PUBLICATIONSJournal of Geophysical Research: Oceans
RESEARCH ARTICLE

Turbulent mixing within the Kuroshio in the Tokara Strait

10.1002/2017JC013049
Key Points:
 Direct measurements of turbulence
were conducted in the Tokara Strait
where many seamounts and islands
exist within the Kuroshio
 Analyses suggest vertical diffusivity
could have been elevated to 1021 m2
s21 around a shallow seamount withwhich the Kuroshio interacts
 Flow-topography interaction andassociated mixing processes are key
to modeling the downstream
evolution of the Kuroshio water
properties

Correspondence to:
E. Tsutsumi,
tsutsumi@riam.kyushu-u.ac.jp

Citation:
Tsutsumi, E., T. Matsuno, R.-C. Lien,
H. Nakamura, T. Senjyu, and X. Guo(2017), Turbulent mixing within the
Kuroshio in the Tokara Strait,
J. Geophys. Res. Oceans, 122, 7082–
7094, doi:10.1002/2017JC013049.
Received 2 MAY 2017
Accepted 10 AUG 2017
Accepted article online 25 AUG 2017
Published online 4 SEP 2017

C 2017. American Geophysical Union.
V

All Rights Reserved.

TSUTSUMI ET AL.

Eisuke Tsutsumi1 , Takeshi Matsuno1, Ren-Chieh Lien2
Tomoharu Senjyu1, and Xinyu Guo4

, Hirohiko Nakamura3,

1

Research Institute for Applied Mechanics, Kyushu University, Fukuoka, Japan, 2Applied Physics Laboratory, University ofWashington, Seattle, Washington, USA, 3Faculty of Fisheries, Kagoshima University, Kagoshima, Japan, 4Center for Marine
Environmental Studies, Ehime University, Matsuyama, Japan

Abstract Turbulent mixing and background current were observed using a microstructure proﬁler andacoustic Doppler current proﬁlers in the Tokara Strait, where many seamounts and small islands exist within
the route of the Kuroshio in the East China Sea. Vertical structure and water properties of the Kuroshio weregreatly modiﬁed downstream from shallow seamounts. In the lee of a seamount crest at 200 m depth, themodiﬁcation made the ﬂow tend to shear instability, and the vertical eddy diffusivity is enhanced by nearly
100 times that of the upstream site, to Kq  O(1023)–O(1022) m2 s21. A one-dimensional diffusion modelusing the observed eddy diffusivity reproduced the observed downstream evolution of the temperaturesalinity proﬁle. However, the estimated diffusion time-scale is at least 10 times longer than the observed
advection time-scale. This suggests that the eddy diffusivity reaches to O(1021) m2 s21 in the vicinity of the
seamount. At a site away from the abrupt topography, eddy diffusivity was also elevated to O(1023) m2 s21,
and was associated with shear instability presumably induced by the Kuroshio shear and near-inertial internal-wave shear. Our study suggests that a better prediction of current, water-mass properties, and nutrients
within the Kuroshio requires accurate understanding and parameterization of ﬂow-topography interaction
such as internal hydraulics, the associated internal-wave processes, and turbulent mixing processes.

1. Introduction
The Kuroshio, which is a western boundary current in the subtropical North Paciﬁc, carries a large amountof heat, salt and momentum from the low- to mid- latitude ocean. The Kuroshio has a potential impact on
biogeochemical processes along its path through nutrient transport [Liu et al., 2014; Guo et al., 2013;
Kodama et al., 2014]. There are horizontal and vertical aspects to nutrient transport within the Kuroshio; thelatter is mainly caused by turbulent mixing [e.g., Guo et al., 2013]. The Kuroshio affects turbulence processes
through propagation and breaking of internal tidal and inertial waves by its current and geostrophic shears[e.g., Alford et al., 2015; Nagai et al., 2015]. Turbulence may modify the temperature and salinity of theKuroshio through mixing with surrounding water, incorporating properties of the water-mass in each area
along its route from the origin (Philippine sea-Luzon Strait) to south of Japan [Nakamura et al., 2013; Andres
et al., 2015; Lien et al., 2015; Kida et al., 2015] as well as its marginal shelf and inner seas [e.g., Yanao andMatsuno, 2013; Tsutsumi and Guo, 2016]. Therefore, it is vital to investigate turbulent mixing processes
within the Kuroshio to understand physical and biogeochemical processes in the western North Paciﬁc.
Besides the surface-induced turbulent mixing, the most likely driving mechanism of mixing within the Kuroshio is ﬂow-topography interactions. Previous studies on sub-tidal ﬂow interaction with topography reported
strong turbulence in hydraulic jumps [St. Laurent and Thurnherr, 2007; Alford et al., 2013; Alford and MacCready,2014; Nishina et al., 2016] and lee waves [Nikurashin and Ferrari, 2010a; Sheen et al., 2013; Waterman et al.,2013]. Such hydraulic jumps can cause huge vertical eddy diffusivity, Kq 5 O(1022)–O(1021) m2 s21 [St. Laurent
and Thurnherr, 2007; Alford et al., 2013; Nishina et al., 2016]. Internal tides are another candidate for promoting
mixing. At the margin of the South China Sea, such as in the Luzon Strait where strong internal tides are generated, internal wave propagation and breaking and their relation to the Kuroshio and mesoscale and submesoscale variabilities have been studied extensively [Klymak et al., 2011; Rainville et al., 2013; Lien et al., 2013;
Alford et al., 2015]. Tidal currents can also produce hydraulic jumps and lee waves as they interact with topography [Legg and Klymak, 2008; Nakamura et al., 2010; Mohri et al., 2010; Gregg and Klymak, 2014] and cause
enhanced eddy diffusivity of O(1022)–O(1021) m2 s21 [Klymak and Gregg, 2004; Alford et al., 2011].

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Strong turbulent mixing due to internal waves and Kuroshio interaction with topography has been measured or inferred along the path of the Kuroshio. Rainville and Pinkel [2004] observed high-wavenumber
internal waves trapped by the horizontal shear of the Kuroshio near the shelf break of the East China Sea(ECS) and within the current core of the Kuroshio west of Kyushu Island, Japan. The turbulent energy dissipation rate E, estimated using ﬁne-scale parameterization, was 0.5–1.5 31028 W kg21. Near the shelf breakof the ECS, Matsuno et al. [2005] measured the dissipation rate using a microstructure proﬁler. They foundan increase in dissipation rate in the thermocline, E 5 O(1028)–O(1027) W kg21, and discussed its relation toobserved high-wavenumber M2 internal tide around the shelf edge. This dissipation rate was similar to theestimate by Rainville and Pinkel [2004]. At the Tokara Islands chain within the Kuroshio south of Kyushu
Island, Japan, Hasegawa et al. [2008] reported formations of cold water and estimated the turbulent dissipation, E 5 0.2–1.1 31024 W kg21, which was more than two orders of magnitude greater than the reported
value at the ECS shelf edge. Chang et al. [2013] observed similar cold eddy formation in the wake of Green
Island, east of Taiwan within the Kuroshio. They also estimated an energy dissipation rate of E 5 O(1027)–
O(1025) W kg21. Recently, Chang et al. [2016] reported generation of extremely strong turbulence over aseamount within the Kuroshio east of Taiwan. Kelvin-Helmholtz billows were generated as a result of theKuroshio interacting with a seamount, leading to enhanced turbulent dissipation rates, O(1026)–O(1023)
W kg21. From these studies, it is clear that the Kuroshio-topography interaction plays an important role inproducing strong turbulent mixing.
Here, we present the observational evidence of strong turbulent mixing in the Tokara Strait. The Tokara
Strait is the passage and the marginal area between Yakushima and Amami-oshima Islands where the Kuroshio exits from the ECS to the northwestern Paciﬁc (Figures 1a and 1b). The strait is distinctively characterized by many abrupt topographic features such as seamounts and small islands, and they are shallower
than 300 m depth in the path of Kuroshio, as shown by green contours in Figure 1. The depths of the abrupt
topography in the Tokara Strait are comparable to or shallower than the typical depth of the base of theKuroshio ﬂow in the ECS, 400–500 m [e.g., Guo et al., 2013]. We deﬁne the Kuroshio path based on the

Figure 1. Map showing the geography of the Kuroshio in East China Sea (ECS) and our experimental site in the Tokara Strait. (a) A typical pathway of the Kuroshio from east of Taiwan(TW) to the east of Kyushu (KS) Island. Location of the Tokara Strait is indicated by dashed-line box. (b) Location of microstructure stations in the Tokara Strait (blue dots). Microstructure
surveys were conducted in two meridional sections A and B across the Kuroshio. A chain of islands and seamounts are present between sections A and B. Blue arrows show temporal
averages of velocities at 24 m depth measured by shipboard ADCP. Yakushima Island and Amami-oshima Island are indicated by ‘‘YS’’ and ‘‘AO,’’ respectively. (c, d) Enlarged views of two
seamounts. In each plot, red and green contours represent 200- and 300 m isobaths, respectively.

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average of the Kuroshio axis position data set 1955–2006 by the Japan Hydrographical Association, following
previous studies [e.g., Nakamura et al., 2012]. The Kuroshio almost always ﬂows through the section between
Yakushima and Amami-oshima Islands (‘YS’ and ‘AO’ in Figure 1b, respectively). The Tokara Strait is therefore
the most likely area where the Kuroshio interacts with topography at the margin of the ECS. Observational evidence of strong turbulence in this region is limited to a few studies [e.g., Hasegawa et al., 2008].
The Tokara Strait is also one of the major generation sites of internal tides in the North Paciﬁc. Niwa andHibiya [2004] estimated 9.3 GW of semidiurnal (M2) internal tide energy is converted from barotropic tide at
the Tokara Strait, while Varlamov et al. [2015] estimated it as 3.8 GW. These values are signiﬁcant comparedwith the conversion rate at the energetic Luzon Strait. For M2: 14 GW [Niwa and Hibiya, 2004], 16 GW [Kerryet al., 2014] and 11 GW [Varlamov et al., 2015]; for M21S2: 11 GW [Jan et al., 2008]; or for four major constituents, 24 GW [Alford et al., 2011]. Numerical simulation indicates that a signiﬁcant fraction of the internal tideenergy is dissipated locally and therefore, turbulence generation is expected in the Tokara Strait [Niwa andHibiya, 2004]. To date, almost no observation of internal tides and the associated turbulence in the Tokara
Strait has been reported.
Identifying the locations, strengths and driving mechanism of vertical mixing within the Kuroshio is important for understanding the water-mass modiﬁcation, material transport and biological productivity in its
marginal area. As noted above, the Tokara Strait is the most likely spot to produce energetic turbulent mixing in the ECS because of abrupt topography, tides, and the Kuroshio, although they are poorly understood.
In the following, we report a systematic survey of microstructure, currents and water properties in the
Tokara Strait for the ﬁrst time.

2. Experiment
An observational experiment was conducted on board T/V Kagoshima-maru to study turbulent mixing andwater-mass modiﬁcation along and across the Kuroshio in the Tokara Strait in November 2015. This experiment was motivated by a need for a better understanding of the spatial and temporal variations of microstructure turbulence and interactions among the Kuroshio, tidal currents and bottom topography over theentire strait. A mooring with an up-ward looking Teledyne RDI 75 kHz Long Ranger ADCP was deployed at alocation where the water depth is 650 m in the pathway of the Kuroshio. The moored ADCP obtained an
ensemble of 27-ping data every 1 min (2.22 s ping rate) with a vertical bin size of 8 m for 6 days from
0830JST (Japan Standard Time: UTC19 h) on 15 November to 1200JST on 21 November.
During the mooring observation period, we carried out measurements of turbulence, currents, temperatureand salinity using a loosely tethered, free-falling microstructure proﬁler, TurboMAP-L (JFE Advantech Co.),
shipboard 75-kHz Ocean Surveyor ADCP (RDI) and shipboard SBE-9p CTD (Sea-bird Electronics Inc.). Bin sizeand ensemble interval of the shipboard ADCP were 16 m and approximately 10 min, respectively. Theseobservations were made at 19 stations along the two transects across the Kuroshio (Line A and B: Figure1b). These two transects were chosen to capture along- and cross-stream variabilities of turbulence andwater properties in the Kuroshio. At each station shown in Figure 1b, double TurboMAP-L casts and single
SBE-9p cast were performed, except for Stn.A4u/d, stations labeled by ‘c’, and the mooring site. Double
TurboMAP-L casts and single TurboMAP-L/SBE-9p cast were made at Stn.A4u and A4d, respectively. Notethat subscripts ‘u’ and ‘d’ mean upstream and downstream of a seamount, respectively (Figure 1c). At stations ‘c’, a single SBE-9p cast was performed. At the mooring site, a series of TurboMAP-L and SBE-9p casts
were made at nearly 2 h intervals for 25 h starting at 0630 JST on 20 November.
The TurboMAP-L measures turbulent shear and temperature ﬂuctuations using two orthogonally-orientatedshear probes and a fast-response thermistor (FP07), respectively. All microstructure sensors sample at 512
Hz. Conductivity, temperature and pressure are measured by standard CTD sensors at 64 Hz. The
TurboMAP-L falls from surface to 500–600 m depth, not reaching to the sea ﬂoor, at a speed of 0.6 m s21.
At some stations where the vertical shear of horizontal velocity was too strong such as Stn.A4d and Stn.B4,
the proﬁler stopped descending at half of the targeted depth because of a limited cable length.
The surface wind, measured by shipboard meteorological sensors, was moderate during most of the observational period. The wind speed increased to >10 m s21 for 1.5 days after midnight on 18 November
because of the passage of a low-pressure system (ﬁgure not shown). The poor sea state interrupted our

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measurements at Stn.B7 for 1/2 day from the afternoon on 18 November. The atmospheric disturbances did
not seem to have signiﬁcant effect on oceanic conditions below the surface mixed layer.
The dissipation rate of turbulent kinetic energy, E, is computed from turbulent shear by ﬁtting its wavenumber spectrum to an empirical spectrum [Nasmyth, 1970] and integrating the shear spectrum in wavenumber
space for each 1024-point segment (equivalent to 1.2 m in vertical) with half overlapping. Proﬁles of E werethen interpolated onto a 1 m vertical grid. Potential temperature T and salinity S were calculated using the insitu temperature, conductivity, and pressure after adjusting the response lag of the thermistor relative to the /@z) is calculated fromconductivity sensor to minimize salinity spikes. Buoyancy frequency, N2 5 2(g/q0)(@ p ispotential density q where g is the gravitational acceleration, q0 is a reference density (1025 kg m23) and p
the mean density, which is sorted to be gravitationally stable. The vertical displacement of a water parcel due
 ). The vertical eddy diffusivity is estimated by
to a turbulent ﬂuctuation d is computed as d 5 z(q) 2 z(p22Osborn’s method, Kq 5 CE N , with a constant mixing efﬁciency C 5 0.2 [Osborn, 1980].
The dissipation rate and eddy diffusivity are also estimated based on the Thorpe scale method,
ET 5 0.64LT2N3 and KqT 5 CET N22, where LT is the Thorpe scale deﬁned as the root-mean-square of d withineach overturn [Thorpe, 1977; Dillon, 1982]. We estimated the vertical turbulent heat ﬂux Jq 5 q0cpKT (@T/@z)
where cp is the heat capacity of seawater (4 3 103 J kg218C21) and KT is the vertical eddy diffusivity of heat.
Positive values of Jq represent downward heat transport. In this study, we assume KT 5 Kq.

3. Results
3.1. Spatial Variation of Currents and Turbulence
Figure 1b shows surface velocities at 24 m depth from the shipboard ADCP. During the experimental period,
the core of the Kuroshio, with a typical speed of 1 m s21 and width of 50 km, ﬂowed eastward
at Stn.A3–A5 and turned south-eastward at Stn.B2–B4. This pathway was characterized as the northernmode by Nakamura et al. [2003] who reported that the Kuroshio exhibits a bi-modal (northern and southernmodes) pathway in the Tokara Strait.
Signiﬁcant eastward and southeastward currents with magnitude of 0.5–
1 m s21 were also observed aroundA7 and B6, respectively. These areprobably branches of the Kuroshio
separated by the Tokara Islands andrelated to a double-core velocity
structure in the Kuroshio reported in
the area south of Yakushima Island(Figure 1b) [Feng et al., 2000; Oka andKawabe, 2003; Nakamura et al., 2003].

Figure 2. Depth-averaged turbulent dissipation rate in the main pycnocline shownby colored circles. Depth-averaging was performed between the base of the surface mixed layer and the bottom of proﬁle, typically 500–600 m depth. Dissipation
rates are also averaged using two casts in each station, except for Station A4d andthe mooring station where they were taken from a single proﬁle and averaged for
25 h (or 23 casts), respectively. Isobaths are the same as Figure 1b. Dotted lines
represent a selected section along the Kuroshio core shown in Figure 3.

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Depth-averaged turbulent dissipation
rate shows the spatial variation in turbulence strength in the Tokara Strait(Figure 2). Depth-averaging was performed from below the base of the surface mixed layer, deﬁned as the depth
where potential density exceeds 0.01
rh relative to its shallowest value,
down to the bottom of the proﬁle (typically 500–600 m depth). Therefore, thisaverage represents mean turbulence
strength in the main pycnocline. The
depth-averaged turbulent dissipation
rates are typically O(1028)–O(1027) W
kg21. The turbulent dissipation rates
are signiﬁcantly elevated to 2.8 3 1027

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W kg21 at A4d and 1.1 3 1026 W kg21 at B4 in the Kuroshio core. This observed strong turbulence is likely tohave originated from interaction between the Kuroshio and the complex topography, namely Hiki-sone Seamount at A4 and Hira-se Seamount near B4 (Figures 1c and 1d). Detailed analyses of the Kuroshio-topographyinteraction will be presented in the next subsection, in connection with the vertical shear of the Kuroshio velocity enhanced by seamounts.
3.2. Vertical Structure of Currents, Shear Instability, and Turbulence
Downstream evolution of the velocity structure, stratiﬁcation and turbulence strength along the Kuroshio
core highlights the impact of the topography on the Kuroshio current and turbulence (Figure 3). Here, weFigure 3. Vertical proﬁles of ﬂow velocity, stratiﬁcation, and turbulence at the stations in the pathway of the Kuroshio core: A5, A4u/d, mooring site and B4. (a) along-stream velocity V(positive in the downstream direction), (b) Buoyancy frequency squared N2 (blue shading) and vertical shear squared divided by a factor of 4, S2/4 (orange line), (c) turbulent dissipation
rate E (blue shading) and parcel displacement d (purple line, the scale is given at the lower right), (d) vertical eddy diffusivity Kq (blue shading), (e) vertical turbulent heat ﬂux Jq deﬁned
as positive downward (blue shading) and its vertical divergence @Jq/@z (orange line, the scale is given at the lower right). Solid lines indicate isopycnals at an interval of 0.5 rh. Parcel displacements are calculated from shipboard CTD data except for A4u. Proﬁles at the mooring site are from the last cast of 25 h measurement. Horizontal arrows in Figures 3b and 3c represent the depths where gradient Richardson number around the pycnocline is smaller than 1/4. Orange lines in Figures 3c and 3d show estimates of E and Kq by the Thorpe scale
method, ET and KqT, respectively. In each plot, bottom topography along the dotted line marked in Figure 2 is schematically shown by the black shade.

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focus on two shallow seamounts in the Kuroshio path, Hiki-sone Seamount (hereinafter, Seamount I) adjacent to Stns.A4u/A4d and Hira-se Seamount (hereinafter, Seamount II) about 15 km upstream of B4 (Figures
1c and 1d). Proﬁles at Stn.A5 and the mooring site, which are located far from any signiﬁcant abrupt topography, are presented to illustrate the undisturbed state of the Kuroshio and turbulence upstream of the
seamount.
At Stn.A5, ﬂow is characterized by the Kuroshio with 0.5–1 m s21 speed and 300 m thickness (Figure 3a).
These features correspond to the typical values of the Kuroshio in the ECS [James et al., 1999; Andres et al.,2008; Guo et al., 2012]. Gradient Richardson number, Ri 5 N2S22, is larger than 1/4 at most depths of thewater column and turbulent dissipation rate is O(10210)–O(1028) W kg21 (Figures 3b and 3c). At this site,
ﬂow is free from topographic effects and therefore the turbulence is considered to represent a typical value
in the Kuroshio in the ECS.
At Stn.A4d, a few kilometers downstream of Seamount I, the magnitude of the Kuroshio sharply weakens
below the 200 m depth and the ﬂow reverses below 250 m, while the ﬂow remains almost the same as thatin the upper 200 m layer at A5. Such a velocity drop cannot be found at A4u, a few kilometers upstream of
Seamount I. Vertical shear is enhanced in the lower pycnocline at A4d, and the Richardson number is correspondingly smaller than 1/4 at several depths below 200 m (indicated by white arrows in Figures 3b and3c). Layers of shear instability coincide with layers of strong turbulent dissipation reaching O(1027)–O(1026)
W kg21, indicating that shear instability is the driving mechanism for the energetic turbulence. Signiﬁcantdensity overturning at order of O(1)–O(10) m is observed in the small Ri layer (Figure 3c, purple lines).
At the mooring site, the eastward Kuroshio current again penetrates deeper than 300 m, with a speed of
0.3–0.8 m s21 (Figure 3a). In Figure 3, we show a typical proﬁle of 25 h TurboMAP-L casts. Temporal evolutions of currents and turbulence at the mooring site are described later. Turbulent dissipation rate and eddy
diffusivity have a peak reaching E 5 O(1027) W kg21 and Kq 5 O(1023) m2 s21, respectively at 250 m depth(25.6 rh isopycnal) where is Ri is smaller than 1/4 (Figures 3c and 3d). Overall, vertical diffusion at themooring site is weaker than at A4d, but it is signiﬁcant at 200–300 m depth.
At Stn.B4, located 50 km downstream from the mooring site and 15 km downstream from Seamount II, vertical proﬁles of current and turbulence change drastically. The eastward Kuroshio current is limited to theupper 200 m and a strong subsurface counter-current with a speed of 0.5 m s21 appears below the Kuroshio (Figure 3a). This velocity structure leads to a thick and enhanced shear layer in the upper pycnocline
in 130–200 m depths, corresponding to the shallowest depth of Seamount II, 150 m depth (Figure 3b).
Within this layer, the ﬂow is in favor of shear instability, Ri < 1/4, and the turbulent dissipation rate is elevated, E 5 O(1026) W kg21, which is 100–1000 times that in the same density layer at the upstream mooringsite (Figure 3c). Although microstructure measurement stopped at 250 m depth at B4, large vertical overturns d, observed by the shipboard CTD, with small Richardson numbers suggest the occurrence of elevatedturbulence in the deeper layers, e.g., 300 and 450 m depths (Figure 3c). An estimation based on the Thorpe
scale method, which nearly agrees with the microstructure estimate, indicates that turbulent dissipation isindeed enhanced in the deeper layer at B4, E 5 O(1027) W kg21 at 400–500 m (orange lines in Figure 3c).
This value is comparable to high dissipation rates measured at around 150 m depth at B4. Strong verticaleddy diffusivity reaching Kq 5 O(1023)–O(1022) m2 s21 is observed downstream of Seamount II (Figure 3d).
The vertical heat ﬂux Jq is elevated in the pycnocline near and downstream of the seamounts (Figure 3e). Itsvertical divergence @Jq/@z has a magnitude of 5–10 W m23 at A4u/d and B4, which is 1000–10,000 times
larger than those upstream of seamounts. Such vertical divergence may lead to a temperature evolution of
0.1–0.28C in 1 day. The observed vertical mixing is expected to result in strong water-mass modiﬁcation.
We speculate that the observed elevated turbulence within the Kuroshio downstream of seamounts is dueto the shear instability resulting from the blocking effect on the Kuroshio deep-ﬂow, similar to that reported
by Chang et al. [2016]. This hypothesis is supported by the observational fact that the vertical shear of theKuroshio increases at depths similar to the top summits of both seamounts: shear peaks appear at 200 m
depth near Seamount I and at 150 m depth downstream of Seamount II (Figure 3b). Flow over topography
may be characterized by the topographic Froude number Frt 5 U0/(Nh0), where U0 is the upstream velocity
and h0 topography height [Baines, 1995; Klymak et al., 2010]. At Seamount II, U0 5 0.5 m s21, N 5 1022 s21,
and h0 5 500 m yields Frt21 5 Nh0/U0 5 10. The large inverse Froude number suggests that the upstream
water is partially blocked by the topography, as evident in our observations, and lee waves are generated

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10.1002/2017JC013049[Baines, 1995; Klymak et al., 2010]. The Kuroshio-topography interaction probably triggers internal hydraulics
and internal lee waves. Nonlinear steepening of the lee waves probably leads to wave breaking and turbulent mixing. We expect turbulent mixing in the vicinity of the seamount would be much stronger than atour observational sites, which will be demonstrated later.
3.3. Temporal Variations of Currents and Turbulence at the Mooring Site
At the mooring site, we observed modulation of the Kuroshio ﬂow and turbulence by tides and waves. Figures 4a–4e show the temporal variations of barotropic tidal velocities, baroclinic tidal velocities, and timeaveraged velocity. Here, tidal velocity is deﬁned as an anomaly from time-average. Barotropic and baroclinic
tidal velocities are calculated as depth-averaged tidal velocity and as an anomaly from the depth-averaged
tidal velocity, respectively.
Barotropic velocity during the 25 h of proﬁling is mainly semidiurnal and typically has a magnitude of 0.1 m
s21 (Figure 4a). Baroclinic tidal currents have a magnitude of 0.1–0.3 m s21 which are comparable to timeaveraged velocities, induced mainly by the Kuroshio, with a magnitude of 0.5 m s21. The baroclinic currents have a high-vertical-wavenumber structure, as well as a low-mode semidiurnal one, creating timeevolving enhanced shear layers (Figure 4f). The turbulent dissipation rate is elevated to O(1027) W kg21,
especially within strong shear layer at 200–300 m depths during the latter half of the proﬁling period. Thisstrong turbulence is clearly associated with small Richardson numbers within the enhanced shear layer(Ri < 1/4, Figure 4g). Vertical diffusivity is similarly elevated at 200–300 m depths to O(1024)–O(1022) m2 s21(Figure 4h).
In the enhanced shear layer at 200–300 m depths, vertical movement of isopycnals (e.g., 25.0 and 25.5 rh) is
diurnal rather than semidiurnal (Figure 4). The enhanced shear and turbulence in the latter half of the proﬁling period also imply diurnal variability. At the mooring site (30.468N), the inertial frequency (0.9973 cpd:
cycle per day) is nearly same as the diurnal frequency (K1 constituent: 1.0029 cpd).
Previous numerical model simulations showed that strong semi-diurnal internal tides are generated in
the Tokara Strait and suggested that they can lead to local mixing [e.g., Niwa and Hibiya, 2004]. However,
our observation suggests that strong turbulence is related to diurnal/inertial baroclinic motion rather
than a semi-diurnal one. Rainville and Pinkel [2004] and Nagai et al. [2015] indicated that elevated turbulence in the Kuroshio is related to high-wavenumber near-inertial internal wave shear. We speculate thatnear-inertial waves play an important role in the modulation of the vertical shear and turbulence strength
observed at the mooring site, although the hypothesis cannot be demonstrated from our limited
observations.
The relatively weak turbulence strength at the mooring site suggests that internal tides may have, at most,secondary impacts on turbulent mixing in the Tokara Strait [Niwa and Hibiya, 2004]. The turbulent mixing inTokara Strait is driven primarily by the Kuroshio deep current interacting with the abrupt topography. In thefollowing discussion, we focus our scope on the turbulent mixing and water-mass modiﬁcation around the
Seamount II.

4. Discussion
4.1. T-S Transformation by Vertical Mixing Along the Kuroshio Pathway
Turbulent mixing can modify the T-S properties of water masses along the Kuroshio. Here, we examine T-S
evolution upstream and downstream of Seamount II using observations at the mooring site and B4, respectively. Figure 5 shows T-S relation at the mooring site and B1–B8. The 25 h-averaged T-S properties at themooring site represent typical Kuroshio water (black dots in Figure 5). Water masses at B5–B8 (yellow-green
dots in Figure 5) are nearly identical to the upstream Kuroshio water, whereas those at B1–B2 (bluish dots in
Figure 5) are similar to coastal water, with low salinity (S < 34.75). The T-S properties at B3 and B4 in the Kuroshio core (reddish dots in Figure 5) are similar to each other and are considered to be representative of
the Kuroshio water downstream of Seamount II. We compare T-S properties at B4 with those of the Kuroshio
water at the mooring site. Their T-S properties are nearly identical in the surface (rh < 23.3) and in the
deeper (rh >24.9) layers whereas they are distinctly different in the intermediate layer.

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Figure 4. Time evolution of tidal currents, stratiﬁcation, vertical shear and turbulence proﬁles at the mooring site. (a) eastward (blue) and northward (red) barotropic tidal velocities, (b)eastward and (c) northward baroclinic tidal velocities (d) time-averaged eastward and (e) northward velocity proﬁles (f) total vertical shear squared S2 (g) gradient Richardson number Ri(bluish shade with purple shade indicating Ri < 1/4) and turbulent dissipation rate E (reddish shade) (h) vertical eddy diffusivity Kq. Solid lines in Figures 4b, 4c and Figures 4f–4h represent potential density rh. Horizontal axis indicates time in Japan Standard Time (JST: UTC 19 h).

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T / °CThe Kuroshio water at themooring site is characterized by
Mooringa subsurface salinity maximum
23
B1(S > 34.85) existing over 100–B2
150 m depths, one of the disB3
24
tinct characters of the Kuroshio
B4
B5
in the ECS [e.g., Yanao andB6
Matsuno, 2013; Mensah et al.,B7252014]. Downstream of SeaB8
mount II (Stn.B4), the salinity
maximum decreases signiﬁcantly in the layer of 23.3–24.9
26
rh. This decrease in salinity islikely due to the water-masstransformation induced by vertical mixing. The density range
27
23.3–24.9 rh is equivalent to adepth range of 100–200 m at
B4 (Figure 3, contour line)
34.4
34.5
34.6
34.7
34.8
34.9
where large eddy diffusivity of
S / PSUKq 5 2–10 3 1023 m2 s21 wasobserved (Figure 3d). Note that
Figure 5. Temperature-salinity (T-S) plot from observations at the mooring site and thethere is no apparent abrupt
section B (Figure 1b): 25 h average at the mooring site (black dots), B1–B2 (bluish dots),change of topography along
B3–B4 (reddish dots), and B5–B8 (yellow–green dots). Contour lines indicate potential
density.
the Kuroshio path between themooring site and Seamount II(Figure 3). The eddy diffusivity is generally small, Kq  O(1025) m2 s21, in the layer of 23.5–25.0 rh at themooring site (Figure 4d). Nevertheless, T-S properties drastically changed at B4. We expect that the watermass upstream Seamount II had the same T-S properties as the mooring site and that most of changes in
the water-mass occurs between Seamount II and B4.
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
34.3

Observed T-S

To further investigate the mixing process, we considered a simple one-dimensional diffusion balance,
expressed as


@T @
@T
5
KT
@t @z
@z
(1)


@S @
@S
5
Ks
@t @z
@z

where KT and KS are vertical eddy diffusivity of temperature and salinity, respectively. We adopt the observed
eddy diffusivities at B4 and assume KT 5 KS 5 Kq. The observed eddy diffusivity proﬁle is low-pass ﬁltered in
the vertical and is extrapolated using a value, Kq 5 1 3 1023 m2 s21 (shown by red line in Figure 6b) based on
the observations. Note that the extrapolation does not have signiﬁcant impact on the following analysis. Equations (1) are numerically integrated in time using the implicit Euler method. A second-order central difference
scheme in the vertical is used to evaluate the turbulent ﬂux divergence. Observations of the averaged T-S at
the mooring site (black dots in Figure 5) are used as the initial condition (t 5 0: black dots in Figure 6).
Figure 6a shows the temporal evolution of T-S properties due to the vertical divergence of turbulent ﬂuxes.
The subsurface salinity maximum at the mooring site decreases as a result of turbulent mixing. After 10days of vertical turbulent mixing, the T-S properties have evolved to resemble the observed T-S properties
at B4 (red dots in Figure 6a). The advection time scale from Seamount II to B4 is about Dtm 5 Dx/U  14 h
where Dx 5 15 km the distance between the seamount and B4 and U 5 0.3 m s21 the Kuroshio speed averaged over 100–200 m depths.
The much longer diffusion time scale than the advection time scale suggests that the turbulent mixing closer
to Seamount II is likely at least 10 times greater than observed at B4, i.e., Kq 5 O(1022)–O(1021) m2 s21

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Figure 6. Examinations of T-S modiﬁcation within the Kuroshio near Seamount II with simple diffusion models: (a) evolution of the T-S properties at the mooring site with the vertical diffusion based on low-pass ﬁltered eddy diffusivity observed at B4 shown in Figure 6b: original Kq proﬁle (blue) and the low-pass ﬁltered one (red). The low-pass ﬁltered proﬁle is extrapolated assuming a constant value of 1023 m2 s21 below 260 m depth. Different markers represent T-S properties at different times: t 5 0 (black dots), t 5 1 day (blue dots), t 5 4 days (blueopen circle), t 5 7 days (blue open diamond), t 5 10 days (blue open triangle). T-S at B4 is also shown by red dots. (c) Same as Figure 6a but for the horizontal diffusion with a constanthorizontal eddy diffusivity, Kh 5 100 m2 s21. (d) T-S evolution at t 5 1 day with combined vertical and horizontal diffusion. The vertical eddy diffusivity is 10 times larger than one used in
the vertical diffusion experiment.

near Seamount II. Following Klymak et al. [2010], we estimate the horizontal scale of lee waves, which we
believe are responsible for turbulent mixing in the vicinity of Seamount II. The horizontal wavelength of lee
waves kx over the seamount is estimated as, kx  2pUm/(aN), where a and Um are the topographic aspectratio and the upstream velocity of the obstacle crest, respectively. For Seamount II where a 0.1 and Um
1 m s21, the estimated kx 5 O(1) km is much shorter than Dx 5 15 km, suggesting that the turbulent mixing occurs at the vicinity of the seamount. We thus speculate that the turbulent mixing near Seamount II ismuch more than 10 times (e.g., 100 times) higher than the observed one at B4. Further turbulence observations and numerical experiments are needed to conﬁrm the suggested strong turbulence near Seamount II
and to understand the dynamics of the turbulent processes.
4.2. Horizontal Mixing
As discussed in the previous section, the modiﬁcation of water-mass observed at B4 can be explained byvertical mixing induced by Kuroshio-topography interaction. However, lateral mixing between coastal water(B1–B2) and Kuroshio water (B5–B8) may also lead to the decrease in the salinity maximum observed at B3–
B4 (Figure 5). To assess the effect, we consider horizontal diffusion between the coastal and the Kuroshio
waters.
We considered the effect of horizontal mixing to the water-mass modiﬁcation based on a one-dimensional
horizontal diffusion equations,
@T
@2T
5Kh 2
@t
@x
(2)
2

@S
@ S
5Kh 2
@t
@x

where Kh is depth-independent horizontal eddy diffusivity. Here we consider the evolution of T-S properties
due to horizontal mixing with coastal water (B2) and the Kuroshio water. The horizontal diffusivity Kh is set
to 100 m2 s21, following Chang et al. [2013] where they investigated Kuroshio-induced island wake characterized by quite similar length and velocity scales as those in the Tokara Strait. We have tested various different values of Kh, and conﬁrmed that the conclusion of this analysis is not sensitive to varying horizontal
diffusivity in its reasonable range, 1–500 m2 s21.

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Equations (2) are numerically integrated similarly as the case of the vertical diffusion. The horizontal diffusion decreases salinity of the water-mass throughout the entire depth (Figure 6c). It is obvious that at any
time, the horizontal diffusion cannot explain the observed water-mass modiﬁcation at B4 at all in regard tovertical proﬁle.
We also performed a diffusion experiment with combined vertical and horizontal diffusion. Vertical and horizontal diffusivities are the same as those used for the vertical and horizontal diffusion experiments, respectively, but the former is increased by 10 times based on our speculation noted in section 4.1. The
experiment reproduces the observed T-S properties after 1 day integration similarly as the vertical diffusioncase, demonstrating the effectiveness of our speculation (Figure 6d). We thus conclude that vertical mixing
plays the dominant role in modiﬁcation of the Kuroshio subsurface water observed at B4 and that the contribution of lateral mixing is secondary.

5. Conclusion
This study provided evidence of strong turbulence generation in the Tokara Strait. The striking feature of
the strait is that Kuroshio-topography interaction generates highly-elevated turbulence caused by manysmall islands and seamounts within the Kuroshio ﬂow ﬁeld. The vertical diffusivity in the Kuroshio downstream of a seamount is enhanced to Kq  O(1023)–O(1022) m2 s21 in a 70 m thick elevated shear layer
with Ri < 1/4, an increase in diffusivity of nearly 100 times from the upstream site. The observed values of
Kq are much larger than the canonical value Kq 5 1 3 1024 m2 s21 [Munk, 1966; Munk and Wunsch, 1998]
and the estimates at the margin of the ECS from the Argo ﬂoats, Kq 5 O(1025)–O(1024) m2 s21 [Whalen
et al., 2012]. The strong vertical turbulent diffusion leads to signiﬁcant water-mass modiﬁcation along theKuroshio. A one-dimensional vertical diffusion model using the observed eddy diffusivity reproduces theobserved water-mass transformation. However, the diffusion time scale is 10 times greater than the advection time scale from the seamount to the observed station B4, suggesting much stronger turbulent mixing
occurs in the vicinity of the seamount than at B4, i.e., Kq  O(1022)–O(1021) m2 s21
We also observed that:at a site away from the abrupt topography, high eddy diffusivity Kq  O(1023) m2 s21 is related to modulation of the Kuroshio shear by internal waves motion.
An important feature of the Tokara Strait is that strong turbulent mixing is generated in the upper layer,
shallower than 200 m. This is due to the presence of many shallow-water topographic features within the
Kuroshio. The depth of strong vertical mixing is important for biological production; it controls nutrient supply to the euphotic zone from deeper layers. In the Kuroshio, the depth of the 1-% light intensity is usually
greater than or equal to 100 m [e.g., Shiozaki et al., 2011]. The shallow mixing in the Tokara Strait can have
impacts on high biological production there and in the downstream region [e.g., Watanabe et al., 1996].
Turbulent mixing induced by ﬂow-topography interactions is generally the strongest in the area adjacent totopography [Nikurashin and Ferrari, 2010b; Sheen et al., 2013; Alford et al., 2013; Nishina et al., 2016]. Nishina
et al. [2016] observed huge eddy diffusivity (Kq  O(1021) m2 s21) in internal hydraulics in the deep Kerama
Gap. Sheen et al. [2013] observed that locally enhanced turbulent dissipation caused by breaking lee waves
radiated from rough-bottom region in the Antarctic Circumpolar Current region. The turbulence observed
at B4 cannot be the decaying turbulence generated at the seamount, because the decaying time scale ofturbulence is N21  O(102) s, which is much shorter than the advection time scale from the Seamount II to
B4, 1 day. We hypothesize that hydraulics and nonlinear steepening of internal lee waves lead to turbulent mixing and the associated water-mass modiﬁcation. They might occur locally in the vicinity and downstream of the seamount.
Our observations revealed a feature in the Tokara Strait similar to the shear instability resulted from theblocking of the deep Kuroshio ﬂow by a seamount east of Taiwan reported by Chang et al. [2016]. They
reported estimation of vertical eddy diffusivities of Kq  O(1021) m2 s21 just above a seamount in the Kuroshio, which is consistent with our estimation. These facts suggest that the Kuroshio is strongly modiﬁed at
the inlet and the outlet of the ECS. The pathway of the Kuroshio in the Tokara Strait varies on an intraseasonal time scale [Nakamura et al., 2006], similar to the Kuroshio east of Taiwan [Zhang et al., 2001]. If theKuroshio takes the southern-mode pathway in the Tokara Strait unlike during the present observations, it
may still interact effectively with steep topography associated with the Tokara Islands [Hasegawa et al.,TSUTSUMI ET AL.

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2008]. Turbulent mixing in the Tokara Strait likely depends on the Kuroshio pathway and varies on an intraseasonal time scale.
To understand turbulent mixing in the Tokara Strait, further investigations of hydraulics, generation andbreaking of internal waves near the seamounts are needed. Furthermore, effects of such topographicallyinduced, localized turbulent mixing on modifying the total energy of the Kuroshio over the Tokara Strait
remains as an open question for future studies [Gula et al., 2016; Mashayek et al., 2017]. Our study suggeststhat a better model prediction of the Kuroshio and water-mass properties in the Kuroshio requires an accurate parameterization of the Kuroshio interaction with topography and the associated turbulent mixing.
Acknowledgments
We would like to thank the Captainand crew of T/V Kagoshima-maru for
their help in this ﬁeld experiment andto thank Keunjong Lee, Daisuke
Hasegawa, and Ayako Nishina for their
help in collecting data. Bottom
topography used in this study is basedon the J-EGG500 produced by Japan
Oceanographic Data Center (http://
www.jodc.go.jp) and the ETOPO1(http://rda.ucar.edu/datasets/ds759.4).
The Kuroshio axis position data set
was produced by Marine Information
Research Center, Japan Hydrographical
Association (http://www.mirc.jha.or.jp/
en/index.html). We thank Eric D’Asaro
at University of Washington for
constructive comments. Commentsfrom two anonymous reviewers arehelpful in improving the original
manuscript. Data used in this paper
are available at https://doi.org/10.
6084/m9.ﬁgshare.5135086. This study
is supported by Grant-in-Aid for
Scientiﬁc Research on Innovative Areas(MEXT KAKENHI grants: JP15H05821
and JP15K21710). Lien’s involvementin this analysis is supported by theOfﬁce of Naval Research (N00014-15-12318).

TSUTSUMI ET AL.

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