Evidence of enhanced double-diffusive convection below the main stream of the Kuroshio Extension
Abstract
In this study, a Navis-MicroRider microstructure float and an EM-APEX float were deployed along the Kuroshio Extension Front. The observations deeper than 150 m reveal widespread interleaving thermohaline structures for at least 900 km along the front, presumably generated through mesoscale stirring and near-inertial oscillations. In these interleaving structures, microscale thermal dissipation rates χ are very high
(
K2s−1), while turbulent kinetic energy dissipation rates ϵ are relatively low
(
Wkg−1), with effective thermal diffusivity
of
(
m2s−1) consistent with the previous parameterizations for double-diffusion, and,
is two orders of magnitude larger than the turbulent eddy diffusivity for density
. The average observed dissipation ratio Γ in salt finger and diffusive convection favorable conditions are 1.2 and 4.0, respectively, and are larger than that for turbulence. Our results suggest that mesoscale subduction/obduction and near-inertial motions could catalyze double-diffusive favorable conditions, and thereby enhancing the diapycnal tracer fluxes below the Kuroshio Extension Front.
1 Introduction
Fronts are ubiquitous in coastal and open oceans. They are sites of along-isopycnal stirring [Okubo, 1970; MacVean and Woods, 1980; Ledwell et al., 1998; Smith and Ferrari, 2009; Badin et al., 2011], diapycnal mixing [Thomas and Lee, 2005; Nagai et al., 2009, 2012; D'Asaro et al., 2011], watermass formation and subduction [Pollard and Regier, 1992; Rudnick, 1996; Nurser and Zhang, 2000]. Oceanic fronts are formed by across-front contrasts in seawater properties, such as temperature and salinity, which are often associated with the across-front density differences and along-frontal jets [Uda, 1938]. These jets exhibit meanders caused by barotropic and baroclinic instabilities, from which many mesoscale eddies emanate.
Since subinertial motions due to mesoscale stirring move water mostly along the sloping isopycnals constituting fronts, they are ineffective in stirring the density laterally, but efficient at stirring temperature and salinity when their isopleths are inclined to isopycnals, as is the case for the Kuroshio Extension Front (Figures 1 and 2). Consequences of the lateral stirring are filaments of temperature and salinity, which have no density signatures [Rudnick and Ferrari, 1999; Ferrari and Rudnick, 2000], so called T-S compensated filaments. Because these mesoscale eddy-induced filamentations are driven by confluent flows due to eddy convolutions and mesoscale meanders of fronts, T-S compensated anomalous features can be subducted on the dense side and obducted on the light side of a front [Hoskins and Bretherton, 1972]. As a result, T-S compensated filaments of temperature and salinity are frequently observed as tongue like structures roughly along sloping isopycnal of fronts [e.g., Nagai et al., 2012].

Satellite sea surface temperature on 18 July 2013 with trajectories of (blue) the EM9032 and (cyan) Navis-MR. Digits along the EM9032 trajectory indicate days after the deployment. Black line represents across-front transect shown in Figures 4a, 4c, 4e, and 5.

Potential temperature-salinity plot for data obtained (red) by an EM9032 deployed along the main stream of the Kuroshio Extension Front and (black) from across-frontal CTD surveys. Black and blue contours are for isopycnals and isolines of the spiciness [Flament, 2002], respectively.
An alternative mechanism of forming the T-S compensated filaments is double-diffusive intrusion [Stommel and Fedorov, 1967; Stern, 1967; Garrett, 1982]. The intrusion is driven by density flux divergence due to larger density flux by salt fingers than that due to diffusive convection. The typical vertical thickness of the intrusion is 10–100 m [Toole and Georgi, 1981]. Because these intruding layers are formed by processes driven by molecular diffusion, the tracer variance inversely cascade up to the filament scales. May and Kelley [1997] have suggested that when such double-diffusive intrusions occur in baroclinic fronts, slopes of the isopycnal of fronts affect the growth of the interleaving, depending on the density gradient along the intrusion. Previous studies have also pointed out that vertical shear due to frontal currents and near-inertial waves could suppress salt-finger fluxes by deforming salt fingers into two-dimensional horizontal laminae [Kunze, 1990; Stern et al., 2001; Smyth and Kimura, 2007; Radko, 2013]. Although the effects of vertical shear on the salt-finger fluxes remain unclear, as the timescales of subinertial (days) or near-inertial rotation (day) and onset of salt-finger (minutes) are rather decoupled, suppression effect due to shear is probably limited to that caused by deformation of the salt fingers into two dimensional sheets (by a factor of 2–2.5) [Radko, 2013].
In contrast to the inverse cascade double-diffusive intrusion scenario, Haynes and Anglade [1997] demonstrated the forward cascade of tracer variance; they showed that it is vertical mixing that dissipates tracer variance and limit the horizontal scale of filaments, under the simultaneous thinning effects of horizontal confluence and vertical shear. Ferrari and Polzin [2005] analyzed data obtained from the North Atlantic Tracer Release Experiment (NATRE) [Ledwell et al., 1998], and showed that the average rate of change in the thermal variance is dominated by the balance between variance input from mesoscale lateral stirring and average thermal dissipation below 800 m depth, where intermediate and Mediterranean waters convolve, consistent with the former mesoscale lateral stirring scenario, and an oceanic analog of Haynes and Anglade [1997]. Smith and Ferrari [2009] have also shown that vertical shear and mixing near fronts are crucial to cascade tracer variance in a realistic mesoscale stirring field. This is illustrated as in Smith and Ferrari [2009] by a steady-state equation for tracer C,
, assuming a barotropic tracer front under the confluent flow,
, where y and v are across-front distance and flow, α confluence, and subscripts represent derivatives, with isotropic turbulent eddy diffusivity K. Based on the values estimated from NATRE data [Ledwell et al., 1998],
s−1 and
m2s−1, a horizontal scale of a filament
is only 6 m, which is much smaller in width than that reported from the observations, 300 m [Smith and Ferrari, 2009], highlighting the important contribution from KCzz, where z is vertical coordinate, which is omitted in the above barotropic argument. Further, they show numerically that vertical mixing is important and sufficient to dissipate the tracer variance at these fine vertical scales, which, in turn, limits the horizontal scale of filaments, consistent with the arguments of Haynes and Anglade [1997]. Irrespective of whether interleaving structures or T-S filaments are caused by mesoscale lateral stirring or double diffusive intrusion, these filamentations are very important for lateral fluxes. Ruddick et al. [2010] developed and tested a model of lateral thermal mixing for all forms of fine thermal structures, and found good agreement with the observations near a Meddy front.
It is important to note that the lateral stirring can generate streaks of T-S compensated filaments, but not new watermasses. Microscale mixing accompanied by vertical or diapycnal fluxes, is required to form new watermasses. One such watermass forms in the Kuroshio-Oyashio confluent regions [Yasuda et al., 1996; Joyce et al., 2001; Kouketsu et al., 2007]. When the warm-salty Kuroshio water is convolved by mesoscale meanders and eddies with the cold-fresh Oyashio water, North Pacific Intermediate Water (NPIW) is formed internally and eventually spreads all through the subtropical North Pacific [Yasuda et al., 1996; Joyce et al., 2001; Kouketsu et al., 2007]. However, the mechanism of how the Oyashio water is mixed internally with the Kuroshio water to form an intermediate watermass has been elusive [Yasuda et al., 1996; Joyce et al., 2001; Kouketsu et al., 2007].
Two fundamental vertical mixing processes that dissipate tracer variances and form new watermasses are (1) mechanical turbulent mixing and (2) double-diffusive convective mixing. Diapycnal mechanical mixing in the ocean interior is associated with breaking of internal waves. Although internal waves are ubiquitous in the stratified ocean, high turbulent dissipation rates have previously been measured at very few locations associated with internal-wave generation, most of which are close to the bottom, lateral, or surface boundaries [St. Laurent et al., 2001; Naveira Garabato et al., 2004]. In contrast, recent in-situ observations during calm summer conditions show very large turbulent kinetic energy dissipation rates in the thermocline under the main stream of the Kuroshio [Nagai et al., 2009]. Repeated observations revealed dissipation rates in the Kuroshio thermocline on average 10–100 times greater than typical thermocline values, which were accompanied by near-inertial internal-wave velocity shear along isopycnals [Nagai et al., 2015]. Winds are the primary power source of near-inertial waves. However, recent theoretical, numerical, laboratory and field studies have suggested that frontal instabilities can spontaneously emit near-inertial internal waves by geostrophic adjustment [Snyder et al., 1993; Plougonven and Snyder, 2005, 2007; Williams et al., 2008; Danioux et al., 2012; Alford et al., 2013; Shakespeare and Taylor, 2014; Nagai et al., 2015]. Irrespective of whether they are spontaneously or wind generated, because near-inertial internal waves can be trapped and amplified by geostrophic horizontal [Kunze, 1985] and vertical shear [Mooers, 1975; Whitt and Thomas, 2013], enhanced turbulent kinetic energy dissipation observed with banded shear can be attributed to breaking of near-inertial waves under the Kuroshio, although Nagai et al. [2015] showed numerically that most of the spontaneously generated near-inertial waves are reabsorbed into subinertial flow, without inducing significant kinetic energy dissipation and turbulent mixing.
Even with no turbulence, tracers in the ocean interior can be mixed vertically by double-diffusive convection [Schmitt, 1981; Schmitt and Georgi, 1982; St. Laurent and Schmitt, 1999; Merryfield, 2005; Schmitt et al., 2005]. The effects of double-diffusion are often seen as the characteristic thermohaline staircases in the deep sea. Several numerical studies have suggested that double-diffusion significantly influences the meridional overturning circulation [Gargett and Holloway, 1992; Gargett and Ferron, 1996; Zhang et al., 1998]. In the Kuroshio-Oyashio Mixed Water Region, Talley and Yun [2001] found that salt fingering has significant influences in setting the watermass properties of Oyashio water. In the same region, Inoue et al. [2007] directly confirmed the occurrence of double diffusion when turbulence was weak, and parameterized diffusivities due to double diffusion, using microstructure measurements. Schmitt [1999] points out that widespread patterns with density ratio
in the surface mixed layer, increasing to
in the midlatitude thermocline, are suggestive of ubiquitous double-diffusion occurrence. Here density ratio is defined as
, where α and β are coefficients of heat and salt expansion of seawater, vertical gradients of potential temperature Θz and salinity Sz.
Several studies pointed out that double-diffusion plays a role in supplying nutrients to the upper layers [Hamilton et al., 1989; Oschlies et al., 2003; Dietze et al., 2004]. Oschlies et al. [2003] estimated from a coarse resolution numerical model that salt-finger driven nutrient supply to the euphotic layer is as large as that due to turbulence and mesoscale eddies. However, these previous studies could have underestimated the nutrient flux, because they were based on the thermohaline distributions computed by a rather coarse resolution model.
In contrast, a recent field study at the Agulhas Current suggested that thermohaline interleaving structures are generated also by near-inertial oscillations with relatively small vertical wavelengths ∼200 m [Beal, 2007]. Because fronts are often associated with large variations of spiciness, and they are also the sites of near-inertial wave generations caused by wind, spontaneous adjustment, amplification and trapping, and because near-inertial wave induced oscillating currents are nearly along isopycnal, it is plausible that near-inertial waves provide an additional mechanism to cause T-S compensated filaments [Beal, 2007].
In this study, we report observations which indicate that vertical shear of near-inertial internal waves as well as subinertial flow could create interleaving thermohaline structures along the main stream of the Kuroshio Front, accompanied by very large microscale thermal dissipation rates with weak turbulence, suggesting that subinertial stirring and near-inertial shear promote double-diffusive convection and forward cascade of tracer variance.
The manuscript is organized as follows. §2 describes field observations. In §3, we show that observed thermohaline structure under the main stream of the Kuroshio Extension Front exhibits subinertial and near-inertial variability similar to Smith and Ferrari [2009] and Beal [2007]. These interleaving thermohaline structures are accompanied by strong microscale thermal dissipation rates (§4). Estimated effective thermal diffusivity is compared with the previous parameterizations for double-diffusive convection in §5, followed by the conclusions (§6).
2 Observations
During July 2013, we measured temperature, salinity, pressure, current velocity, microscale turbulent kinetic energy dissipation rates ϵ, and microscale thermal dissipation rates χ along the Kuroshio Extension Front using autonomous profiling floats and across the Kuroshio with a shipboard ADCP (38KHz Teledyne RDI) and a tow-yo CTD (Underway-CTD, Teledyne Oceanscience, Carlsbad, USA). Three EM-APEX floats (Teledyne Webb Research, North Falmouth, USA) [Sanford et al., 2011] were deployed to measure horizontal currents, temperature, salinity and pressure. Two of the EM-APEX floats were deployed 30–40 km south of the Kuroshio axis, and one (Hereinafter EM9032) was deployed in the Kuroshio axis. In this paper, only EM9032 data taken along the Kuroshio main stream are shown. To profile turbulent kinetic energy dissipation rate ϵ, microscale thermal dissipation rate χ, temperature and salinity, a Navis-Float (Sea-Bird Electronics, Bellevue, USA) equipped with MicroRider (hereinafter Navis-MR, Rockland Scientific, Victoria, Canada) microstructure sensors (two shear probes and two Fp07 thermistors) was deployed at the roughly same position as the EM9032. After the deployments, they flowed rapidly eastward along the Kuroshio axis together (Figure 1). The Navis-MR was recovered after about 3 days, while EM9032 was kept profiling for over 10 days. The EM9032 and the Navis-MR profiled approximately 500 m water columns every 2 h and 4 h, respectively.
Turbulent kinetic energy dissipation rates ϵ are computed using data from two shear probes by integrating turbulent shear spectra from approximately 1 cpm to half the Kolmogorov wavenumber, where the spectra agree with the Nasmyth model spectrum [Nasmyth, 1970] (Figure 3a). The shear spectra are computed for the data segments over 16 s and converted to wavenumber spectra using the free-rising speed of the float, 0.11–0.26 ms−1. The noise from instrument vibrations contaminating the shear data is removed using the Goodman coherent noise removal algorithm [Goodman et al., 2006], with the two available components of accelerometer data. Because our microstructure platform is a profiling float, noises from the buoyancy pump typically contaminate the turbulent shear signal for the bottom 100 m. However, because the noise from the buoyancy pump appears to be at frequencies higher than 30–40 Hz, moderate levels of turbulence,
(
Wkg−1), are not likely affected (blue in Figure 3a). Temperature gradient spectra are also computed similarly for data obtained by two fast response thermistor sensors. To recover the lost thermal variance due to temporal response limitation at high wavenumbers, a response correction function identical to Gregg et al. [1978] and Li and Yamazaki [2001] is applied to the spectra. The recovered variance is negligible at the wavenumber less than 100 cpm. The microscale temperature dissipation rate χ is obtained by integrating temperature gradient spectra for the range without electronic noise at higher frequency. Once χ is determined, the Kraichnan spectrum [Kraichnan, 1968] is fitted to the computed spectra using the Ruddick maximum likelihood algorithm [Ruddick et al., 2000] for various dissipation rates ϵ (Figure 3b). With slow rising speeds of the float, the temperature gradient spectra show excellent agreement with Kraichnan spectrum (Figure 3b).

Wavenumber spectra of (a) microscale shear (s−2 cpm−1) and (b) microscale temperature gradient (K2m−2 cpm−1) are shown for two data segments indicated by the same colors, blue and red in Figures 3a and 8c, and green and magenta in Figures 3b and 8d. Nasmyth spectra and Kraichnan spectra are shown as black curves in Figures 3a and 3b, respectively.
After the deployment of profiling floats, across-front surveys were carried out to measure currents, temperature and salinity (Figures 1, 4a, 4c, and 4e). The Kuroshio made a hairpin turn to flow eastward around 36–37°N and 142–143°E, where all the floats were deployed (Figure 1). A few days after the deployments of the floats, the western tip of the hairpin meander retreated eastward and disappeared.

Across-frontal depth-latitude plots for (a) ADCP along-front flow (ms−1), (c) potential temperature (°C), and (e) salinity (PSU) measured by Underway-CTD along the observation line shown as solid black line in Figure 1. Along-frontal depth-time plots of (b) across-frontal flow (ms−1), (d) potential temperature (°C), (f) salinity (PSU) measured by EM9032 along the Kuroshio Extension Front for 10 days. White boxes in Figures 4d and 4f are time-depth ranges covered by Navis-MR data in Figure 9. Solid contours are
.
3 Velocity and Thermohaline Structure Across and Along the Kuroshio Extension
ADCP data measured during the across-front survey show that EM9032 and the Navis-MR float were deployed in the middle of a strong frontal (east-northeast) current
m s−1 of the Kuroshio Extension (Figure 4a). Trajectory of EM9032 shows that it traversed Kuroshio meanders, passing a meander crest during days 1–3 and 6–7, and trough during days 4–6 and 8–9 after the deployment (Figure 1).
To analyze the velocity measurements taken by EM9032 separately for along and across-frontal components, the current direction of the Kuroshio was first determined by computing 500 m mean low-pass velocity at 30 h with a third-order Butterworth filter. The along and across-frontal flow are then obtained by referencing the velocity data to the coordinate, which consists of the normal and parallel axes to the obtained current direction of the Kuroshio.
Along the meandering Kuroshio Extension, across-frontal velocity reveals up- and downward phase transitions of the near-inertial waves as well as subinertial flows (Figures 4b and 6d). For the internal waves away from the front, up- and downward phase transitions with time indicate down- and upward energy propagations, respectively. However, near the front, the same vertical propagation direction for phase and energy can occur when frontal isopycnals are steep enough [Whitt and Thomas, 2013]; the direction of energy propagation cannot be unequivocally determined from our available data alone.
Vertical sections of temperature and salinity illustrate thermohaline contrasts across the Kuroshio Extension Front, with a cold-fresh water tongue of vertical scale ∼50 m extending from north to south along the sloping isopycnals between
(Figures 4c and 4e), similar to Nagai et al. [2012]. Blobs of low salinity water below 300 m depth of over ∼100 m thickness are also seen (Figure 4e). Large variations in spiciness across the Kuroshio Extension Front seen in the θ-S plot (Figure 2) illustrate that interleaving layers may arise when along-isopycnal transports occur in intermediate layers [MacVean and Woods, 1980; Smith and Ferrari, 2009]. In EM9032 data, these interleaving thermohaline structures are also observed along the Kuroshio Extension Front for over 900 km, especially deeper than 200 m (
26–26.9), where the NPIW is frequently identified (Figures 4d and 4f). These interleaving structures are reminiscent of that found in equatorial Pacific, whose formation mechanisms are attributed to inertial instability [Richards and Edwards, 2003]. However, in our observations, the interleaving layers are found mostly subsurface below 150 m depth, away from the surface and bottom boundary layers, in a zonal baroclinic front; inertial instability is unlikely because its stability condition can not be violated before symmetric instability, which requires Ertel potential vorticity to change its sign. Symmetric instability is more likely to happen near the viscous boundary layers due to PV flux [Thomas and Lee, 2005; Nagai et al., 2012], rather than at depth. Turner angle Tu computed for EM9032 data shows many layers with
(dark red in Figure 5b) and
(dark blue in Figure 5b) below 150 m depth. Here Turner angle is defined as
where atan2 is the four-quadrant inverse tangent, and
and δS the temperature and salinity variations with depth, respectively [Ruddick, 1983]. When
, thermohaline stratification is favorable for salt fingers, and when
for diffusive convection. Along-front variations of 5 m mean gradient Richardson number
, where N is buoyancy frequency and uz and vz are the vertical shear for along- and across-frontal velocity, indicate that relatively low
appears along the layer,
, which exhibits up- and downward depth transition due to mesoscale meanders (Figure 5d). The low Richardson number Ri appeared to be lowered further when EM9032 profiled during days 4–8, from the meander trough through the crest. Across-front variations in gradient Richardson number Ri, shows this low
layer inclines with the sloping isopycnal of
(Figure 5c). Below this layer, isopycnal of
exhibits patchy low
, which could be due to near-inertial waves on the south side of the Kuroshio, as in Inoue et al. [2010]. These suggest that shear due to Kuroshio Extension current and that due to near-inertial waves persistently lower the gradient Richardson number Ri, and that the Kuroshio meander modulates Ri.

Across-frontal depth-latitude plots for (a) Turner angle, Tu (°), (c) gradient Richardson number, Ri based on 16 m ADCP data, and (e) estimated double-diffusion induced effective thermal diffusivity
(m2s−1) along the observation line shown as solid black line in Figure 1. Along-frontal depth-time plots of (b) Turner angle, Tu (
), (d) gradient Richardson number, Ri based on 5 m average EM9032 data, and (f) estimated double-diffusion induced effective thermal diffusivity
(m2s−1) along the Kuroshio Extension Front for 10 days. Solid contours are
.
Schmitt [1990] showed that density ratio
can be varied by flow vertical shear with along isopycnal salinity gradient. The vertical shear of along-frontal horizontal current obtained by EM9032 indicate that shear due to the subinertial Kuroshio current is very strong in the density layer of
(Figure 6a), where Richardson number Ri is low (Figure 5d). In contrast, shear of across-frontal flow is influenced mostly from high vertical wavenumber shear presumably caused by internal waves (Figure 6b). Along-isopycnal frequency spectra computed for vertical shear of along-frontal flow indicate that dominant subinertial (
) variance with some contributions from near-inertial (
-2f) shear (Figure 6c). For vertical shear of across-frontal flow, along-isopycnal frequency spectra show dominant near-inertial (
-2f) oscillations with the subinertial (
) variance of similar magnitude in light water (
, Figure 6d). In this study, the near-inertial frequency band is defined as a somewhat broad range
, because the minimum internal-wave frequency can be modulated by geostrophic shear and Doppler-shift while the EM9032 float is profiling. Similarly the along-isopycnal spectra for spiciness and rate of change in spiciness show that spiciness is modulated mostly with the subinertial frequencies with some contributions from near-inertial fluctuations (Figure 6e). On the other hand, the near-inertial frequency contribution becomes larger, when spectra are computed for the rate of change of spiciness (Figure 6f). Squared coherence spectra computed between shear of along and across-frontal flow and spiciness shows high correlation at the subinertial frequencies (
; Figure 7). The spiciness is more strongly correlated with the vertical shear of across-frontal flow than that with along-frontal flow at the near-inertial frequencies (
-f; Figures 7a and 7b). These trends are very similar in the coherence computed with the rate of change in spiciness (Figures 7c and 7d). The results suggest that both the subinertial vertical shear and the vertical shear of near-inertial across-frontal flow could provide thermohaline interleaving structures associated with along isopycnal variations in spiciness, and subsequent changes in density ratio
, or Turner angle Tu.

Vertical shear measured by EM9032 along the Kuroshio Extension Front for 10 days for (a) along frontal flow (s−1), and (b) across-frontal flow (s−1). Along-isopycnal power spectral density for vertical shear of (c) along-frontal flow (s−2 Hz−1) and (d) across-frontal flow (s−2 Hz−1). Along-isopycnal power spectral density for (e) spiciness (Hz−1) and (f) along isopycnal rate of change of spiciness with time (s−2 Hz−1). Color in Figures 6c–6f is in log scale. Three black vertical lines indicate near-inertial frequencies at
, f and 2f. Solid contours are
.

Along-isopycnal squared coherence spectra between (a) spiciness and along-frontal flow vertical shear, and (b) between spiciness and across-frontal vertical shear. Coherence spectra between (c) rate of change in spiciness and along-frontal flow vertical shear, and between (d) rate of change in spiciness and across-frontal flow vertical shear. Three black vertical lines indicate near-inertial frequencies at
, f, and 2f.
The shipboard measurements show that the cold-fresh tongue at 37.3°N at 250 m depth with a vertical scale of ∼50 m extends ∼5 km in the cross-frontal direction roughly along sloping isopycnals
of the front (Figures 4c and 4e). This lateral intrusion scale is consistent with the excursion distance by
(0.1 ms−1) near-inertial wave current speed over 12 h (Figure 4b). The maximum allowed slope of the double-diffusion driven interleaving can be estimated by
, where k/m is a ratio of horizontal to vertical wavenumber of the interleaving,
, ρ density, S salinity, and the subscripts y and z are derivatives for across-frontal and vertical directions, respectively [May and Kelley, 1997; Beal, 2007]. This estimated slope nearly matches the observed slope of the tongue,
. Although the possibility of the double-diffusive interleaving can not be ruled out, the coherence between across-frontal vertical shear and spiciness suggests that the thermohaline interleaving structures observed along the Kuroshio Extension Front can be formed by both subinertial and near-inertial lateral advection. The former is attributed to mesoscale meandering of the front and the latter to near-inertial waves, both of which transport water nearly along the sloping isopycnals of fronts.
4 Microstructure Profiling Float Data Along the Kuroshio Extension
Along the Kuroshio Extension Front, the microstructure profiling float Navis-MR was deployed along with EM9032 (Figure 1). One of the profiles taken by Navis-MR shows many temperature and salinity inversions with Turner angles Tu favorable for diffusive convection (
) and for salt fingers (
; Figure 8). In these double-diffusive favorable inversion layers, measured microscale temperature gradient magnitudes are high (Figure 8d;
). Corresponding dissipation rates for microscale thermal variance are as large as
(red curve in Figure 8e) with relatively low turbulent kinetic energy dissipation rates,
10−8 Wkg−1 (black curve in Figure 8e). The large thermal variance dissipation with weak turbulence indicates the onset of double-diffusion [Schmitt et al., 2005; Inoue et al., 2007]. These results are similar to the previous observations in frontal regions near a Meddy [Armi et al., 1989], and Azores Front [Georgi and Schmitt, 1983]. Depth-time plot of turbulent kinetic energy dissipation rates ϵ shows patchy distributions of moderately high values around 200 m depth (
) and around 400 m depth (
; Figure 9a). Strong turbulence is confined to upper 20–30 m within the surface boundary layer due to strong stratification caused by solar heating during summer. Since the 5 m gradient Richardson number Ri at around 200 m depth (
) is relatively low
(1) (Figure 5d), the breaking of the near-inertial internal waves trapped below the front [Whitt and Thomas, 2013] likely elevates the turbulent kinetic energy dissipation. The measured dissipation rates appear to be positively correlated with 10 m shear and buoyancy frequency, consistent with the scaling models of internal-wave induced turbulent dissipation [Gregg, 1989; Winkel et al., 2002]. The striking result of this study is that high values of the microscale thermal dissipation rates χ of
(> 10−7 K2 s−1) all through below 150 m depth in relatively weak turbulent layers persist for 3 days over 300 km along the main stream of the Kuroshio Extension (Figures 9a and 9b). The comparison between temporal average dissipation rates for turbulent kinetic energy (black curve in Figure 9c) and microscale thermal variance (red curve in Figure 9c) illustrates this contrast.

Vertical profiles of (a) Temperature (black; °C), salinity (red; PSU) and
(blue; kg m−3), measured by Navis-float CTD and (b) computed Turner angle (°). Dashed black vertical lines are at Tu = 45 and −45°. Microstructure vertical profiles observed by the MicroRider mounted on the Navis-float (Navis-MR) for (c) microscale shear (s−1), (d) microscale temperature gradient (K m−1), and (e) turbulent kinetic energy dissipation rate (black), ϵ (W kg−1) and microscale thermal dissipation rate (red), χ (K2 s−1). In Figures 8c and 8d, data segments for spectral computations in Figure 3, are indicated by horizontal bands with the same color, blue and red in Figure 3a and 3c, green and magenta in Figure 3b and 3d.

Depth-time plots of microstructure data observed by the microstructure profiling float (Navis-MR) for (a) turbulent kinetic energy dissipation rate
(W kg−1), (b) microscale thermal variance dissipation rate
(K2 s−1), (d) turbulent eddy diffusivity for density
(m2 s−1) in log scale, and (e) effective thermal diffusivity
(m2 s−1) in log scale. Solid contours are
. (c) Temporal average (black) kinetic energy dissipation rate ϵ (W kg−1) and (red) microscale thermal variance dissipation rate χ (K2s−1). (f) Temporal average (black) turbulent eddy diffusivity for density
(m2 s−1) and (red) effective thermal diffusivity
(m2 s−1). White circles in Figures 9a, 9b, 9d, and 9e indicate the time that the profile shown in Figure 8 was obtained.
Depth-time plot for Turner angle Tu computed for 10 m average temperature and salinity suggests that strong thermal dissipation rates deeper than 150 m (
) are accompanied by double-diffusion favorable conditions,
for salt fingers and
for diffusive convection (Figure 10a). Buoyancy Reynolds number
, where ν is kinematic viscosity computed using Navis-MR data, shows mostly small values
(Figures 10b and 10d), suggesting that observed turbulence is not isotropic, except turbulence in the upper 20 m and in a number of turbulent patches below 100 m depth. Between 25 and 375 m depth, roughly 60% of the buoyancy Reynolds number Reb values are less than 20, for which turbulence is not strong enough to support density flux [Yamazaki, 1990]. Temporal average of buoyancy Reynolds number Reb shows
in upper layers between 25 and 200 m depth, suggesting that turbulent density flux is negligible on average. Dissipation ratio,
where Θz is the mean temperature vertical gradient, exhibits values much larger than that for mechanical turbulence, 0.2 [Osborn, 1980; Oakey, 1988] (Figure 10c). Very large dissipation ratios
tend to coincide with the Turner angle (
) favorable for diffusive convection (Figures 10a and 10c). Somewhat large dissipation ratios
are also seen with Turner angle (
) favorable for salt fingers (blue curve in Figure 11b).

Depth-time plots of Navis-MR data for computed (a) Turner angle Tu (°), (b) buoyancy Reynolds number
, and (c) dissipation ratio
in log scale. Solid contours are
. (d) Temporal average buoyancy Reynolds number Reb. White circles in Figures 10a–10c indicate the time that the profile shown in Figure 8 was obtained.

Color indicates (a) number of samples of the 5 m mean microstructure data, (b) bin-averaged dissipation ratio
, (c) bin-averaged turbulent kinetic energy dissipation rate
(W kg−1), (d) bin-averaged microscale thermal dissipation rate
(K2 s−1), as a function of Tuner angle Tu (°) and Richardson number Ri. Richardson number Ri is obtained from the EM-APEX Float data, which flowed along a similar trajectory to that of Navis-MR float. In Figure 11a, blue solid line represents number of samples as a function of Tuner angle Tu every 5°. In Figures 11b–11d, blue solid lines are (Figure 11b) average dissipation ratio Γ, (Figure 11c) average TKE dissipation rate ϵ, and (Figure 11d) average thermal dissipation rate χ as a function of Tuner angle Tu (°). In Figures 11b-11d, the averaged values are computed excluding the data when number of samples in Figure 11a is less than 10, and dissipation ratio Γ is greater than its three standard deviations.
Turbulent eddy diffusivity for density estimated following Osborn [1980]
shows patchy distribution with relatively large values
(10−5 to 10−4 m2 s−1) below 200 m depth (Figure 9d). Effective diffusivity for heat computed by
[Osborn and Cox, 1972] shows one to two orders of magnitude larger diffusivity
(10−4 to 10−3 m2 s−1) than that for density
all through below 150 m depth (Figure 9e). Average thermal diffusivity
is 1.7 × 10−3 m2 s−1 and the average turbulent eddy diffusivity for density
is 2.8 × 10−5 m2 s−1 between 150 m and 400 m depth (Figure 9f). The low turbulent eddy diffusivity may partially work against the double-diffusion induced negative diffusivity, which decreases the potential energy as opposed to turbulence, preventing double-diffusive layer formations. These observed results indicate that along the Kuroshio Extension Front below 150 m, the dominant agent for tracer vertical mixing is double-diffusive convection.
The two-dimensional histogram of the microstructure data indicates that most of the observed thermohaline structure is in dynamically stable (Ri > 1; Figure 11a) and in double-diffusive favorable conditions (blue curve in Figure 11a). Specifically, 46% and 16% of the total microstructure data are in salt fingers and diffusive convection favorable conditions, respectively. The gradient Richardson number Ri is computed using the EM9032 velocity and CTD data, which is then interpolated to the longitude-depth domain traversed by Navis-MR. The trends that the bin-average microscale thermal dissipation rates χ increase as Tuner angles approach from 45° to 90°, and from −45° to −90°, are strong indications that the observed pronounced thermal dissipation is caused by double-diffusive convection (Figure 11d). Such a trend is not seen for the turbulent kinetic energy dissipation rate ϵ (blue curve in Figure 11c).








The dissipation ratio ΓDD computed using (1) and (3) is 1.18 over the range
(
), and that obtained with (2) is as large as ∼5 at
, consistent with the observational estimates (blue curve in Figure 11b).
The observational results presented here indicate that along the Kuroshio Extension Front below 150 m depth, thermal variance, provided both by vertical shear in subinertial and across-frontal near-inertial wave flows, is accompanied by double-diffusion favorable interleaving thermohaline structures, and dissipated at microscale mostly by double-diffusive convection. In the next section, the computed effective thermal diffusivities from observed microstructure data are compared with the previous empirical parameterizations to demonstrate further if this is the case, and to extrapolate the results for farther downstream of the Kuroshio Extension, where microstructure data are not available.
5 Comparison With the Previous Parameterizations for Double-Diffusion
A number of studies have developed empirical parameterizations for double-diffusion induced effective diffusivities. Here estimated effective thermal diffusivities
from the observed thermal dissipation rates χ are compared against the previous parameterizations for double diffusion [Schmitt, 1999; Large et al., 1994; Fedorov, 1988; Zhang et al., 1998; Radko and Smith, 2012]. These parameterizations based on the density ratio
are included in the Appendix Appendix A.
Thermal diffusivity
obtained from measured thermal dissipation rates by Navis-MR increases as Turner angle Tu approaches to 90° and −90°, or
, consistent with all the parameterizations (Figure 12a), suggesting that the observed large thermal dissipation rates are strongly influenced by double-diffusive convection. Excluding thermal diffusivity estimates with the buoyancy Reynolds numbers Reb exceed 20, the highest log correlation among four parameterizations is found with Radko et al. [2014] for salt fingers
(A6) with a correlation coefficient 0.53, N=217, and p-value 7 × 10−17 (Figure 12b). For diffusive convection, the Fedorov [1988] parameterization (equation A3; dashed blue curve in Figure 12a) reproduces observed average thermal diffusivity better than Kelley [1984] (equation A5; dashed red curve in Figure 12a).

(a) Comparison of effective thermal diffusivity
(m2s−1) between observation and the previous parameterizations for salt fingers, red (A1): Schmitt [1981]; magenta (A2): Large et al. [1994]; green (A4): Zhang et al. [1998]; blue (A6): Radko and Smith [2012], and for diffusive convection, dashed red (A5): Kelley [1984]; dashed blue (A3): Fedorov [1988], as a function of Tuner angle Tu (°). Excluding the data with buoyancy Reynolds number
, solid black line represents bin-average thermal diffusivity with a standard deviation in purple shading. No standard deviation for 2 of average Γ values for the diffusive convection range (
), is because number of sample N = 1 after excluding the data with
. (b) Scatter plot of estimated effective thermal diffusivity
(m2s−1) against the model developed by Radko and Smith [2012].
Based on these results, salt-finger parameterization by Radko et al. [2014] (A6) and diffusive convection parameterization from Fedorov [1988] (A3) are employed to extrapolate double-diffusion induced thermal diffusivity
, using
measured along and across the Kuroshio Extension Front, where microstructure data are not available. Estimated double-diffusion induced thermal diffusivity below the Kuroshio Extension is larger with
(10−5 to 10−4 m2 s−1) on the cold side than that on the warm side of the front (Figure 5e). This high thermal diffusivity deduced below the Kuroshio Extension Front extends 900 km downstream (Figure 5f). The low Richardson number, Ri < 1 region appears mostly along the
isopycnal around 100–250 m depth (Figures 5c and 5d). Below this strong shear layer, the estimated thermal diffusivity is elevated all through the Kuroshio Extension Front, suggesting that enhanced double-diffusive convective mixing is widespread below the Kuroshio Extension Front and could have a pronounced impact on diapycnal fluxes of heat, salt and other tracers including nutrients (Figure 13). Because the elevated double-diffusive features are observed within the pycnostad of
, where the North Pacific Intermediate Water (NPIW) spreads, it is plausible that double-diffusion may play an important role in forming the NPIW.

Schematic summary of this study. Mesoscale subduction and near-inertial oscillations of cold-fresh water along the sloping isopycnal of the front provides continuously double-diffusion favorable condition, enhancing microscale thermal dissipation and vertical or diapycnal tracer fluxes.
6 Conclusions
In this study, microstructure profiling float data and EM-APEX float data taken along the Kuroshio Extension Front, and CTD data obtained from across-front surveys are analyzed. Thermohaline structures measured by the across-front surveys in the upstream of the Kuroshio Extension Front show characteristic interleaving layers below the
isopycnal (Figures 4c and 4e). In the layer between
and 26.5, we observed a several 10s of meters thick cold-fresh water tongue extending from north toward the deeper layer south along sloping isopycnals of the front, and several 100 m thick blobs of cold-fresh water in deeper layer (Figures 4c and 4e). Along front observations using profiling floats reveal that these thermohaline interleaving structures are spread farther downstream over 900 km along the front (Figures 4d and 4f). Turbulent kinetic energy dissipation rates ϵ measured using a microstructure float along the Kuroshio Extension Front show patchy distribution of moderately strong turbulent dissipation rates
(10−8 W kg−1) around 200 m depth and below 400 m depth (Figure 9a). Averaged turbulent eddy diffusivity for density
is 2.8 × 10−5 m2 s−1 between 150 and 400 m depth (Figures 9d and 9f). On the other hand, microscale thermal variance dissipation rates χ measured along the Kuroshio Extension Front show very large values
(>10−7 K2 s−1) below 150 m depth all along the trajectory of the microstructure float (Figure 9b). Average thermal diffusivity
between 150 m and 400 m depth based on the thermal dissipation rates is 1.7 × 10−3 m2 s−1 (Figures 9e and 9f), that is two orders of magnitude larger than the turbulent eddy diffusivity for density
(Figures 9d and 9f). It is found that 62% of the microstructure data are in double-diffusion favorable conditions (Figures 10a and 11a) with high microscale thermal dissipation rates (Figures 9b and 11d) and higher average dissipation ratio Γ than that found for mechanical turbulent mixing, 0.2 [Osborn, 1980] (Figures 10c and 11b). The estimated effective thermal diffusivity for the EM9032 data, using double-diffusion parameterizations is
(10−5 to 10−4 m2 s−1) below 150 m depth along the front (Figures 5e and 5f). These results indicate that along the Kuroshio Extension Front for at least over 900 km below 150 m depth, the dominant agent for diapycnal transport is double-diffusive convection.
Spiciness, which depends on the thermohaline variabilities along the isopycnal is found to be correlated with the vertical shear of the subinertial (
) and that of near-inertial (
-f) across-frontal flow (Figure 7). Subinertial (a few days) thermohaline fluctuations are likely due to subduction and obduction by mesoscale meanders, and near-inertial (a day) fluctuations are caused by near-inertial internal waves. Both of these processes could advect heat, salt and other tracers quasi-horizontally roughly along sloping isopycnals of fronts. This along isopycnal advection with vertical shear and spiciness (Figure 7) likely creates double-diffusion favorable conditions repeatedly, providing observed large thermal dissipation and tracer fluxes even with weak mechanical mixing due to turbulence. Accordingly, observational results support our hypothesis that mesoscale subduction, obduction and near-inertial waves near oceanic fronts have catalytic effects to enhance subsurface double-diffusive convection as observed (Figure 13). The enhanced thermal dissipation below the Kuroshio Extension with
(10–100 m) vertical scale thermohaline structures strongly support the forward cascading scenario of Smith and Ferrari [2009], which showed that tracer variance provided by mesoscale stirring is dissipated by microscale vertical mixing processes at thermohaline filaments. Our results suggest that, in the strong frontal regions with large across front variations in spiciness, such as the Kuroshio Extension Front, double-diffusion is an important and vital player in dissipating tracer variances, and promoting diapycnal fluxes of heat, salt and other tracers including nutrients (Figure 13). It is plausible that the enhanced double-diffusion signatures observed in pycnostad of
below the Kuroshio Extension Front, could play an important role in forming the North Pacific Intermediate Water (NPIW) there. However, because our data were obtained from a single campaign and only from summer season, more repeated and intensive direct observations are required to elucidate whether elevated double-diffusion persists in different time and seasons in the Kuroshio Extension.
Acknowledgments
We thank Capt. Inoue, crews of R.V. Kaiyo (JAMSTEC), Okada at NME Ltd. for assists in field surveys, all those who participated in the cruise including Lueck at RSI, Li, Kokubu, Mabuchi at JFE-Advantech, Hasegawa at FRA, all the students and staff of the lab (Homma, Masunaga, Foloni-Neto, Yukawa, Nishi, Furuyama, Takeuchi, Nakamura, Sugata, Hohman, Allmon), Hosoda, Hirano and Nakajima at JAMSTEC, Dunlap at APL, and Larson, Mitchell and Quittman at SBE for the float configuration and operations, Wolk and Stern at RSI, and Yazu at JFE-Advantech for the Micro-Rider integrations, Ruddick for the Maximum Likelihood analysis code, Lynn Allmon for editorial assistance, and reviewers including Schmitt and Ruddick for their insights. TN thanks JSPS (KAKENHI 24684036),“The Study of Kuroshio Ecosystem Dynamics for Sustainable Fisheries (SKED)” funded by MEXT, MIT-Hayashi Seed Fund. AT thanks NSF-1434512 and ONR-N000141310456 for support. Please contact the corresponding author at [email protected] to obtain the data described in this paper.
Appendix A: Previous Empirical Parameterizations for Double-Diffusive Convection

























