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Internal Hydraulic Transition and Turbulent Mixing Observed in the Kuroshio overthe I-Lan Ridge off Northeastern Taiwan
MING-HUEI CHANG,a,b YU-HSIN CHENG,c YU-YU YEH,a YIING JANG YANG,a,b SEN JAN,a CHIH-LUN LIU,dTAKESHI MATSUNO,e TAKAHIRO ENDOH,e EISUKE TSUTSUMI,f JIA-LIN CHEN,g AND XINYU GUOhaInstitute of Oceanography, National Taiwan University, Taipei, Taiwanb
Ocean Center, National Taiwan University, Taipei, TaiwancDepartment of Marine Environmental Informatics, National Taiwan Ocean University, Keelung, TaiwandCollege of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis, OregoneResearch Institute for Applied Mechanics, Kyushu University, Fukuoka, Japanf
Atmosphere and Ocean Research Institute, University of Tokyo, Tokyo, Japang
Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, TaiwanhCenter for Marine Environmental Studies, Ehime University, Ehime, Japan(Manuscript received 28 October 2021, in ﬁnal form 3 July 2022)
ABSTRACT: Complex small-scale processes and energetic turbulence are observed at a sill located on the I-Lan Ridge
that spans across the strong Kuroshio off Taiwan. The current speed above the sill is strong (1.5 m s21) and unsteady(60.5 m s21) due to the Kuroshio being modulated by the semidiurnal tide. Above the sill crest, isothermal domes, withvertical scales of ;20 and ;50 m during the low and high tides, respectively, are generated by turbulent mixing as a resultof shear instability in the bottom boundary layer. Tidally modulated hydraulic character modiﬁes the small-scale processes
occurring on the leeward side of the sill. Criticality analysis, performed by solving the Taylor–Goldstein equation, suggeststhat the observed lee waves and intermediate layer sandwiched by two free shear layers are related to the mode-1 andmode-2 critical control between the sill crest and immediate lee, respectively. Around high tide, lee waves are advected further downstream, and only mode-1 critical control can occur, leading to a warm water depression. The shear instabilities
ensuing from the hydraulic transition processes continuously mediate ﬂow kinetic energy to turbulence such that the statusof marginal instability where the Richardson number converges at approximately 0.25 is reached. The resultant eddy diffusivity Kr is concentrated from O(1024) to O(1023) m2 s21 and has a maximum value of 10 m2 s21. The sill on the western
ﬂank of the Kuroshio is a hotspot for energetic mixing of Kuroshio waters and South China Sea waters.
KEYWORDS: Internal waves; Kelvin-Helmholtz instabilities; Small scale processes; Topographic effects; Turbulence

1. Introduction
The generation of turbulence by tidal and geostrophic ﬂows
over steep topography serves as a pathway for the energy cascade in the ocean where kinetic energy from winds and tides
is transformed into microscale turbulent dissipation and mixing (Kunze et al. 2006; Nikurashin and Ferrari 2011). The
transformation requires a downscale cascade from ﬂow energy to microstructure turbulence (,1 m). The commonly
seen small-scale processes that mediate the energy transformation include lee waves (Kunze and Lien 2019; Legg 2021)
and hydraulic jumps (Farmer and Armi 1999; Wesson and
Gregg 1994; Moum and Nash 2000; Nash and Moum 2001;
Armi and Farmer 2002; Alford et al. 2013; Winters 2016)
occurring in the immediate lee of the obstacle. These are too
costly to be resolved in large-scale models. Therefore, parameterizing drag and turbulent mixing due to lee waves is required in oceanic and climate models (MacKinnon et al. 2017;

Denotes content that is immediately available upon publication as open access.
Corresponding author: Ming-Huei Chang, minghueichang@ntu.
edu.tw

Kunze and Lien 2019; Moum 2021; Legg 2021). Fundamentally, a better understanding of these processes occurringat the subgrid scale is needed to improve physics-based
parameterization schemes. As the small-scale processes generated by tidal ﬂow over topography have been observed ingreater detail than those driven by geostrophic ﬂow (Legg2021), in this paper, we examine the energetic small-scale processes that extract the geostrophic ﬂow kinetic energy tonear-ﬁeld turbulence at a sill above the I-Lan Ridge in thestrong Kuroshio northeast of Taiwan (Fig. 1a). As will beshown later, the Kuroshio ﬂow speed is tidally modulated.
The Kuroshio is the western boundary current in the northern Paciﬁc, which transports sizeable amounts of warm andsalty water from the low-latitude to midlatitude ocean, modulates the global climate, and dominates regional ocean dynamics along its path. Its transport and maximum velocity axis are
signiﬁcantly modulated by mesoscale eddies (Lien et al. 2014;
Jan et al. 2015; Cheng et al. 2017; Jan et al. 2017; Chang et al.
2018). Recent observations further revealed that ﬂow interactions with abrupt topography along the Kuroshio main axis,e.g., headlands (Cheng et al. 2020), continental slopes (Endohet al. 2016), seamounts (Chang et al. 2016), small reefs (Hasegawa
et al. 2021), and islands (Chang et al. 2013; Hasegawa et al.
2004; Tsutsumi et al. 2017; Chang et al. 2019), are the primarysources of submesoscale vortical motions, which ultimately

DOI: 10.1175/JPO-D-21-0245.1
Ó 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright
Policy (www.ametsoc.org/PUBSReuseLicenses).
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FIG. 1. (a) Bathymetry and surface current vectors around Taiwan derived from satellite absolute dynamic topography (ADT) on 11 May 2018. (b) Detailed bathymetry within the black box in (a), with the thick black line denoting
the track of cross-sill (along-stream) surveys conducted during the 2021 cruise (Ex2). The red lines in (a) and (b) represent the 500-m isobath. The blue lines in (a) and (b) represent the 1000-m isobath. The thin black lines in (b) reﬂect
isobaths from 50 to 500 m with an interval of 50 m. The Suao tidal station is denoted as a yellow star in (a). The locations of proﬁling station G2 and mooring G3 are denoted as the green circles in (b). The interval between P1 and P2
is the survey track in the 2018 cruise (Ex1).

lead to a downscale energy cascade and trigger turbulent mixing and dissipation. The near-inertial wave shear around topography also contributes to turbulence generation (Nagai
et al. 2017). Enhanced turbulent mixing can extend ;100 km
along the Kuroshio in the Tokara Strait (Nagai et al. 2021). In
addition to its dynamical inﬂuences, the most striking biochemical effects of the resulting turbulence on the Kuroshio
are 1) mixing could rapidly and signiﬁcantly change the hydrographic properties of the Kuroshio, e.g., the modiﬁcation of
the subsurface salinity maximum (Tsutsumi et al. 2017), and2) turbulent nitrate ﬂux could promote production of phytoplankton (Kobari et al. 2020; Hasegawa et al. 2021; Acabado
et al. 2021) in the oligotrophic Kuroshio.
The I-Lan Ridge spans the main path of the Kuroshio
stream (Fig. 1b). The topographic passage on the I-Lan Ridge
is known as the East Taiwan Channel (ETC), which is an entrance for the Kuroshio ﬂowing into the East China Sea. The
shallow shelves on the ridge characterized by the 500-m isobath (red curve in Fig. 1a) obstruct the Kuroshio and strongly
affect the ﬂow. Of particular interest are the small-scale processes on the shelf extending from Taiwan’s coast (black box
in Fig. 1a). Detailed bathymetry shows an isolated sill separated from the extended shelf by a narrow channel (Fig. 1b).
The sill was selected as the targeting area in our experiments,
where the Kuroshio ﬂows at speeds varying between 1.5 and2 m s21 during our measuring period as a result of tidal modulation, presumably due to the generation of M2 internal tides(Lien et al. 2013). The encounter of the strongly unsteady
ﬂow with the sill leads to the generation of a rich ﬁeld ofsmall-scale processes in the near ﬁeld, fast evolution, and intense turbulent mixing that changes over time, which haverarely been observed before.
To gain an overall insight into the physical processes, we startby evaluating the nonlinearity of the stratiﬁed ﬂow by estimating the lee wave Froude number (Aguilar and Sutherland 2006;
Legg 2021)
FrL 5 Nh0 /U0 ,(1)where N is the buoyancy frequency, h0 is the vertical scale ofthe sill, and U0 is the upstream ﬂow speed. For FrL , 1, when
the sill has a small height and/or stratiﬁcation is weak, the lee
waves are linear; therefore, the classic linear theory (Bell1975) can be applied. In the regime of FrL . 1, the ﬂow ischaracterized by partial blocking upstream and the generationof nonlinear lee waves, hydraulic control of the jet, and a stagnant wedge with well-mixed water downstream of the sill
(Baines 1987; Winters 2016; Legg 2021). The ﬂow kinetic energy is partly converted to a hydraulically controlled jet anddissipated in a hydraulic jump. According to our observations

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upstream, FrL is 1.8–2.4, given N ; 0.012 s21, h0 ; 300 m, andU0 is 1.5–2 m s21, suggesting the likely presence of nonlinear
lee waves, hydraulic jumps, and wedges of well-mixed layers.
In this study, based on two ﬁeld experiments, we analyze theﬂow criticality, detail the evolution of the hydraulic transitionand lee wave, and quantify their resulting turbulent mixing
underlying the strong and tidally modulated Kuroshio ﬂow
over a sill. The processes of lee wave breaking due to Kelvin–
Helmholtz (KH) instability and ﬂow advection above the sill
crest are also presented. The signiﬁcant modiﬁcation of thehydrographic properties due to strong turbulent mixing are
examined.

2. Experiments and data
Experiments were performed on two cruises conducted in
May 2018 (Ex1) and May 2021 (Ex2) around the spring tideperiod. The ﬁrst cruise (Ex1) was conducted on board R/V
Ocean Researcher 2 (OR2), and the second cruise (Ex2) wason board R/V New Ocean Researcher 2 (NOR2). Overall,these measurements were focused on the 45-km cross-sill andalong-stream transects (Fig. 1b). During Ex1, a subsurface
mooring deployed at G3 in the immediate lee of the sill
(Fig. 1b) was operational for 5 days (11–16 May). One upwardlooking 600-kHz acoustic Doppler current proﬁler (ADCP)
and one downward-looking 300-kHz ADCP were mounted ona main frame of the mooring at ;80 m. The pair of ADCPs
measured velocity proﬁles over 30–180 m with bin sizes of 2
and 4 m, respectively, every 30 s. Simultaneously, the mooring
was equipped with 47 thermistors with a sampling interval of
10 s. Forty-three of the thermistors were attached to the mooring line distributed with a vertical resolution of 1–2 m spanning
85–165 m (red dots in Figs. 7a,d and 8a,d). Three of the four
remaining thermistors were attached above 85 m and the remaining one was set below 165 m. A bottom-mounted mooring was simultaneously deployed at G2 but was not recovered
due to unknown reasons. The hourly tidal sea levels recorded
at a nearby tide gauge station Suao (indicated by a star sign in
Fig. 1a), maintained by Taiwan’s Central Weather Bureau,
were used to indicate the tidal phase during our measuring
period. Shipboard measurements of two transect surveys andstation proﬁling were carried out in the period of mooredmeasurements (as indicated by the horizontal lines in Fig. 4c).
A 12.5-km transect from P1 to P2 (P1–P2 line) was chosen(Fig. 1b) for measurements, consisting of a shipboard ADCP
(150-kHz TRDI ADCP) and echo sounder (120-kHz Simrad
EK60) with sampling intervals of 1 min and 5 s, respectively.
Shipboard time series stations were conducted at G2 (100 m)
on the sill crest and G3 (220 m) in the immediate lee of the sillfor .24 h using simultaneous shipboard measurements andturbulence proﬁles using a loosely tethered vertical microstructure proﬁler (VMP-500), manufactured by Rockland Scientiﬁc International, Inc. (RSI).
Three runs of shipboard surveys along the full 45-km transect (Fig. 1b) were performed in Ex2. Observations weretaken using a combination of a shipboard 75-kHz ADCP and
tow-yo turbulence proﬁler. The tow-yo turbulence proﬁler
used was the vertical microstructure proﬁler-250 (VMP-250)

manufactured by RSI. The details for the operation can befound in Nagai et al. (2017) and Chang et al. (2021). In addition, temperature, conductivity, and ﬂuorescence sensors
were installed on the VMP-250, and the data were calibrated
by a CTD cast that was proﬁled simultaneously. Microstructure proﬁles taken from VMP-500 (Ex1) and VMP-250 (Ex2)provided measurements of centimeter- to millimeter-scale
shear so that the dissipation rate of turbulent kinetic energy(TKE) e was estimated (see the appendix). The processing of
the microstructure data and estimate of e is based on the routines provided by RSI (ODAS; Douglas and Lueck 2015).
In the following analysis, all measured currents are expressedas the cross-stream velocity u and along-stream velocity y obtained by rotating the coordinate system 228 (mean upstream
current direction) clockwise.

3. Internal hydraulic control, shear instability, andturbulencea. Hydrography and turbulence
Three repeated cross-sill surveys along the 45-km transect(Ex2; Fig. 1b) reveal remarkable discrepancies in temperature, salinity, and e from the upstream to the downstream
ﬂow (Fig. 2). The temperature transects (Figs. 2a,d,g) show
isothermal doming mostly above the crest of sill, followed by
an isothermal depression. In the ﬁrst and second surveys,
there is a well-mixed layer below the depression. The salinity
transect in the third survey (Fig. 2h) clearly demonstrates thatthe upstream ﬂow could climb on the sill crest because the salinity maximum at ;100–200 m near the southern end of thetransect (3 km) rises to 50–100 m above the sill crest. The salinity maximum (34.8–35 psu) at 100–200 m, a typical featureof West Philippines Sea Tropical Water (WPSTW) (Chen
2005; Mensah et al. 2014; Jan et al. 2015), disappears after theimmediate lee of the sill. A similar spatial change in salinity
distribution occurs in the second (Fig. 2e) and ﬁrst (Fig. 2b)runs, but the breakpoint is shifted ahead of the sill.
The salinity within the isothermal dome is 34.5–34.6 psu,
which is between 34.8 and 35 psu in the upstream layer of thesalinity maximum and 34.3–34.4 in the upper layer above thesill (0–40 m). This suggests dramatic mixing processes occurred above the two sills. Indeed, a strong TKE dissipation
rate e ranging from O(1027) to O(1024) W kg21 is found within
the isothermal doming and leeward side of sill (Figs. 2c,f,i).
Clearly, the region above the sill acts as a hotspot of turbulence
mixing the high-salinity water advected and raised from the upstream ﬂow with the low-salinity water in the upper layer above
the sill. This is a striking example of small-scale processes contributing to sudden changes in larger-scale hydrographic properties. The
detailed relationship between turbulent mixing and temperature–salinity (T–S) changes will be discussed in section 5.

b. Flow instability and hydraulic criticality
The upstream and downstream along-transect velocities (y)are mostly 1–2 and 0–0.5 m s21, respectively, in the upper 100 m(Figs. 3a,e,i). A signiﬁcant reduction in y occurs 0–4 km
downstream from the immediate lee of sill. Above the sill,

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FIG. 2. Distance–depth contours of temperature, salinity, and TKE dissipation rate for (a)–(c) the ﬁrst transect run, (d)–(f) the second
transect run, and (g)–(i) the third transect run in Ex2 (2021). The black contour lines range from 168 to 278C with an interval of 18C. The
red and magenta lines are the 238 and 188C isotherms, respectively. The red and black vertical dashed lines denote the locations of G2 andG3, respectively. Locations of VMP proﬁling are denoted by yellow triangles at the top of (a), (d), and (g). Red arrows in (a) and (b) indicate the possible sources of intermediate water in the lee.

y signiﬁcantly decreases downward, presumably due to bottom friction. The dramatic change in y in the along-stream
direction and in the vertical direction is due to sill (obstacle)
obstructing. First, a strong shear squared (S2) of 1023 s22 isfound primarily above sill (Figs. 3b,f,j). The velocity shear
squared is computed as S2 5 (­u/­z)2 1 (­y /­z)2 , where u isthe cross-transect velocity. Furthermore, the Richardson
number (Ri) is computed as Ri 5 N2/S2, where buoyancy
frequency squared N2 5 2(g/r0 )­r/­z. The occurrence of
shear instability is indicated primarily above the sill andin the downstream ﬂow from the sill, where the value ofRi , 0.25 occurs (Figs. 3c,g,k). The strong turbulence(Figs. 2c,f,i) likely results from the shear instability, as they
are mostly collocated. Therefore, the shear instability as aresult of the bottom boundary shear above the sill explains
the isothermal doming. In addition, an intermediate wellmixed layer following the doming can be seen (Figs. 2a,b).
The hydraulic character of the ﬂow (e.g., Farmer and Armi
1999; Armi and Farmer 2002) is examined to link the ﬂow variations to small-scale processes. Typically, this is made by estimating the internal Froude number by assuming a two-layer

ﬂow (i.e., Armi and Farmer 1986; Wesson and Gregg 1994;
Moum and Nash 2000). However, the assumption of two-layer
ﬂow such that only mode-1 hydraulic character can be examined is not suitable for our observations showing a multimodal
hydraulic structure (Fig. 2). Therefore, the better method ofdetermining criticality is to directly estimate the phase speedof the long internal wave modes of the ﬂow, which accounts
for continuous variations in both velocity and stratiﬁcation(Pratt et al. 2000; Gregg and Pratt 2010; Liu et al. 2012; Smythand Carpenter 2019). The criticality is determined by whether
long internal waves can propagate against the ﬂow upstream(subcritical ﬂow) or not (supercritical ﬂow). Implementations
for obtaining the internal wave speed are made by solving the
Taylor–Goldstein (TG) equation:
d 2 ŵ
N2
1
d 2U
2
1
2
2 k ŵ 5 0,(2)
dz2
(U 2 c)2 (U 2 c) dz2
where eigenvalue c is the phase speed corresponding to theeigenmode ŵ that characterizes the modal structure of vertical velocity, k is wavenumber, and U is the background ﬂow.

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FIG. 3. Distance–depth contours of along-stream velocity y, S2, and Ri21 for (a)–(c) the ﬁrst transect run, (e)–(g) the second transect
run, and (i)–(k) the third transect run in Ex2 (2021). Time series of mode-1 (black dots) and mode-2 (blue dots) internal wave propagation
speeds for (d) the ﬁrst transect run, (h) the second transect run, and (i) the third transect run, with gray shading showing the area between
minimum and maximum current velocity. The black contour lines range from 168 to 278C with an interval of 18C. The red and magentalines are the 238 and 188C isotherms, respectively. The black vertical dashed lines denote the locations of criticality transition. The red horizontal dashed lines denote velocity equal to 0 m s21. Locations of VMP proﬁling are denoted by red triangles at the top of (c), (g), and(k). The white contour lines in (c), (g), and (k) are Ri21 5 4 (Ri 5 0.25).

The TG equation is solved using the numerical method proposed by Lian et al. (2020). Here, k 5 1026 m21 is taken to
approach the long wave limit (Liu et al. 2012). The buoyancy
frequency squared N2 computed from the VMP hydrographic
proﬁles and the corresponding along-transect velocity measured by the shipboard ADCP are applied to (2). The outcomes include discrete neutral (internal wave) modes, which
are our focus, and unstable (growth) modes if Ri , 0.25 isreached (Miles 1961; Howard 1961). Essentially, each internal
wave mode arises in a pair, with the phase speed in opposite

directions in a U-following frame (Pratt et al. 2000). The
phase speeds of the ﬁrst mode (black dots) and second mode
(blue dots) internal waves are shown in Figs. 3d, 3h, and 3l forthe three runs, respectively. Mostly, the phase speed pair falls
outside the region enclosed by the minimum and maximum of
the velocity proﬁle (gray shading) which is in agreement withprevious work. An exception occurs for the estimates above
the sill due to the simultaneous presence of the unstablemode when Ri , 0.25 (Pratt et al. 2000; Liu et al. 2012). The
ﬂow above the sill is apparently supercritical (bounded by

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FIG. 4. Time–depth contours of the 1-min average (a) along-stream velocity y, (b) verticalvelocity w, and (c) temperature at G3 in Ex1 (2018). The tidal height recorded at the nearby tidegauge station Suao, denoted as a star in Fig. 1a, is superposed in (a)–(c) (thick black lines). The
horizontal blue and red lines in (c) denote the time periods of microstructure proﬁling at G2 andG3, respectively. The two green lines in (c) denote the time periods of the ﬁrst and second
along-track measurements in the 2018 cruise (Ex1). The black contour line in (a) is the 0 m s21
isotach. The two black contour lines in (c) are isotherms at 188 and 238C.

vertical dashed lines in Fig. 3) because the mode-1 wave pair
has identical downstream propagation, whereas the ﬂow upstream and downstream of the sill is subcritical as the mode-1
wave pair propagates in opposite directions. The same occurs
to the mode-2 wave. These results suggest that hydraulic control occurs near the northern slope of sill, where the ﬂow transits from supercritical to subcritical conditions. The analyses
from the three runs provide a general understanding of the interaction. All three runs are made during low to midtide.
Note that the transect surveys are composite (or quasi-synoptic)
views of rapidly evolving processes. Inferring and categorizing theevolution from the three runs would be irrelevant since the timeneeded for each run is ;5 h and, as we will unveil, the time scaleof the hydraulic transition processes is much shorter than the survey time and the criticality is modulated by tides.

4. Evolution
a. Tidal modulation
During Ex1, mooring G3 was deployed in the immediatelee of sill, located at the downstream edge of the isothermal
dome (black dashed line in Fig. 2). The time–depth plot of themoored temperature over a time segment of 3 days mostly
shows a three-layer column that is well characterized by the
188 and 238C isotherms (Fig. 4c). This three-layer structure

could be distorted around the high tide, as we will point out
later. By comparing with the ﬁrst two temperature transects
in Ex2, it is well recognized that the top of the isothermal
doming separates the upper layer and intermediate layers.
The lower interface at ;150 m separates the intermediate andlower layers. Strong e mainly occurs in the intermediate layer(Figs. 2c,f), which may lead to well-mixed water in the layer.
The water in the layer is likely to originate from the mixed
water above the sill via the hydraulic process because T–S
properties are similar to those above the sill, which are particularly clear in run 1 (as indicated by red arrows in Figs. 2a,b).
The upper, intermediate, and lower layers have along-stream
velocity y values of 0.5–1.5, 0–0.5, and ,0 m s21 (Fig. 4a). The
along-stream velocity and temperature show variability related
to sea level height (thick black curve in Fig. 4) varying during
a semidiurnal tidal period. Generally, the time series showsthat the intermediate layer descends from low tide to hightide, followed by ascending from high tide to the next low tide.
Around high tide, the upper bound of the intermediate layer(238C isotherm) presents a series of high-frequency ﬂuctuations in the range of 50–150 m, distorting the three-layer structure. In particular, these high-frequency ﬂuctuations generatestrong vertical velocities (w) of ;0.1–0.4 m s21 (Fig. 4b).
The concurrent 24-h station proﬁling at G2 on 13 May(measuring period as indicated by the blue line in Fig. 4c) on
the sill shows that the along-stream velocity (Fig. 5a) has a

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FIG. 5. Time–depth contours of the (a) along-stream velocity y, (b) temperature, (c) salinity, (d) S2/N2, and (e) e bystation proﬁling at G2 and (f) time series of mode-1 (black lines) and mode-2 (blue lines) internal wave propagation
speeds in Ex1 (2018). The black contour lines in (a) are the isotachs from 0 to 2 m s21 at an interval of 0.2 m s21. The
black contour lines in (b), (d), and (e) are isotherms ranging from 148 to 288C with an interval of 18C. The black contour lines in (c) range from 34.1 to 35.2 psu with an interval of 0.1 psu. The red contour lines are 238C isotherms. Gray
shading in (f) shows the area between minimum and maximum current velocity. The vertical dashed lines denote thetime at maximal tidal height.

period of ;12 h and is highly correlated with tidal height variations. The maximum temperature and salinity differences inthe vertical direction can reach 108C and 1 psu, respectively.
Similarly, the top of the isothermal dome is well characterized
by the 238C isotherm (red curves in Fig. 5), which verticallydisplaces with its maximum amplitude (;30 m) ;2 h lagging
from the maximum tidal current (Figs. 5a,b). Salinity within
the dome has a high value, 34.7–35.1 psu (Fig. 5c), resembling
those observed in run 3 in Ex2 (Fig. 2h), showing that thesalinity maximum in the upstream ﬂow is carried onto the sill
crest. The coexisting regions of Ri , 0.25 (Fig. 5d) and stronge (1027–1024 W kg21; Fig. 5e) within the dome below the
238C isotherm suggest that the dome forms presumably due
to the turbulent mixing resulting from the shear instability
above the sill crest. The corresponding variations at G3 aredetailed in Fig. 6. The current speed is generally ;0.5 m s21
weaker than above the sill (Fig. 6a). The intermediate layer is
enclosed by 188 and 238C isotherms (Fig. 6b). Obviously, thewater in the upper and intermediate layers here has plunged(30–50 m) from the upper warm water and bottom well-mixed
water above the sill, respectively. A clear three-layer structure
remains except for the 3-h time segment centered at high tide(vertical black dashed line in Figs. 5 and 6), when the tidal
current above the sill is strongest. Around the high tide, theintermediate layer displaces downward with entrained warm
water and numerous small ﬂuctuations from its top. The criterion of shear instability, Ri , 0.25, mostly occurs within theintermediate layer aside from the high tide (Fig. 6d). Aroundthe high tide, the occurrences of shear instability in the intermediate layer are suppressed. The vertical shear is likely
weakened due to the occurrences of turbulent mixing as we
will demonstrate later that the layer has reached status of
marginal instability, i.e., cyclic circumstance in balance between shear forcing and turbulence (Fig. 14b).

b. Unsteady lee waves and KH billows
The transition from the three-layer structure to the mode-1
dominated structure is further revealed by the echo sounderimages of two shipboard transects taken from P1 to P2(Fig. 1b) during the low tide and midtide (two green horizontal lines in Fig. 4c) of a tidal cycle. The mooring data enclosedby the black box in Fig. 4c are included for further analysis.
The P1–P2 line is positioned 14.5–27 km from the 45-km fulltransect. Here, focus is placed on the along-track distance ofUnauthenticated | Downloaded 11/17/22 11:57 PM UTC

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FIG. 6. Time–depth contours of the (a) along-stream velocity y, (b) temperature, (c) verticalvelocity, and (d) S2/N2 at mooring G3 and (e) time series of mode-1 (black lines) and mode-2(blue lines) internal wave propagation speeds in Ex1 (2018). The white contour lines in (a) are
the isotachs from 1 to 2 m s21 at an interval of 0.2 m s21 at G2. The black contour lines in(b) are isotherms ranging from 148 to 288C with an interval of 18C. The red and magenta lines
are the 238 and 188C isotherms, respectively. The vertical dashed lines denote the time at maximal tidal height. The red horizontal dashed lines denote velocity equal to 0 m s21.

23.5–27 km, where the echo sounder images of the two surveys reveal the rich ﬁeld of small-scale processes characterized by strong acoustic backscatter bands (Figs. 7a and 8a).
During survey 1 (Fig. 7a), a clear train of KH billows, characterized by aligned forward inclination and S-shaped bands(Geyer et al. 2010; Chang et al. 2016), is nearly attachedto the crest. This supports the previous conjecture of theoccurrences of KH instability using the criterion of Ri , 0.25
(Figs. 3c,g,k, 5d) in Ex2. Lee waves, with a vertical scale of;40 m, are observed at the downstream ﬂank of the sill (indicated by two yellow arrows). Two nearly parallel strong
acoustic scattering bands at ;60 and ;150 m (indicated by
two white arrows) are the predominant features on the leeward side of the sill. The strong acoustic backscatter bands

are collocated with the region of strong temperature gradients,suggesting a strong stratiﬁcation, measured by the mooring as
indicated by the vertical black dashed line in Figs. 7b and 7c,when the ship passes through the G3 mooring at 0244 UTC.
Noticeably, the strong stratiﬁcation is mostly accompanied bystrong shear. An intermediate layer is sandwiched by the twobands of strong stratiﬁcation/shear (Figs. 7b,d). Hereafter, thebands are termed the free shear layer (FSL). The upper FSL
lowers slightly at 0305 UTC, followed by a successive plunge ofwarm water in conjunction with small undulations initiating at
approximately 0430 UTC (highlighted by the red arrow in
Fig. 7b), while the strong ﬂow in the upper layer begins to separate, forming a jet-like ﬂow at approximately 80–100 m. The
FSL collocated with the jet ﬂow in the upper periphery of the

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FIG. 7. (a) Echo sounder image taken during survey 1 in Ex1 (2018). Time–depth contours of(b) along-stream velocity, (c) vertical velocity, and (d) temperature measured by mooring G3.
The contour lines in (b)–(d) show that the thermal variations range from 148 to 288C with an interval of 0.58C. The vertical white lines in (a) denote the positions of stations G2 and G3. The
red dots in (a) and (d) are the locations of the temperature sensors. The black and yellow dashedlines in (b)–(d) mark the time point when the ship passed through mooring G3 for the ﬁrst andsecond surveys, respectively. The inset shows the time series of the tidal height, with gray shading
showing the time segment of (b)–(d) and with two red boxes showing the durations of surveys
1 and 2.

intermediate layer becomes wavy from 0530 to 0730 UTC(Figs. 7b and 8b). This can be thoroughly explained by combining
the echo sounder images taken during survey 2 (Fig. 8a).
In survey 2, the preceding lee waves observed in survey 1
are advected downstream, with additional lee waves forming
close to the sill, numbered from 1 to 4 in Fig. 8a. The ship surveys from the sill to the lee of the sill and passes throughmooring G3 at 0619 UTC (denoted as a vertical yellow dashedline in Figs. 7b–d). As indicated by previous studies (Winters
2016; Musgrave et al. 2016), the structure of the lee wave consists of an upwelling region and a downwelling region in thefront (downstream) and trailing (upstream) edges, respectively. Indeed, a downward velocity of w 5 20.2 m s21 is measured by the moored ADCP during approximately the periodthat the ship passes G3 (vertical yellow dashed line in Fig. 7c),
while the mooring is at the trailing edge of lee wave 3 (Fig. 8a).
It is clear that lee wave 2 is advected downstream due to the acceleration of tidal currents from low to midtide and is then captured by the mooring at 0655–0725 UTC. Evidence includes
1) the strong backscatter revealing the trough of lee wave
2 (highlighted by the upper blue dashed line in Fig. 8a) correlating well with the strong temperature gradient at 120–130 m

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FIG. 8. (a) Echo sounder image taken during survey 2 in Ex1 (2018). Contour plots of(b) along-stream velocity, (c) vertical velocity, and (d) temperature measured by mooring G3.
The contour lines in (b)–(d) show that the thermal variations range from 148 to 288C with an interval of 0.58C. The vertical white lines in (a) denote the position of station G3. The red dots in(a) and (d) are the locations of the temperature sensors. The inset shows the time series of thetidal level, with gray shading showing the time segment of (b)–(d) and with two red boxes showing the durations of surveys 1 and 2. The two horizontal dashed lines in (a)–(c) denote depths of
90 and 170 m.

(highlighted by the upper cyan dashed line in Fig. 8b) and 2) a
clear pair of upwelling and downwelling (;0.4 m s21; Fig. 8c) isrelated to the front and trailing edges of lee wave 2 (Fig. 8d). It
is noted that the strong jet mentioned previously is depressed
and then elevated, i.e., nearly ﬂowing along the trough of the
wave (Fig. 8b).
Another signiﬁcant feature captured by the echo sounder isthe S-shaped acoustic scattering bands below the lee waves(Fig. 8a). These S-shaped acoustic backscatter bands resemble
the manifestation of KH billows (Geyer et al. 2010; Changet al. 2016). The moored observations lend further support tothe process. The S-shaped acoustic scattering band below lee
wave 2 (highlighted by the lower blue dashed line in Fig. 8a)corresponds to the downward plunging of the strong temperature gradient (lower cyan dashed lines in Figs. 8b–d). Notethat both the lee wave and S-shaped acoustic backscatterband captured by the echo sounder are ﬂipped in the time–
depth contour of the mooring measurement because the front
side of the features are measured earlier and vice versa.
Indeed, the contour of thermal variation (Fig. 8d) shows aroll-up of temperature at 0705–0710 UTC, which suggests a
KH billow growing at the front trough of lee wave 2. It is
likely that the KH billow grows at the expense of the kinetic
energy of the jet ﬂow at the lower periphery of the wave.
The following wave marked by 1 in Figs. 8b–d is expected
to be lee wave 1, as shown in Fig. 8a. Lee waves 1 and 2

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FIG. 9. (a) Time series of the tidal level. Contour plots of (b) along-stream velocity, (c) verticalvelocity, and (d) temperature measured by mooring G3. The contour lines in (b)–(d) show thatthe thermal variations range from 148 to 288C with an interval of 0.58C. The gray shading in theinset shows the time segment of (b)–(d). The two red boxes in the inset show the durations ofsurveys 1 and 2.

revealed by the echo sounder image have similar structures.
However, there is no clear correspondence between the echosounder image and the moored measurement for lee wave 1(0745–0800 UTC). The measurements of the moored thermistor chain show that lee wave 1 has a breaking waveform, characterized by a chaotic thermal patch and numerous billowlike rollups at 50–170 m (Fig. 8d). Presumably, the breaking
waveform results from the collapse in KH instability. Hereafter (0800–0850 UTC), the upper warm layer with strong
ﬂow is upwelled to above 50 m, and the intermediate layer becomes thicker (;100 m) but is ;38C warmer (Figs. 8d and9d), likely due to entrainment and turbulent mixing with theupper warm layer. Meanwhile, the roll-up structure as a resultof KH instability is frequently observed in this stage, which isapproximately the period of high tide. Two clear examples ofroll-up are indicated by two arrows in Fig. 8d. Just after thehighest tidal level (0850 UTC), implying the beginning of tidal
ﬂow deceleration, lee wave 1 returns to the G3 mooring, as revealed by the contour plot at 0850–0925 UTC (enclosed byblack boxes in Figs. 9b–d), showing the nearly mirrored structure of that previously measured at 0745–0803 UTC (enclosedby black boxes in Figs. 8b–d). Lee wave 1 captured at
0745–0803 UTC has a series of three patches of strong positive w (Fig. 5c) that gently lower, followed by a strong negative w at 20–90 m. The strong positive velocity is locatednear the upward rolling side of the billows. In contrast, thefeatures are ﬂipped in the time axis during the second measurement (Fig. 9c), i.e., the strong negative w in the upper
layer (0850–0900 UTC) is followed by a series of threepatches of strong positive w (0900–0925 UTC), two of
which have their negative counterpart that is absent in theﬁrst measurement. The structure of KH billows becomeswell deﬁned, whereas they are unclear in the ﬁrst measurement. The subsequent wave at 0930–1010 UTC is likely the
returned lee wave 2, showing the ﬂipped w in the time axis
as earlier observed downwelling followed by upwelling due
to its upstream movement. The previously observed billows
disappear here. Both returned waves have longer timescales, possibly due to the varied translating speed, andthe vertical scale and w becoming stronger. Subsequently,
the processes return to the predominance of the intermediate well-mixed layer.

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FIG. 10. (a) Time series of the tidal height at Suao (black line) and tidal velocity at G2 (redline). (b) The wavelet power spectrum for vertical velocity averaged over 50–150 m at G3.
Time–depth contours of the (c) S2/N2 at mooring G3. The black contours in (b) enclose the regions of conﬁdence level larger than 95%. The vertical dashed lines denote the time of maximum
tidal level. The cyan contour lines in (c) are the 198 and 258C isotherms.

c. Interpretation
The driving mechanisms leading to the evolution shown in
Figs. 7–9 can be interpreted by the transition of the hydrauliccharacter as a result of the tidal ﬂow modulation. Returning
to the simultaneous observations at G2 (Fig. 5) and G3(Fig. 6), the ﬂow is clearly supercritical with respect to bothmode-1 and mode-2 waves above the sill at G2 (Fig. 5f) as
their wave pairs propagate downstream throughout the two
tidal periods, although the wave speeds determined using the
TG equation are strongly modulated by the tide. However,the criticality at G3 is varied (Fig. 6e). At G3, with respect tothe mode-1 wave, the ﬂow is mostly subcritical. In contrast,with respect to the mode-2 wave, the ﬂow is mainly supercritical around the high tide but is subcritical in the low and midtides. This suggests the presence of a mode-1 and a mode-2
critical control section between G2 and G3 or adjacent to G3
during the period of low and midtides. Speciﬁcally, the mode1 and mode-2 perturbations could be arrested and accumulate
between G2 and G3. The (mode-1) lee waves and the threelayer structure, i.e., the intermediate layer, likely result fromthe accumulation of the mode-1 and mode-2 perturbations,
respectively (Figs. 7a and 8a). Lee wave formation as a resultof ﬂow criticality was demonstrated by Xie and Li (2019).
Around the high tide, the tidal ﬂow is strengthened so thatthe lee waves are advected downstream and only the mode-1
critical control section could occur between G2 and G3, resulting in the mode-1 warm-water depression/entrainment(0800–0850 UTC in Figs. 8d and 9d), accompanied by strong
ﬂow ranging only in the upper 50 m. The presence of thestrong ﬂow suggests that the ﬂow above the sill is extended
further leeward at G3, leading to the supercriticality of mode-2
waves at G3. The signals of upper strong ﬂow are well-identiﬁedin the 3-day time series during high tide (Fig. 4). The above
processes repeatedly occur in each tidal cycle in our measuring
period.
We further elucidate the tidal modulation using the 5-day
moored measurements (Fig. 10). The along-stream tidal velocity (red curve in Fig. 10a) above the sill, obtained from thedepth-averaged and demeaned 24-h shipboard ADCP measurements (Fig. 5a), is well correlated with the tidal height at
Suao (black curve in Fig. 10a). Thus, tidal height is a relevant
indicator of tidal ﬂow magnitude above the sill. The wavelet
analysis of vertical velocity (Fig. 10b) shows a band of highwavelet power centered on the M2 tidal period. Moreover,the signiﬁcant wavelet power regions roughly centered on
50 min and shorter than 10 min, as enclosed by a 95% conﬁdence level, are related to the unsteady lee waves and KH instabilities, respectively, which occur predominantly aroundthe high tide. The simultaneous occurrences of lee wave andshear instability signatures (Fig. 10b) suggest instability growing along with the lee wave, as shown in Fig. 9d. The criterionof shear instability, Ri , 0.25, occurs more intensively aroundthe high tide (Fig. 10c), which lends further support. Overall,
the wavelet spectra reveal a downscale energy cascade from
Kuroshio ﬂow to lee waves and shear instabilities, both modulated by the tidal ﬂow. The next section will present the subsequent downscale cascade to turbulent mixing.

5. Turbulent mixing
a. Statistics
The microstructure proﬁles were taken in two tidal cycles(Fig. 11c), as denoted by the red line in Fig. 4c. The ship heads
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FIG. 11. (a) Time series of the tidal height at Suao. (b) Contour plot of 1-min average temperature at mooring G3. (c) Time–depth plot of TKE dissipation rate from (c) shear probe measurements (e) and (d) estimate of Thorpe scale method based on the VMP hydrographic data (eVH).
The contour lines in (b)–(d) show that the thermal variations range from 148 to 288C with an interval of 18C. The thick contour lines in (b)–(d) are the 198 and 258C isotherms.

ensure the VMP-500 is slackly tethered and freely sinks.
The ship could occasionally run against the current aroundthe high tide phase, leading to a low falling rate and tiltingof VMP-500 and resultant poor data quality. Therefore,
we omit the data sampled at tilting angle . 108 or fallingrate , 0.2 m s21 (Douglas and Lueck 2015); this results in the
missing data around high tide (Fig. 11c). In addition, e atO(1023) W kg21 is excluded from our analysis because the angles of attack of shear probe could be larger than 208 (see theappendix). TKE dissipation rate estimated using Thorpe scale
method (Thorpe 1977; Dillon 1982; Galbraith and Kelley1996) based on VMP hydrographic data (eVH; Fig. 11d) shows
consistent variations with shear probe measurements (e).
Though eVH has a relatively low vertical resolution, the timeseries of depth-averaged log10eVH nearly coincides with thatof log10e. The comparison results give conﬁdence to the microstructure observations.
The strong TKE dissipation rate mostly occurred in the depth
range enclosed by the 198 and 258C isotherms (Figs. 11b–d),which approximately characterized the intermediate well-mixed
layer at approximately low and midtides (Fig. 11a). Similarly, e
was also modulated by the tide. Around low tide, e was mostlyO(1027–1025) W kg21 and became stronger around midtide[O(1026–1024) W kg21]. Around high tide, the strongest e,

O(1024) W kg21, occurred. The measured e ranged from 10210
to 1024 W kg21. The value of the most frequent occurrence
was O(1026–1027) W kg21, which accounted for 48% of the occurrence. Eddy diffusivity was estimated using Kr 5 G«N22(Osborn 1980), where G 5 0.2 is the mixing efﬁciency. The water properties of the Kuroshio east of Taiwan are highly diverse
regarding the signiﬁcant discrepancy in temperature-salinity relationships reported in Mensah et al. (2014). They further estimated that a value of Kr ; O(1023) m2 s21 was needed to mix
the water masses, which was likely a result of ﬂow inﬂuenced by
local topography. Our measured Kr was concentrated on a
range of high values, from O(1024) to O(1023) m2 s21. Changet al. (2013) and Chang et al. (2016) reported hotspots of strong
ﬂow–topographic interactions on the leeward side of Green Island and a seamount sitting in the main path of the Kuroshio,
respectively. Our microstructure measurements suggest an additional hotspot}the I-Lan ridge, revealing that 36% of the Kr
was larger than the regional mean value of 1023 m2 s21 proposed by Mensah et al. (2014).

b. Impacts on water masses
As shown in Fig. 2, the 45-km transect exhibited strong discrepancies in T–S properties. The role of turbulent mixing on
the variability of water mass properties was examined. The

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FIG. 12. Aqua/MODIS SST taken at (a) 0500 UTC 15 May 2021 and (b) 0430 UTC 12 May 2021. (c) T–S diagram observed on the leeward side of Green Island (black dots) and off the southeastern coast of Taiwan (gray dots). The thick black, blue, and green lines in(a) and (b) are the hydrographic transects around the sill (same as Fig. 1b), on the leeward side of Green Island and off the southeastern
coast of Taiwan, respectively. The magenta, cyan, and green curves are the averaged T–S curves for Kuroshio water east of Luzon Island,West Philippines Sea Tropical Water (WPSTW), and South China Sea Tropical Water (SCSTW), respectively (Jan et al. 2015).

2021 cruise (Ex2) was conducted during 10–17 May. Transect
surveys (black line in Figs. 12a,b) around the sill on the I-Lan
Ridge were performed during the ﬁrst three days. Anothertwo upstream transects on the leeward side of Green Island(blue line) and off the southern tip of Taiwan (red line) were
performed after the I-Lan Ridge surveys. Satellite sea surface
temperature (SST) on 15 May (Fig. 12a) revealed that thetransect at Green Island (blue line) had a warm SST due toKuroshio warm water, whereas the onshore side southeast of
Taiwan (red line) had a 18C colder SST. The onshore cold water became more signiﬁcant and was likely attached with theonshore ﬂank of the Kuroshio, forming a front adjacentand parallel to our transect on the I-Lan Ridge (black line in
Fig. 12a). Hydrographic measurements along the Green Island transect show T–S properties of the water mass (black
dots in Fig. 12c) were close to (cyan curve in Fig. 12c) those of
the WPSTW (Jan et al. 2015; Mensah et al. 2014), which is the
typical water mass in the Kuroshio east of Taiwan. In contrast,hydrographic measurements off southeastern Taiwan show
T–S properties (gray dots in Fig. 12c) resembling those of theSouth China Sea Tropical Water (SCSTW; green curve in
Fig. 12c), which has been frequently found along the onshore
ﬂank of the Kuroshio (Chen 2005). The front passed throughour transect on 12 May during our sill survey (Fig. 12b), withcold and warm SSTs in the northern and southern parts of thetransect, respectively.
The cold SST was an indicator of SCSTW because thewater mass property of SCSTW was distinct north of thetransect (Figs. 13a,c,e). WPSTW became noticeable southof the transect. However, the two water masses lost their identity, as T–S properties were mostly scattered between thecharacteristic T–S curves of WPSTW and SCSTW, particularly in the middle of the transect, where the sill is located.
Strong mixing frequently occurs in regard to T–S properties
scattered between the two masses (Figs. 13b,d,f), which provides further veriﬁcation. It should be noted that the sourcesof SCSTW could also originate from the Taiwan Strait via the
Taiwan Strait throughﬂow in northern Taiwan, as indicatedby Jan et al. (2006), except for that originating from the onshore side of the Kuroshio. Since the WPSTW–SCSTW front
is persistently present adjacent to the sill (Jan et al. 2013), theregion of the sill transect is a hotspot eliciting mixing between
two water masses initiated by the hydraulic transition, as wasevident in our observations.

c. Mechanisms leading to turbulent mixing
Shear instability was demonstrated to occur in the bottom
boundary layer above the sill and in the immediate lee where
the hydraulic transition is predominant using the criterion
Ri , 0.25 (Figs. 3c,g,k, 5d, 6d, and 10c). These billows weredirectly observed above the sill (Fig. 7a), in the lee waves(Figs. 8a,d and 9d), and within the warm depression (Fig. 8d).
KH billows appeared in the free shear layer as well (Fig. 14a).
Therefore, the shear instability seems to act as the ﬁnal piece totransform the ﬂow kinetic energy to turbulence via the hydraulic transition that spawns the intermediate layer sandwiched by

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FIG. 13. T–S diagram observed in the (a),(b) ﬁrst transect run, (c),(d) second transect run, and (e),(f) third transect run. Dot colors in(a), (c), and (e) represent the transect distance. Dot colors in (b), (d), and (f) represent log10Kr, which is gray shaded if log10Kr , 24. The
magenta, cyan and green curves are the averaged T–S curves for Kuroshio water east of Luzon Island, WPSTW and SCSTW, respectively(Jan et al. 2015).

two free shear layers, the lee waves, and the warm depression.
On the whole, this can be further summarized by the probability density function (PDF) of Ri estimated using the 5-day timeseries of current and temperature measurements at 50–180 m,
where the above small-scale processes result in the hydraulictransition (Fig. 14b). The distribution of Ri ﬂuctuates at a center

value near 0.25, which is a key feature of marginal instability
status (Thorpe and Liu 2009; Smyth 2020; Chang 2021). Thiscan be interpreted as a cyclic circumstance in balance between
shear forcing and turbulence. The small-scale processes basedon the hydraulic transition progressively strengthen shear
such that the ﬂow reaches the condition of shear instability

FIG. 14. (a) Time–depth contour of temperature at G3 from 0200 to 0220 UTC 13 May 2018 and (b) probability
density function of log10 (Ri) estimated using the mooring data at G3. The three arrows point out three examples of
KH billow.

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Ri , 0.25. Consequently, turbulent mixing as a result of the collapse of shear instability reduces the shear. Ri then increases restoring the stability. Eventually, the probability distribution of
Ri concentrates at a value near 0.25. The results suggest thatthe shear instability plays a crucial role in the turbulent transition. The marginal instability above the sill boundary layer islikely. However, it is difﬁcult to verify because the near-bottom
current is measured poorly by the shipboard ADCP. Furthermore, there may be other processes leading to turbulence. The
convective instability due to warm water downwelling andthe distortion of leeward waves forced by advection could be
the secondary factor responsible for the turbulent transition.
Finally, the frontal area may favor the occurrences of the interleaving process, as found by Jan et al. (2019). Indeed, interleaving,
indicated by the zigzag-like T–S distribution, can be observed in
the T–S diagrams (Figs. 13a,c,e). The convective instability andinterleaving merit a further study.

6. Discussion and conclusions
Understanding the turbulent mixing driven by stratiﬁed ﬂow
over topography requires the observational examination of internal hydraulic ﬂows and lee waves (Legg 2021). Previous observations were mostly made over either tidal ﬂow-dominatedsills or subinertial ﬂow-dominated (abyssal) seamounts, whereas
their combining effects were rarely observed. A detailed review
was provided in Legg (2021). Lee waves (Klymak et al. 2008;
St. Laurent et al. 2012; Alford et al. 2014) and internal hydraulicﬂows (Farmer and Armi 1999; Wesson and Gregg 1994; Moumand Nash 2000; Nash and Moum 2001; Armi and Farmer 2002;
Klymak and Gregg 2004; Alford et al. 2013) were individuallyobserved in these studies though they could coexist. As an exception, Musgrave et al. (2016) reported the advection of abreaking tidal lee wave that extends from the ridge crest to thesurface and the subsequent development of a hydraulic jumpon the ridge's ﬂanks. Tanaka et al. (2021) reported an internal
hydraulic jump when the ﬂow passes over an abrupt sill. The
echo sounder captured 50-m-tall lee wave-like ﬂuctuations,which were not further interpreted. In addition, the observed
hydraulic ﬂows were predominantly mode-1 control so that theinternal Froude number based on two-layer ﬂow was capable ofdetermining the hydraulic character (Wesson and Gregg 1994;
Moum and Nash 2000). Gregg and Klymak (2014) reported ahydraulic control of mode-2 lasting more than 3 h over a continental shelf, corresponding to a TKE dissipation rate from 1028
to 1027 W kg21. Our observations detail the downscale cascade
processes of ﬂow–topography interactions based on subinertial
ﬂow modulated by the tides that comprise mode-1 and mode-2
internal hydraulic ﬂows, unsteady lee waves, shear instability,and vigorous turbulent mixing.
Here, we present observations of complex small-scale processes and energetic turbulence above a sill located at the
I-Lan Ridge that spans across the strong Kuroshio. Multiple
platform measurements include a fast-sampling and highresolution moored thermistor chain and ADCP, shipboard
echo sounder, and turbulence proﬁler. The ﬂow above the sill isstrong (1.5 m s21) and unsteady (60.5 m s21) due to the Kuroshio
ﬂow, which is periodically modiﬁed by the semidiurnal tidal

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current. In other words, the ﬂow speed oscillates with a large
amplitude but has a consistent ﬂowing direction because of thestrong mean ﬂow, suggesting that tidally induced ﬂow reversal
does not exist. Therefore, these processes are mainly driven by
geostrophic ﬂow in which the ﬂow magnitude is signiﬁcantly
modulated by the tidal current.
Our observations demonstrate the encountering of thestrongly unsteady ﬂow with the sill leads to the generation ofa rich ﬁeld of small-scale processes, fast evolution, and intense
turbulent mixing that changes over time, which have rarely
been addressed before. Above the sill, isothermal domes are
possibly generated by turbulent mixing as a result of shear instability occurring in the bottom boundary layer. The verticalscale of isothermal domes ranges from 20 to 50 m and is modulated by tidal ﬂow. Alternatively, ﬂow advection could play arole. One of our three cross-sill sections shows the upstream
ﬂow could climb on the sill crest as the salinity maximum at;100–200 m observed in the upstream rises to 50–100 m
above the sill crest (Fig. 2h), which is, however, absent in theother two sections (Figs. 2b,e). Stratiﬁcation could restrictvertical displacements, driving the ﬂow to pass around rather
than over the sill; this is examined by Burger number
Bu 5 [Nh0 /(fL)]2 , where f and L are Coriolis parameter andhorizontal scale of the sill, respectively. The average N ; 0.012 s21
in the upstream is nearly consistent in the three transects.
Bu is ;140, much larger than 1, given h0 ; 300 m,
f ; 6 3 1025 s21, and L ; 5 km. This suggests ﬂow is mostly
inﬂuenced by stratiﬁcation (Cushman-Roisin and Beckers2011), pointing out turbulent mixing plays a more importantrole in shaping the isothermal dome. High Bu also suggests
the occurrence of lateral shear layer and eddies in the lee ofthe sill, which is ignored in this study.
Observations suggest that the small-scale processes on theleeward side of the sill are initiated by the tidally modulated
hydraulic character. The criticality determined by the TG
equation shows that the ﬂow is supercritical with respect toboth mode-1 and mode-2 waves above the sill over the whole
tidal phase. In contrast, the criticality in the immediate leeward side has a dependence on the tidal phase. The ﬂow ismostly subcritical with respect to the mode-1 wave throughout the tidal phase. However, the mode-2 wave has a slower
phase speed, which is sensitive to the strong background ﬂow.
With respect to the mode-2 wave, the ﬂow is subcritical in the
low and midtides but is supercritical around the high tide.
This suggests the presence of a mode-1 and a mode-2 criticalcontrol section between the sill crest and the immediate leeduring the period of low and midtides. As a result, both themode-1 and mode-2 perturbations are expected to accumulate. The mode-1 lee waves and the three-layer structure, i.e.,
the intermediate layer, likely develop from the accumulationof the mode-1 and mode-2 perturbations, respectively. Aroundthe high tide, the lee waves are advected further downstream,
and only the mode-1 critical control section occurs such thatthe hydraulic transition forms the mode-1 warm water depression. The above processes repeatedly occurred in each of thetidal cycles in our measuring period.
Shear instability serves as the ﬁnal piece transforming theﬂow kinetic energy to turbulence via the above hydraulic

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FIG. A1. Example wavenumber spectra of velocity shear from VMP-500 with TKE dissipation rate of (a) O(1025), (b) O(1024), and(c) O(1023) W kg21. The red and green lines are the spectral curves of shear probes 1 and 2, respectively. The solid and dashed lines are
the best-ﬁt Nasmyth empirical spectra for shear probes 1 and 2, respectively.

transition that spawns the intermediate layer sandwiched by
two free shear layers, the lee waves and warm depression.
Therefore, the marginal instability status of shear and observed KH billows provide evidence that mixing is linked tothe collapse of the shear instability. In addition, convective instability could occur because of the entrainment between thetwo interfaces and the distortion of lee waves due to advection. Distortion of lee waves can also trigger the KH instability, as shown in Figs. 8 and 9. Our estimated eddy diffusivity
Kr is concentrated in a range of high values, from O(1024) toO(1023) m2 s21, and has a maximum value of 101 m2 s21. Approximately 36% of the Kr is larger than the regional hydrographic data-deduced mean value of 1023 m2 s21 in the
Kuroshio east of Taiwan (Mensah et al. 2014).
Acknowledgments. The authors thank the ofﬁcers and crew
on R/V Ocean Researcher 2 (OR2) and R/V New Ocean Researcher 2 (NOR2). Field work was aided by the hard work of
Wang-Ting Hsieh, Wen-Hua Her, Hsiang-Chih Hsieh, ShihHong Wang, Bee Wang, Wei-Ting Hung, Sin-Ya Jheng, MengChaio Heieh, and Chieh-Yuan Tsai. Prof. Takeyoshi Nagai
greatly helped the training of the UCTD deployment of ourteam. We thank the editor and two anonymous reviewers
whose comments signiﬁcantly improved the original manuscript.
MHC, YJY and SJ were supported by MOST Grants 110-2611M-002-002, 108-2611-M-002-018 and 110-2611-M-002-026, respectively. YHC was supported by the CWB of Taiwan throughGrant 1092037C and MOST Grant 110-2611-M-019 -020. T.
Matsuno, T. Endoh, E. Tsutsumi, and X. Guo were supportedby the Ministry of Education, Culture, Sports, Science andTechnology (MEXT) of Japan (15H05821), and S. Jan and T.
Endoh were supported by the Collaborative Research Programof Research Institute for Applied Mechanics (RIAM), Kyushu
University (18EA-2, 19EA-3, and 20EA-2).
Data availability statement. The remote sensing data of
SST can be obtained from https://oceandata.sci.gsfc.nasa.gov/.

The Ssalto/Duacs altimeter data can be obtained from theCopernicus Marine and Environment Monitoring Service(CMEMS) (http://www.marine.copernicus.eu). The bathymetry data used here were provided by the MOST Ocean Data
Bank (http://www.odb.ntu.edu.tw/en/). Data drawn from shipbased and moored measurements used to produce the ﬁgures
can be obtained from the Zenodo repository (https://doi.org/
10.5281/zenodo.5607210).

APPENDIX
Turbulent Velocity Shear Spectrum
Turbulent velocity shear is measured at a sample rate of
512 Hz by two airfoil probes mounted on the VMP. Basedon the isotropic turbulence and Taylor’s frozen hypothesis,
TKE dissipation rate e is estimated from the VMP measurements of vertical turbulent velocity shear ­u /­z as

e5

 2

15 ­u
15y
5 y f(k) dk,
2
2
­z

(A1)

where y is the molecular viscosity, (­u /­z)2 is turbulent
shear variance, f(k) is the shear spectrum, and k is the vertical wavenumber. The e is obtained by integrating the velocity shear spectra. Details for performing the integrationand correction can be found in Lueck (2016). Three examples of shear spectra having TKE dissipation rate O(1025),
O(1024), and O(1023) W kg21 are shown in Figs. A1a–c,
respectively. The Nasmyth spectral curves (black solid anddashed lines in Fig. A1) are used to supplement shear variance not captured by the airfoil probe at higher wavenumbers and to check on shear data quality. Compared with the
Nasmyth spectra, the attenuation of probe signal at highwavenumber (k . 150 cpm) can be found. It is induced by
the combined effect of 1) limited spatial resolution of theshear probe (Macoun and Lueck 2004; Lueck 2016) andUnauthenticated | Downloaded 11/17/22 11:57 PM UTC

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2) the cutoff frequency (98 Hz) of the antialiasing ﬁlter(Lueck 2016). The former is because of the ﬁnite size of the
airfoil probe that makes it spatially average the velocity
ﬂuctuations at eddy size comparable to the width of theprobe. Aside from the high wavenumber regime, the measured turbulent shear spectra show a good agreement with
the Nasmyth empirical shear spectra, particularly in theinertial subrange, where the slope is ;k1/3. The shear spectrum for O(1025) W kg21 (Fig. A1a) resolves both the inertial subrange and a part of the viscous subrange, i.e., theroll-off of the Nasmyth spectrum. The spectra for O(1024)
and O(1023) W kg21 (Figs. A1b,c) resolve only the inertial
subrange since the shear spectrum shifts to larger wavenumbers as e increases (Macoun and Lueck 2004). Practically,an accurate ﬁtting of the shear spectra at higher wavenumbers in the viscous subrange is not critically required forthe estimates of e. Previous measurements of high e values
were obtained mainly by ﬁtting the Nasmyth spectrum tothe inertial subrange of the spectrum (e.g., Wesson and
Gregg 1994; McPherson et al. 2019). Overall, our estimatesof e using shear spectra are acceptable.
The possible limitation to measuring a high e value using
VMP-500 is further discussed. The total velocity relative tothe shear probe is a vector sum of the instrument falling speed
W and the total cross-stream velocity ﬂuctuations, i.e., the turbulent velocity scale u . The angle of attack a 5 tan21 (u /W)should be smaller than 208 for the shear probe to linearly respond to cross-stream velocity ﬂuctuations (Lueck 2016). The
turbulent velocity scale can be inferred from the measured
TKE dissipation rate using u 5 (eL)1/3 (Tennekes and Lumley1972), where L is the integral length scale (scale of energycontaining eddy). Therefore, the largest u (and a) at a constant 2 will originate from eddies having a scale comparable
to the length of VMP-500 (1.5 m) because the larger eddies
will advect the entire instrument. Assuming the measured
e is induced by the largest eddies (L ; 1.5 m), the e value
2.24 3 1023 W kg21 (Fig. A1c) corresponds to u' 5 0.15 m s21.
Given the falling speed of 0.35 m s21, a is 238, larger than thecritical value. The high TKE dissipation rate O(1023) W kg21
appears at four data points recorded in the slow falling speed(W ; 0.3–0.4 m s21) due to the strong horizontal current drag.
The combination of high e and low W makes a comparable toor larger than 208. The above discussion suggests that the measured e O(1023) W kg21 could be problematic and, therefore, isremoved from our analysis. Statistically, the peak turbulent velocity scale could be 3 times of u . If we adopt the strict condition, this will make part of e measurements O(1024) W kg21
having a larger than 208. However, this may be overcorrected
because 1) we have assumed a “largest” eddy size comparable
to the instrument length and 2) the shear spectra generally wellﬁt the inertial subrange.
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