed layer strong dissipation
Turbulent kinetic energy dissipation rates are highest in the surface mixed layer during storm passage with
b. Layer of suppressed turbulence
Turbulent dissipation rates ε ∼ 10−10 W kg−1 and thermal diffusivities
Vertical averages between the base of mixed layer and 300-m depth of (a) turbulent dissipation rates ε and (b) thermal diffusivities kT along float trajectories in the Kuroshio–Oyashio confluence during 2016 and 2017. Both ε and kT are reduced by more than one order of magnitude inside anticyclonic eddies and increase by more than an order of magnitude upon exiting anticyclones.
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
Near-inertial shear squared S2 and gradient Froude numbers S/N are also weaker in this depth range (Figs. 13b,d). The ray-tracing simulations of the previous section suggest that the upper eddy perimeter is a turning-point shadow zone for trapped near-inertial waves (Fig. 10a). suggesting that mechanisms for amplifying wave shear are weak in this depth range.
c. Patches of intense turbulence
Small-scale inertial-period turbulence patches with ε ∼ 10−8 W kg−1 and kT ∼ 10−4 m2 s−1 occur in 150–300 m (Figs. 12e, 13, 15). The turbulence patches appear to be associated with the remote wave packet generated by Typhoon Mindulle. They correspond to when near-inertial and subinertial vertical shear are aligned to elevate gradient Froude number above critical (δN > 2), leading to shear instability (Figs. 15a,e,f). Near-inertial waves provide 2–10 times as much shear as the eddy.
Profile time series between 150- and 250-m depth of (a) turbulent dissipation rate ε, (b) shear squared S2, (c) direction of subinertial shear
Citation: Journal of Physical Oceanography 52, 11; 10.1175/JPO-D-21-0278.1
Diminished inertial-period stratification N2 also coincides with the inertial-period turbulence patches (Figs. 12, 13, 15). This stratification variability
Since the turbulent patches are generated as a superposition of subinertial and near-inertial shear (Fig. 15), both near-inertial and subinertial energy should be dissipated. Approximate decay time scales are
Time-average profiles (i) over the entire record and (ii) over intervals of intense turbulence show that the inertial-period turbulent patches between 210- and 280-m depth (Fig. 15a) coincide with elevated shear squared S2, gradient Froude number δN, vertical vorticity gradient magnitudes |∂ζ/∂z| and vertical wavenumber kz, as well as reduced stratification N2 (Fig. 15). Elevated near-inertial shear at these depths may be due to the superposition of incident and reflected waves at a radial turning point near the eddy perimeter (Fig. 10).
d. Turning-point caustics
Turbulence ε ∼ 10−8 W kg−1 is also enhanced below the inertial-period patches, below 300-m depths (Figs. 12, 13, 15) despite decaying stratification N2 and shear squared S2. This again may be due to near-inertial wave amplification through superposition of incident and reflected waves at a radial turning point near the eddy perimeter (Fig. 10). But at these depths, superposition of near-inertial and eddy vertical shear does not modulate turbulence.
e. Microstructure summary
To summarize the microstructure measurements, while past measurements have reported the strongest concentration of turbulent dissipation in critical layers at the base of the eddy center (Lueck and Osborn 1986; Kunze et al. 1995; Joyce et al. 2013), here, the floats found both reduced and elevated turbulence on the previously undersampled perimeter of a mesoscale anticyclone. Interactions with radial gradients of vorticity are expected to trap near-inertial waves in the anticyclone’s core (section 6). The geometry of trapping produces a turning-point shadow zone in the upper half of the eddy perimeter (Fig. 10a) which appears to coincide with the layer of weak measured turbulence (Fig. 12e). Likewise, radial turning-point reflection in the lower half of the eddy perimeter (Fig. 10a) can explain the elevated turbulence (Figs. 12e, 13, 15) through amplification of near-inertial shear by transiently slow group velocities as well as the superposition of incident and reflected waves. Also found were inertial-period turbulence patches (Fig. 12e) due to periodic alignment of superposed inertial and eddy vertical shears (Fig. 15).
8. Summary
Two EM-APEX floats deployed in the Kuroshio–Oyashio confluence during fall 2016 were trapped near the radius of the velocity maximum of an anticyclonic eddy with minimum vorticity −0.3f and maximum velocity exceeding 1 m s−1 (Figs. 1, 2). Float measurements captured two storm-forced near-inertial wave packets (Figs. 3, 4), one generated remotely by Typhoon Mindulle on 22 August 2016 before the float deployments and the other generated locally by Typhoon Lionrock on 30 August 2016 during float measurements.
Inertially back-rotated phase increases with time at a rate of 180° per 4 days, implying a subinertial near-inertial frequency fe = 0.9f (Fig. 5), which is consistent with the blue shift by surface negative vorticity ζ ∼ −0.2f of the anticyclonic eddy so the waves will be trapped in the anticyclone (Perkins 1976; Kunze 1985) and expected to encounter radial turning points within the eddy perimeter (Kunze 1985). The vertical wavenumber, inferred from the vertical variation of phase, is positive (downward energy propagation) in the upper 300 m and elevated in 150–300-m depth (Fig. 5).
In the pycnocline, the time rate of change of HKE is nearly two orders of magnitude greater than local dissipation rates ε (Fig. 6), suggesting that horizontal passage of laterally confined high-vertical-wavenumber wave packets through the float measurements by lateral propagation or relative advection.
Horizontal energy fluxes are inward toward the eddy center (Figs. 7, 8), suggesting reflection or refraction of northward-propagating near-inertial waves from northern eddy perimeter, consistent with the tendency for turning-point reflection (Fig. 10) and near-inertial refraction toward more negative effective Coriolis frequency fe ∼ f + ζ/2 (Kunze 1985; van Meurs 1998; Asselin et al. 2020; Thomas et al. 2020).
Ray-tracing simulations in an idealized model eddy find that near-inertial wave behavior near the eddy rim is largely controlled by radial gradients in eddy vorticity and velocity (Doppler shifting), causing trapping in the negative vorticity core through inward refraction and reflection at radial turning points (Figs. 9, 10). Near the radius of velocity maximum, rays are directed inward, consistent with observations (Fig. 8). A turning-point shadow zone in the upper half of the eddy perimeter where trapped waves are absent (Fig. 10a) is consistent with weak measured near-inertial and turbulent signals in the upper pycnocline (Figs. 12, 13). Turning points in the lower half of the eddy perimeter (Fig. 10a) are expected to lead to elevated wave shear and turbulence, as observed (Figs. 12, 13), due to transient slowing of group velocities and the superposition of incident and reflected waves (Bender and Orszag 1978).
Turbulence measured on the anticyclonic eddy perimeter exhibits four distinct layers (Figs. 12–15):
-
Surface-layer turbulence is the strongest as a result from the direct surface forcing. It is likely underestimated because of nonlocal surface-forced turbulence (Large et al. 1994) and unreliability of local parameterizations when stratification is weak (Osborn and Cox 1972; Osborn 1980).
-
Between 50 and 150 m, turbulence dissipation rates ε are reduced by more than an order of magnitude, and finescale shear is also weak compared to outside the eddy. Ray tracing predicts that the upper part of the eddy perimeter is a turning-point shadow zone (Fig. 10) so there may be no mechanism to amplify near-inertial shear and turbulence production.
-
Between 150 and 300 m, inertial-period patches of enhanced turbulence have ε ∼ 10−8 W kg−1 and kT ∼ 10−4 m2 s−1 due to superposition of near-inertial and eddy shears, as well as near-inertially reduced stratification, periodically leading to shear instability and wave breaking.
-
Below 300 m, persistent turbulence ε ∼ 10−8 W kg−1 can be explained by radial turning points in the lower half of the eddy perimeter (Fig. 10). Shear amplification is expected near turning points because of transiently vanishing group velocities and the superposition of incident and reflected waves.
This paper described the first detailed measurements of both fine- and microstructure on the rim of an anticyclonic eddy that allow examination of how turning points of recently generated vortex-trapped near-inertial waves amplify shear and turbulence. The geometry of wave trapping (Fig. 10) produces a turning-point shadow zone in the upper part of the eddy perimeter where weak shear and turbulence are found. In the lower part of the eddy perimeter, near-inertial shear and turbulence are amplified by turning-point reflections. Superposition of near-inertial and eddy shear also leads to inertial-period modulation of turbulence. Dissipative time scales for the eddy are predicted to be longer than one year, and the wave packet ∼
The measurements presented here were in depth–time near the eddy’s radius of maximum velocity. The ray-tracing simulations suggest that more could be learned about turning-point structure, behavior, and turbulence with radial-depth surveys as a potential future area of research.
Acknowledgments.
The authors would like to express their special thanks to the captain and crew of the Japanese R/V Shinsei-maru from which the EM-APEX floats were deployed and to Avery Snyder and John Dunlap for preparation, operation, and mission management of floats. This work is funded by NSF Grant OCE-1459173 and Grant in Aid for Scientific Research on Innovative Areas (Ministry of Education, Culture, Sports, Science and Technology [MEXT] KAKENHI JP15H05818, JP15H05823, and JP15K21710).
Data availability statement.
The EM-APEX float data are available at the University of Washington ResearchWorks Archive (http://hdl.handle.net/1773/48128). The real-time weather forecasts are distributed by the Japan Meteorological Agency (http://www/jma.gp.jp/jma/). Data products from the Climate Forecast System version 2 (CFSv2) can be found on the UCAR/NCAR Research Data Archive (https://rda.ucar.edu/datasets/ds094.0/). Daily AVISO sea level anomaly is distributed by CMEMS (https://resources.marine.copernicus.eu/).
REFERENCES
Alford, M. H., 2003: Improved global maps and 54‐year history of wind‐work on ocean inertial motions. Geophys. Res. Lett., 30, 1424, https://doi.org/10.1029/2002GL016614.
Althaus, A. M., E. Kunze, and T. B. Sanford, 2003: Internal tide radiation from Mendocino escarpment. J. Phys. Oceanogr., 33, 1510–1527, https://doi.org/10.1175/1520-0485(2003)033<1510:ITRFME>2.0.CO;2.
Anderson, D. L. T., and A. E. Gill, 1979: Beta dispersion of inertial waves. J. Geophys. Res. Oceans, 84, 1836–1842, https://doi.org/10.1029/JC084iC04p01836.
Asselin, O., L. N. Thomas, W. R. Young, and L. Rainville, 2020: Refraction and straining of near-inertial waves by barotropic eddies. J. Phys. Oceanogr., 50, 3439–3454, https://doi.org/10.1175/JPO-D-20-0109.1.
Bender, C. M., and S. Orszag, 1978: Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill, 593 pp.
Bühler, O., and M. E. McIntyre, 2005: Wave capture and wave-vortex duality. J. Fluid Mech., 534, 67–95, https://doi.org/10.1017/S0022112005004374.
D’Asaro, E. A., 1985: The energy flux from the wind to near-inertial motions in the surface mixed layer. J. Phys. Oceanogr., 15, 1043–1059, https://doi.org/10.1175/1520-0485(1985)015<1043:TEFFTW>2.0.CO;2.
D’Asaro, E. A., 1995: Upper-ocean inertial currents forced by a strong storm. Part II: Modeling. J. Phys. Oceanogr., 25, 2937–2952, https://doi.org/10.1175/1520-0485(1995)025<2937:UOICFB>2.0.CO;2.
D’Asaro, E. A., and H. Perkins, 1984: A near-inertial internal wave spectrum for the Sargasso Sea in late summer. J. Phys. Oceanogr., 14, 489–505, https://doi.org/10.1175/1520-0485(1984)014<0489:ANIIWS>2.0.CO;2.
D’Asaro, E. A., C. C. Eriksen, M. D. Levine, C. A. Paulson, P. Niiler, and P. van Meurs, 1995: Upper-ocean inertial currents forced by a strong storm. Part I: Data and comparisons with linear theory. J. Phys. Oceanogr., 25, 2909–2936, https://doi.org/10.1175/1520-0485(1995)025<2909:UOICFB>2.0.CO;2.
Dosser, H. V., and L. Rainville, 2016: Dynamics of the changing near-inertial internal, wave field in the Arctic Ocean. J. Phys. Oceanogr., 46, 395–415, https://doi.org/10.1175/JPO-D-15-0056.1.
Eriksen, C. C., 1988: On wind forcing and observed oceanic wave number spectra. J. Geophys. Res., 93, 4985–4992, https://doi.org/10.1029/JC093iC05p04985.
Furuichi, N., T. Hibiya, and Y. Niwa, 2008: Model‐predicted distribution of wind‐induced internal wave energy in the world’s oceans. J. Geophys. Res., 113, C09034, https://doi.org/10.1029/2008JC004768.
Garrett, C., 2001: What is the “near-inertial” band and why is it different from the rest of the internal wave spectrum? J. Phys. Oceanogr., 31, 962–971, https://doi.org/10.1175/1520-0485(2001)031<0962:WITNIB>2.0.CO;2.
Gill, A. E., 1984: On the behavior of internal waves in the wakes of storms. J. Phys. Oceanogr., 14, 1129–1151, https://doi.org/10.1175/1520-0485(1984)014<1129:OTBOIW>2.0.CO;2.
Gregg, M. C., E. A. D’Asaro, J. J. Riley, and E. Kunze, 2018: Mixing efficiency in the ocean. Annu. Rev. Mar. Sci., 10, 443–473, https://doi.org/10.1146/annurev-marine-121916-063643.
Holliday, D., and M. E. Mcintyre, 1981: On potential energy density in an incompressible, stratified fluid. J. Fluid Mech., 107, 221–225, https://doi.org/10.1017/S0022112081001742.
Joyce, T. M., J. M. Toole, P. Klein, and L. N. Thomas, 2013: A near‐inertial mode observed within a Gulf Stream warm‐core ring. J. Geophys. Res. Oceans, 118, 1797–1806, https://doi.org/10.1002/jgrc.20141.
Kang, D., and O. Fringer, 2010: On the calculation of available potential energy in internal wave fields. J. Phys. Oceanogr., 40, 2539–2545, https://doi.org/10.1175/2010JPO4497.1.
Klein, P., S. Llewellyn Smith, and G. Lapeyre, 2004 Organization of near-inertial energy by an eddy field. Quart. J. Roy. Meteor. Soc., 130, 1153–1166, https://doi.org/10.1256/qj.02.231.
Kunze, E., 1985: Near-inertial wave propagation in geostrophic shear. J. Phys. Oceanogr., 15, 544–565, https://doi.org/10.1175/1520-0485(1985)015<0544:NIWPIG>2.0.CO;2.
Kunze, E., 1986: The mean and near-inertial velocity fields in a warm-core ring. J. Phys. Oceanogr., 16, 1444–1461, https://doi.org/10.1175/1520-0485(1986)016<1444:TMANIV>2.0.CO;2.
Kunze, E., and E. Boss, 1998: A model for vortex-trapped internal waves. J. Phys. Oceanogr., 28, 2104–2115, https://doi.org/10.1175/1520-0485(1998)028<2104:AMFVTI>2.0.CO;2.
Kunze, E., R. W. Schmitt, and J. M. Toole, 1995: The energy balance in a warm-core ring’s near-inertial critical layer. J. Phys. Oceanogr., 25, 942–957, https://doi.org/10.1175/1520-0485(1995)025<0942:TEBIAW>2.0.CO;2.
Kunze, E., L. K. Rosenfeld, G. S. Carter, and M. C. Gregg, 2002: Internal waves in Monterey Submarine Canyon. J. Phys. Oceanogr., 32, 1890–1913, https://doi.org/10.1175/1520-0485(2002)032<1890:IWIMSC>2.0.CO;2.
Lamb, K. G., 2008: On the calculation of the available potential energy of an isolated perturbation in a density-stratified fluid. J. Fluid Mech., 597, 415–427, https://doi.org/10.1017/S0022112007009743.
Large, W. G., J. C. McWilliams, and S. C. Doney, 1994: Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization. Rev. Geophys., 32, 363–403, https://doi.org/10.1029/94RG01872.
Leaman, K. D., and T. B. Sanford, 1975: Vertical energy propagation of inertial waves: A vector spectral analysis of velocity profiles. J. Geophys. Res., 80, 1975–1978, https://doi.org/10.1029/JC080i015p01975.
Lee, D.-K., and P. P. Niiler, 1998: The inertial chimney: The near-inertial energy drainage from the ocean surface to the deep layer. J. Geophys. Res., 103, 7579–7591, https://doi.org/10.1029/97JC03200.
Lelong, M.-P., Y. Cuypers, and P. Bouruet-Aubertot, 2020: Near-inertial energy propagation inside a Mediterranean anticyclonic eddy. J. Phys. Oceanogr., 50, 2271–2288, https://doi.org/10.1175/JPO-D-19-0211.1.
Le Traon, P. Y., F. Nadal, and N. Ducet, 1998: An improved mapping method of multisatellite altimeter data. J. Atmos. Oceanic Technol., 15, 522–534, https://doi.org/10.1175/1520-0426(1998)015<0522:AIMMOM>2.0.CO;2.
Lien, R.-C., T. B. Sanford, S. Jan, M.-H. Chang, and B. B. Ma, 2013: Internal tides on the East China Sea continental slope. J. Mar. Res., 71, 151–185, https://doi.org/10.1357/002224013807343461.
Lien, R.-C., T. B. Sanford, J. A. Carlson, and J. H. Dunlap, 2016: Autonomous microstructure EM-APEX floats. Methods Oceanogr., 17, 282–295, https://doi.org/10.1016/j.mio.2016.09.003.
Lighthill, M. J., 1978: Waves in Fluids. Cambridge University Press, 504 pp.
Llewellyn Smith, S. G., 1999: Near-inertial oscillations of a barotropic vortex: Trapped modes and time evolution. J. Phys. Oceanogr., 29, 747–761, https://doi.org/10.1175/1520-0485(1999)029<0747:NIOOAB>2.0.CO;2.
Lueck, R., and T. Osborn, 1986: The dissipation of kinetic energy in a warm‐core ring. J. Geophys. Res., 91, 803–818, https://doi.org/10.1029/JC091iC01p00803.
Mooers, C. N. K., 1975: Several effects of a baroclinic current on the cross‐stream propagation of inertial‐internal waves. Geophys. Fluid Dyn., 6, 245–275, https://doi.org/10.1080/03091927509365797.
Munk, W. H., 1981: Internal waves and small scale processes. The Evolution of Physical Oceanography: Scientific Papers in Honor of Henry Stommel, B. A. Warren and C. Wunsch, Eds., MIT Press, 264–291.
Nash, J. D., M. H. Alford, and E. Kunze, 2005: Estimating internal wave energy fluxes in the ocean. J. Atmos. Oceanic Technol., 22, 1551–1570, https://doi.org/10.1175/JTECH1784.1.
Olbers, D. J., 1981: The propagation of internal waves in a geostrophic current. J. Phys. Oceanogr., 11, 1224–1233, https://doi.org/10.1175/1520-0485(1981)011<1224:TPOIWI>2.0.CO;2.
Osborn, T. R., 1980: Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr., 10, 83–89, https://doi.org/10.1175/1520-0485(1980)010<0083:EOTLRO>2.0.CO;2.
Osborn, T. R., and C. S. Cox, 1972: Oceanic fine structure. Geophys. Fluid Dyn., 3, 321–345, https://doi.org/10.1080/03091927208236085.
Perkins, H., 1976: Observed effect of and eddy on inertial oscillations. Deep-Sea Res. Oceanogr. Abstr., 23, 1037–1042, https://doi.org/10.1016/0011-7471(76)90879-2.
Polzin, K. L., 2008: Mesoscale eddy/internal-wave coupling I: Symmetry, wave capture and results from the Mid-Ocean Dynamics Experiment. J. Phys. Oceanogr., 38, 2556–2574, https://doi.org/10.1175/2008JPO3666.1.
Price, J., 1981: Upper ocean response to a hurricane. J. Phys. Oceanogr., 11, 153–175, https://doi.org/10.1175/1520-0485(1981)011<0153:UORTAH>2.0.CO;2.
Qi, Y., H. Mao, X. Wang, L. Yu, S. Lian, X. Li, and X. Shang, 2021: Suppressed thermocline mixing in the center of anticyclonic eddy in the north South China Sea. J. Mar. Sci. Eng., 9, 1149, https://doi.org/10.3390/jmse9101149.
Raja, K. J., M. C. Buijsman, J. F. Shriver, B. K. Arbic, and O. Siyanbola, 2022: Near-inertial wave energetics modulated by background flows in a global model simulation. J. Phys. Oceanogr., 52, 823–840, https://doi.org/10.1175/JPO-D-21-0130.1.
Saha, S., and Coauthors, 2010: The NCEP Climate Forecast System Reanalysis. Bull. Amer. Meteor. Soc., 91, 1015–1058, https://doi.org/10.1175/2010BAMS3001.1.
Saha, S., and Coauthors, 2014: The NCEP Climate Forecast System version 2. J. Climate, 27, 2185–2208, https://doi.org/10.1175/JCLI-D-12-00823.1.
Sanford, T. B., J. H. Dunlap, J. A. Carlson, D. C. Webb, and J. B. Girton, 2005: Autonomous velocity and density profiler: EM-APEX. Proc. IEEE/OES Eighth Working Conf. on Current Measurement Technology, Southampton, UK, IEEE, 152–156, https://doi.org/10.1109/CCM.2005.1506361.
Sanford, T. B., J. F. Price, and J. B. Girton, 2011: Upper-ocean response to Hurricane Frances (2004) observed by profiling EM-APEX floats. J. Phys. Oceanogr., 41, 1041–1056, https://doi.org/10.1175/2010JPO4313.1.
Sanford, T. B., B. B. Ma, and M. H. Alford, 2021: Stalling and dissipation of a near‐inertial wave (NIW) in an anticyclonic ocean eddy: Direct determination of group velocity and comparison with theory. J. Geophys. Res. Oceans, 126, e2020JC016742, https://doi.org/10.1029/2020JC016742.
Sheen, K. L., J. A. Brearley, A. C. Naveira Garabato, D. A. Smeed, L. St. Laurent, M. P. Meredith, A. M. Thurnherr, and S. N. Waterman, 2015: Modification of turbulent dissipation rates by a deep Southern Ocean eddy. Geophys. Res. Lett., 42, 3450–3457, https://doi.org/10.1002/2015GL063216.
Thomas, L. N., L. Rainville, O. Asselin, W. R. Young, J. Girton, C. B. Whalen, L. Centurioni, and V. Hormann, 2020: Direct observations of near‐inertial wave ζ‐refraction in a dipole vortex. Geophys. Res. Lett., 47, e2020GL090375, https://doi.org/10.1029/2020GL090375.
van Meurs, P., 1998: Interactions between near-inertial mixed layer currents and the mesoscale: The importance of spatial variabilities in the vorticity field. J. Phys. Oceanogr., 28, 1363–1388, https://doi.org/10.1175/1520-0485(1998)028<1363:IBNIML>2.0.CO;2.
Whalen, C. B., J. A. MacKinnon, and L. D. Talley, 2018: Large-scale impacts of the mesoscale environment on mixing from wind-driven internal waves. Nat. Geosci., 11, 842–847, https://doi.org/10.1038/s41561-018-0213-6.
Whitt, D. B., and L. N. Thomas, 2013: Near-inertial waves in strongly baroclinic currents. J. Phys. Oceanogr., 43, 706–725, https://doi.org/10.1175/JPO-D-12-0132.1.
Young, W. R., and M. Ben Jelloul, 1997: Propagation of near-inertial oscillations through a geostrophic flow. J. Mar. Res., 55, 735–766, https://doi.org/10.1357/0022240973224283.