Progress in Oceanography 222 (2024) 103229

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Progress in Oceanography
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Semidiurnal Internal Tides in a Shelf Sea South of Japan: Characteristics,
Energetics, and Temporal variations
Shuya Wang a, Xinyu Guo a, *, Akihiko Morimoto a, Anzhou Cao b, a, Eisuke Tsutsumi c,
Yasumasa Miyazawa d, Sergey M. Varlamov daCenter for Marine Environmental Studies, Ehime University, Matsuyama, Japan
Ocean College, Zhejiang University, Zhoushan, China
Faculty of Fisheries, Kagoshima University, Kagoshima, Japand
Application Laboratory, Japan Agency for Marine-Earth Science and Technology, Kanagawa, Japanbc

A R T I C L E I N F O

A B S T R A C T

Keywords:
Internal tide
Bungo Channel
Temporal variation

Tidal mixing in a shelf sea south of Japan (Bungo Channel) plays an important role in modulating the waterexchange between the Seto Inland Sea and Pacific Ocean. In this study, based on moored observations and model
results from the Japan Coastal Ocean Predictability Experiment—Tides (JCOPE-T), the generation, propagation,and dissipation of semidiurnal internal tides in the Bungo Channel are investigated. Observational results
indicate that semidiurnal internal tides induce strong baroclinic currents reaching 0.3 m/s. Their energy shows
obvious spring-neap tidal cycles, generally coinciding with the local barotropic tidal forcing. By conducting theempirical orthogonal function analysis, we find that the observed semidiurnal internal tides are mainly domi­
nated by the first two baroclinic modes. The JCOPE-T results suggest two main generation sites for semidiurnalinternal tides in the region: one is located at a narrow strait north of the Bungo Channel, while the other is at theshelf break south of the Bungo Channel. The latter makes a major contribution to the observed semidiurnalinternal tides. Northward internal tides generated at the shelf break are superposed with those generated at thenarrow strait, causing a complex interference pattern in the channel. The temporal variation of semidiurnalinternal tides in the Bungo Channel is affected by several factors. The intraseasonal variation of semidiurnalinternal tides can be modulated by the Kuroshio warm water intrusion (Kyucho) because the occurrence ofKyucho changes the stratification in the channel and hence affects the energy conversion. The seasonal variationof semidiurnal internal tides in the Bungo Channel is determined mainly by the seasonally varying stratification;
while those generated at the shelf break are under the combined influence of seasonal stratification and back­ground currents. Southward internal tides from the shelf break are refracted due to the spatially varying strat­
ification and background currents. The varying Kuroshio path and strength modulate the refraction of internal
tides.

1. Introduction
Internal tides are a kind of internal waves with tidal frequencies,
which induce isopycnal displacements of O(10–100) m in the oceaninterior, with horizontal currents of O(0.1) m/s (Rudnick et al., 2003;
Nash et al., 2006; Alford et al., 2011). When barotropic tidal currents
flow over variable bottom topographies, they push the stratified
seawater up and down over topographies, thereby generating internal
tides (Garrett and Kunze, 2007). Internal tides are considered an inter­mediate step in the oceanic energy cascade. Globally, approximately 1

TW energy is converted from barotropic tides to internal tides andfinally contributes to turbulent mixing via the breaking of internal tides(Simmons et al., 2004; Niwa and Hibiya, 2011; Müller, 2013). It isessential for the maintenance of global meridional overturning circula­tion (Munk and Wunsch, 1998; Nikurashin and Ferrari, 2013).
Marginal seas are regarded as hotspots for internal tides. Previous
studies have indicated high energy conversion rates at the continental
shelf break and slope where large gradients of water depth exist, such as
in Biscay Bay (Gerkema et al., 2004), Monterey Bay (Kang and Fringer,2012), the northern Bay of Bengal (Jithin et al., 2020), and Amazon* Corresponding author.
E-mail address: guo.xinyu.mz@ehime-u.ac.jp (X. Guo).
https://doi.org/10.1016/j.pocean.2024.103229
Received 8 October 2023; Received in revised form 29 January 2024; Accepted 15 February 2024
Available online 17 February 2024
0079-6611/© 2024 Elsevier Ltd. All rights reserved.

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Fig. 1. (a) Bathymetry around the shelf seas west of Japan (shading, unit: km). The red rectangle indicates the study region. (b) Enlarged map for the Bungo Channel.
The black plus indicates the location of moored ADCP. Gray contours in (b) denote isobaths in meters. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

Fig. 2. Depth-averaged power spectrum for the observed baroclinic velocity. Tidal frequencies are indicated by black dashed lines and local Coriolis frequency isdenoted by red dashed lines. Semidiurnal frequency band is denoted by red shading. (For interpretation of the references to color in this figure legend, the reader isreferred to the web version of this article.)

Shelf (Tchilibou et al., 2022). Near the topography, the generated in­ternal tides usually exhibit a beam-like structure due to the super­
position of a series of vertical modes (Gerkema and Zimmerman, 2008).
Because of the low wave speed and strong vertical shear, high modes areusually dissipated locally around the generation sites (Kelly et al., 2013);
while low modes can be radiated offshore to the far field (Zhao et al.,2016; Jithin et al., 2019). Hence, the latter could affect the redistribu­
tion of energy in the ocean.
The breaking of internal tides in marginal seas leads to intensified

turbulent mixing. Lien and Gregg (2001) reported that the energy
dissipation rates exceeded 10-6 W/kg within the semidiurnal internal
tidal beam in Monterey Bay. Nash et al. (2007) observed the bottomenhanced diapycnal diffusivity induced by internal tides on the Ore­gon continental slope, with a magnitude of approximately 10-2 m2/s.
The mixing induced by internal tides further affects other processes inthe shelf seas, e.g., the resuspension of sediments (Cacchione et al.,
2002; Wang et al., 2020), nutrient transport (Xu et al., 2020), and un­
derwater sound propagation (Duda et al., 2019).
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neap tide (Takeoka and Yoshimura, 1988; Takeoka et al., 1993). Further
numerical studies indicate that the Kyucho is attributed to the temporalvariation of tidal mixing. Namely, enhanced tidal mixing in the Bungo
Channel during the spring tide could inhibit the northward intrusion of
the Kuroshio; while weakened mixing during the neap tide enables thewarm water to enter the channel (Nagai and Hibiya, 2012; 2013).
Internal tides are responsible for turbulent mixing in the Bungo
Channel. Observational results by Kawamura et al. (2006) demonstratestrong semidiurnal internal tides associated with isotherm displace­ments over 10 m in the Kitanada Bay of the Bungo Channel, which could
lead to shear instability near the bottom. However, further in­vestigations on internal tides in the Bungo Channel have been rare overthe past decade, leaving several questions that still need clarification: a)What are the characteristics of internal tides? b) Where are the internal
tides generated and dissipated in this region? c) How do the internal
tides vary temporally? To answer the above questions, we carry out thisstudy.
In this study, the dominant internal tides – semidiurnal internal tides
in the Bungo Channel are investigated by using moored observations
and state of the art numerical model (Japan Coastal Ocean Predictability
Experiment—Tides, JCOPE-T) output. The characteristics, energetics,
and seasonal variations of semidiurnal internal tides are analyzed. This
paper is organized as follows. The mooring data, JCOPE-T dataset, andcorresponding processing methods are described in Section 2. Obser­
vational results are presented in Section 3. Energetics and seasonalvariations of semidiurnal internal tides revealed by JCOPE-T results areshown in Section 4. Factors affecting the temporal variation of semi­
diurnal internal tides are discussed in Section 5. Finally, Section 6summarizes this paper.

Fig. 3. (a) Semidiurnal barotropic velocity at the observational station. Depthtime map for (b) zonal and (c) meridional semidiurnal baroclinic velocities(shadings, unit: m/s). (d) Lowpassed depth-averaged kinetic energy of semi­
diurnal internal tides.

The Bungo Channel is located between the Kyushu and Shikoku
Islands, which connects the Seto Inland Sea and the Pacific Ocean(Fig. 1a). The water depth in the channel varies from 60 to 100 m(Fig. 1b). The intrusion of Kuroshio warm water (Kyucho) into the Bungo
Channel promotes the water exchange between the Pacific and thischannel (Takeoka and Yoshimura, 1988; Kaneda et al., 2002; Isobe et al.,2010; Morimoto et al., 2022). It has been observed that the Kyucho ex­hibits an obvious spring-neap variation, which mainly occurs during the

Fig. 4. Results for the EOF analysis on the meridional baroclinic velocities of semidiurnal internal tides. Vertical structures of the first three modes are shown in (a),while the principal components are shown in (c-e), respectively. Meridional semidiurnal barotropic velocity is plotted in (b) for comparison.
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Fig. 5. (a-d) Snapshots of meridional components for semidiurnal baroclinic velocities (shadings, unit: m/s) at z = –10 m. Isobaths are denoted by gray contours. The
observational station is indicated by the black plus. (e-h) Same as (a-d) but along the vertical transect marked by the red dashed line in (a-d). (For interpretation of
the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 6. (a) Depth-integrated barotropic-to-baroclinic energy conversion rate (shading, W/m2) and (b) energy flux (shading, unit: kW/m) of semidiurnal internal
tides. In each panel, vectors of energy flux are indicated by black and green arrows in different scales. Isobaths are denoted by gray contours, while the observational
station is by the black plus. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

2. Data and methodology

the water depth is 97.6 m (Fig. 1b). The ADCP has a sampling interval of
15 min and a vertical bin size of 4 m. It recorded currents from 2016/07/
06 to 2016/10/17.

2.1. Moored observations
An up-looking RDI 300 kHz acoustic Doppler current profiler (ADCP)
was deployed in the Bungo Channel at (132.268◦ E, 32.942◦ N), where
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Fig. 7. Depth-integrated kinetic energy for semidiurnal internal tides (log form, shadings, unit: J/m2) in (a) January, (b) April, (c) August, and (d) October. Isobaths
are denoted by gray contours, while the observation site is by black plus.

2.2. JCOPE-T-NEDO

magnitude higher than those at diurnal frequencies (Fig. 2). That is why
we focus on semidiurnal internal tides in this study. A fourth-order
Butterworth filter is adopted to extract the baroclinic velocity of semi­

The JCOPE-T reanalysis data (JCOPE-T-NEDO) were produced by atide-resolving ocean general circulation model JCOPE-T (Varlamov
et al., 2015) for evaluating the energy potential of the ocean renewal
energy around Japan (Waseda et al., 2016) with the support from New
Energy and Industrial Technology Development Organization (NEDO).
The model covers a horizontal range of 24◦ -48◦ N and 125◦ -148◦ E with ahorizontal resolution of 1/36◦ and 46 vertical z-sigma levels from thesurface to a depth of 6500 m. The surface momentum, heat, and salt
(freshwater) fluxes are provided by bulk formulae (Li et al., 2010) withatmospheric variables from the National Centers for Environmental
Prediction Climate Forecast System Reanalysis (CFSR, Saha et al., 2010)
and Climate and Forecast System Version 2 (CFSv2, Saha et al., 2014).
Lateral climatological monthly mean freshwater inputs from 47 major
Japanese rivers are included in JCOPE-T. Observed features ofgeostrophic phenomena including the major ocean currents and meso­
scale eddies are involved in JCOPE-T through a spectral nudging oftemperature and salinity fields to those provided by the JCOPE2 rean­
alysis data (Miyazawa et al., 2009) with a relaxation time scale of fivedays. The model was run from the oceanic condition interpolated fromthe JCOPE2 data for a period from 2002 to the present with lateralboundary conditions calculated from the JCOPE2 data. The tidal forcing
based on Oregon Tidal Inversion Software (Egbert and Erofeeva, 2002)
is applied at the surface and lateral boundaries. The volume fluxes andsea level anomalies of 11 tidal constituents (Q1, O1, P1, K1, N2, M2, S2,
K2, M4, MS4, MN4) are provided at lateral boundaries. In addition, thesurface pressure gradient included the equilibrium gradient induced by
25 potential tidal constituents: Q1, O1, M1, P1, K1, J1, OO1, 2 N2, MU2,
N2, NU2, M2, L2, T2, S2, K2, M4, MS4, MN4, MM, MF, SSA, SA, MTM,
MSQM. The results of JCOPE-T are validated by comparison with ob­
servations (see Appendix).

diurnal internal tides u′D2 as well as the semidiurnal barotropic velocity
UD2, and the frequency band of [1.73 2.13] cpd is determined from thepower spectrum. The kinetic energy of semidiurnal internal tides iscalculated by
)
1 ( 2
2
KED2 = ρ0 u′D2
+ v′D22(1)

where ρ0 = 1025 kg/m3 is the reference density.
To explore the modal structure of semidiurnal internal tides, theempirical orthogonal function (EOF) method is considered, which is
independent of any dynamical constraints. This method has been suc­cessfully used to clarify the dominant mode of internal tides in previous
studies, which yields modal structures similar to those derived from theeigenvalue equation (e.g., Mackinnon and Gregg, 2003; Lee et al., 2012;
Xu et al., 2013).
For the JCOPE-T data, the same filter as mentioned above is applied
to the baroclinic velocity and pressure perturbation. The latter iscalculated as,
∫0
∫ ∫0
1 0
p′(x, y, z, t) =ρ′(x, y, ̂z , t)gd̂z −ρ′(x, y, ̂z , t)gd̂z dz(2)
H −H −z− zwhere ρ’(x, y, z, t) is the density perturbation calculated by subtracting
the time-averaged density from the instantaneous density field (Nashet al., 2005), and H(x, y) is the water depth. Then the energetics ofsemidiurnal internal tides are diagnosed by the following depthintegrated energy balance equation (Kerry et al., 2014),∇h ⋅FD2 = CD2 − DD2(3)

Terms in the equation denote divergence of baroclinic energy flux∇⋅FD2 , barotropic-to-baroclinic energy conversion rate CD2, and energy
dissipation rate DD2 corresponding to semidiurnal internal tides,
respectively. The baroclinic energy flux and energy conversion rate arecalculated by (Nash et al., 2005; Carter et al., 2008)∫0
FD2 =u′D2 p′D2 dz(4)

2.3. Data processing
For ADCP data, the velocities in the upper 15 m are discarded due tomany abnormal values. For the missing values in the remainder of thedata, linear interpolation is used to fill in them in the temporal domain
at each depth. The baroclinic velocity is obtained by removing thedepth-averaged velocity from the raw velocity. Spectral analysis result
indicates that semidiurnal signals are dominant in baroclinic motions
since the corresponding peak values are basically one order of

− H

and
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Fig. 8. Same as Fig. 6 but for barotropic-to-baroclinic energy conversion (shadings, unit: W/m2) and energy flux (arrows, unit: kW/m). The red and blue dashedrectangles indicate the regions for integrating the energy conversion and dissipation in the Bungo Channel and shelf break, respectively. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version of this article.)

CD2 = − (UD2 ⋅∇H)p′D2 (z = − H)bottom, particularly during the spring tides. This preliminary result
implies that the observed semidiurnal internal tides are largely domi­
nated by mode-1.
The temporal variation of semidiurnal internal tides is indicated bytheir depth-averaged kinetic energy (Fig. 3d). It is easy to find that KED2
exhibits a fortnight cycle, generally coinciding with the local semi­
diurnal barotropic tidal currents shown in Fig. 3a. Such consistency
between KED2 and VD2 indicates that the observed semidiurnal internal
tides could be largely generated by local tidal forcing (Alford et al.,2011; Xu et al., 2014; Pickering et al., 2015; Cao et al., 2017). Moreover,during the observational period, there is no apparent seasonal variationof semidiurnal internal tides from summer to autumn, since the peakvalues of KED2 basically keep a magnitude of 10 J/m3 in each springneap cycle, except for that in the mid-October.
Then EOF method is applied to v′D2 to explore the modal structure of
the semidiurnal internal tides. The first three modes are chosen because
the sum of their variances accounts for 97 % of the total variance. Fig. 4ashows the vertical structures of the first three modes, which have beennormalized by their maximum values. There appear 1, 2, and 3 crosszero points for modes 1–3, respectively, suggesting that the EOF(5)The energy dissipation rate is obtained indirectly from Equation (3) as inprevious studies (e.g., Alford et al., 2011; Kerry et al., 2014; Wang et al.,2021). Note that the calculated DD2 includes both the physical dissipa­
tion of internal tides and some biases caused by numerical dissipationand errors (Kang and Fringer, 2012).
3. Observational results
Observed semidiurnal barotropic and internal tides are shown in
Fig. 3. In the Bungo Channel, the semidiurnal barotropic tidal currents
are dominated by the meridional component. The magnitude exceeds
0.5 (0.3) m/s during the spring (neap) tide (Fig. 3a). In contrast, thezonal component only has a magnitude lower than 0.2 m/s even in thespring tide. The semidiurnal baroclinic velocities are weaker than thebarotropic ones, which are also dominated by the meridional component(Fig. 3b-3c). The magnitude of v′d2 reaches 0.3 m/s during the spring tidebut is lower than 0.1 m/s during neap tide (Fig. 3c). In addition, thesemidiurnal baroclinic velocities are intensified near the surface and6

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4. JCOPE-T results
4.1. Spatial pattern and energetics of semidiurnal internal tides
Although semidiurnal internal tides have been observed in the Bungo
Channel in a previous study (Kawamura et al., 2006) and this work, their
spatial pattern and sources remain unclear because of the limitation of
in-situ observations. Hence, we use JCOPE-T results to clarify the gen­eration and propagation of semidiurnal internal tides in this region.
Because the observation was conducted in the summer and autumn of
2016, in this section, we choose the JCOPE-T results in July 2016 for thecorresponding investigation. As shown in Fig. 5a-5d, semidiurnal in­
ternal tides are observed to propagate southward into the deep Pacific
Ocean from the continental slope south of the Bungo Channel. The
generation of such offshore radiating waves is further illustrated by thevertical transects shown in Fig. 5e-5h, in which a beam radiated from thecontinental shelf break at 32.75◦ N is presented. Because the continental
slope is supercritical (the topographic slope is larger than that of theinternal tidal beam), there exists not only the dominant offshore prop­
agating beam but also the weak onshore propagating one, agreeing withinternal tide generation theory (Griffiths and Grimshaw, 2007; Gerkema
and Zimmerman, 2008). With the increase of distance from the shelf
break, the baroclinic velocity becomes weaker, indicating a quick decayof semidiurnal internal tides towards the Pacific Ocean.
In the Bungo Channel, the semidiurnal internal tides are weaker thanthose in the Pacific Ocean and exhibit complex features. First, thealternative pattern of positive and negative baroclinic velocities in the
deep water is absent in the channel (Fig. 5a-5d). Second, the onshore
radiating beam vanishes after reflection at the sea surface (Fig. 5e-5h).
The above two factors make it difficult for us to determine the propa­
gation direction of semidiurnal internal tides in the Bungo Channel.
Fig. 6a shows the spatial distribution of the energy conversion rate.
Two regions with high CD2 are identified as main generation sites ofinternal tides in this region: one is located at the shelf break south of the
Bungo Channel; while the other is at the Hayasui Strait north of thechannel. For semidiurnal internal tides generated at the shelf break, asmall fraction of their energy is radiated northward into the Bungo
Channel, with energy fluxes of 0.2 kW/m. Because the observational
station is near this generation site, most of the observed semidiurnalinternal tides could be attributed to this source. This result further ex­
plains why the observed KED2 is largely correlated with the local tidal
forcing. In contrast, a large fraction of the internal tidal energy is radi­
ated southward into the Pacific Ocean, with energy fluxes as high as 4
kW/m (Fig. 6b). Two branches of the offshore propagating beam areobserved. The stronger one turns westward near the generation sites;
while the weaker one directly propagates southward into the deep re­gion. Moreover, the interaction between the former one and the conti­
nental slope east of Kyushu Island forms partially trapped slope waves,resulting in an alternative pattern of positive and negative energy con­version rates (Fig. 6a). A similar phenomenon has also been found over
the Tasman Slope (Klymak et al., 2016).
At the Hayasui Strait, the presence of a strong barotropic tidal cur­rent and a large gradient of water depth caused by a depression isbeneficial to the generation of internal tides. Although this generationsite occupies a much smaller area, the conversion rates there are evenhigher than that at the shelf break. Near the Hayasui Strait, the semi­
diurnal energy fluxes have a magnitude of approximately 0.5 kW/m,which is larger than the northward ones radiated from the shelf break(Fig. 6b). However, most of the energy propagates westward into Beppu
Bay or southwestward towards the coastal regions of Kyushu Island.
Only a smaller fraction of energy is radiated southward into the Bungo
Channel, and corresponding energy fluxes are comparable to thenorthward ones from the shelf break. The superposition of these semi­
diurnal internal tides and northward ones from the shelf break leads to acomplex interference pattern in the Bungo Channel since there is no
deterministic direction of energy flux (Fig. 6). This may explain why weFig. 9. Domain-integrated (a) barotropic-to-baroclinic energy conversion and(b) dissipation for the Bungo Channel (blue bars) and continental shelf south ofthe channel (red bars) in different months. (For interpretation of the references
to color in this figure legend, the reader is referred to the web version ofthis article.)modes correspond to the normal modes derived from the eigenvalue
equation as in previous studies (Mackinnon and Gregg, 2003; Lee et al.,2012). We also use a one-month segment to conduct the EOF analysis,
and the calculated vertical structures of modes show a similar pattern tothose obtained with the data during the whole observational period (notshown). This suggests the temporal variation of vertical modal structure
is not significant, agreeing with the results of Xu et al. (2013). Moreover,further sensitivity experiments with the JCOPE-T data at the observa­
tional station indicate that the lack of observations near the surface only
has an influence on the vertical structures of higher modes (modes 2–3)
rather than their principal components.
The contribution of each mode can be reflected by the principal
components shown in Fig. 4c-4e. At the observational station, semi­
diurnal internal tides are dominated by modes 1 and 2 with magnitudesof 0.1–0.2 m/s. The former is stronger than the latter most of the time
(Fig. 4c-4d). In contrast, mode-3 makes only a minor contribution as its
magnitude is always lower than 0.05 m/s (Fig. 4e). A similar feature ofsemidiurnal internal tides has also been found in other shelf seas, such as
the New England Shelf (Mackinnon and Gregg, 2003) and the Yellow
Sea (Wang et al., 2020). Here, the temporal variation of mode-1 shows
good consistency with the semidiurnal barotropic tidal current (Fig. 4b4c). However, mode-2 is less correlated with the local tidal forcing whencompared with mode-1, e.g., in late August and early September(Fig. 4d). Due to the low phase speed of high modes, their propagation ismore easily affected by the varying background field (e.g., stratificationand currents). As a result, they may become out of phase with the tidal
forcing when reaching the observation station (Zhao et al., 2010).

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Fig. 10. Daily average temperature (shadings, unit: ℃) at z = –14 m and currents (arrows) from JCOPE-T results. In each panel, isobaths are indicated by graycontours. Blue and red pluses in (a) indicate the locations in the Bungo Channel and at the shelf break for analyses of barotropic tidal currents and stratification in
Fig. 11. Note the different ranges of color bars for the upper and lower panels. (For interpretation of the references to color in this figure legend, the reader is referredto the web version of this article.)cannot determine the propagation direction of internal tides directlyfrom the wavefield (Fig. 5a-5d). This feature of internal tides has also
been found in other shelf seas, such as the Yellow Sea (Liu et al., 2019)
and the East China Sea (Lien et al., 2013). Additionally, although theobserved semidiurnal internal tides are mainly generated at the shelf
break, there also exist weak southward internal tides radiating from the
Hayasui Strait. The latter may be out of phase with the local tidal forcing
at the shelf break, hence causing the appearance of weak decorrelation
between the observed KED2 and local tidal forcing at some times during
the observational period (Fig. 3, Kelly and Nash, 2010). Nevertheless,the long distance to the mooring site and weak energy flux implies that
this source has only a limited contribution to the observed semidiurnal
tides.

their propagation is modulated in different seasons.
In January and April, the energy conversion rate around the Hayasui
Strait nearly approaches zero; and correspondingly, no energy radiationfrom the strait is observed (Fig. 8a-8b). In addition, the northward ra­
diation of internal tidal energy from the shelf break into the Bungo
Channel is also weak. Such lack of local generation and external energy
input consequently results in weak semidiurnal internal tides in the
Bungo Channel (Fig. 7a-7b). Differing from that at the Hayasui Strait,
the internal tidal generation at the shelf break is not suppressed.
Although the energy conversion there in April is weaker than that in
January, a strong beam radiating southwestward along the coast of
Kyushu Island appears in both seasons (Fig. 8a-8b).
However, the results for July and October exhibit a different patternfrom those analyzed above. Internal tide generation at the Hayasui Strait
is greatly enhanced, associated with higher energy conversion rates ofover 0.4 W/m2 and larger energy fluxes of about 0.5 kW/m (Fig. 8c and8d). Also, northward energy fluxes from the shelf break into the Bungo
channel are much larger than those in July and October. This is why
intense semidiurnal internal tides are found in the two months as
mentioned before. At the shelf break, energy conversion becomesslightly larger in October, accompanied by the strongest beam radiating
southeastward among the four seasons.
Another interesting phenomenon is that the radiation of semidiurnalinternal tides towards the deep Pacific Ocean exhibits varying patterns
in different seasons. For the southwestward branch, it travels a long
distance along the coast of Kyushu Island towards the Pacific Ocean in
April and October (Fig. 8b and 8d); but decays quickly near the gener­
ation sites in July (Fig. 8c). The weak southward branch is more easily
refracted and hence changes its direction, which even forms a loop-likestructure in energy flux in January (Fig. 8b).
Energy conversion and dissipation of semidiurnal internal tides in
the Bungo Channel and shelf break south of the channel are integrated to

4.2. Seasonal variability
Because of the limited temporal range of moored observations, thewhole seasonal cycle of semidiurnal internal tides cannot be determined.
Therefore, JCOPE-T data are used for the corresponding investigation.
Four months (January, April, July, and October) in 2016 are chosen to
represent different seasons (winter, spring, summer, and autumn). Fig. 7
shows the depth-integrated KED2, which reflects the intensity of semi­
diurnal internal tides. It is easy to find that semidiurnal internal tides in
the Bungo Channel exhibit an apparent seasonal cycle, which is weak in
January and April (Fig. 7a-7b) but strong in July and October (Fig. 7c7d). Their kinetic energy in July and October is nearly one order ofmagnitude higher than that in January and April. Also, semidiurnalinternal tides in July and October do not show differences in their in­tensity (Fig. 7c-7d), agreeing with the observational results analyzed in
Section 3. Around the shelf break, KED2 does not show significant vari­ation in different seasons. However, the spatial distribution of KED2
varies in the deep region south of the continental shelf, implying that
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Fig. 11. (a) Semidiurnal meridional barotropic tidal currents at the shelf break (blue curve) and in the Bungo Channel (red curve) from 2016/06/15–2016/08/31.
Note that the tidal current at the shelf break is enlarged by a factor of 5 for better comparison. The four stages of spring tides are denoted by colored numbers.
Integrated energy conversion of semidiurnal internal tides (b) at the shelf break and (c) in the Bungo Channel. Note that the results are smoothed with a 25-h runningaverage to remove high-frequency variation. (d) Depth-averaged stratification within the upper 60 m at the shelf break (blue curve) and in the Bungo Channel (redcurve). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.). (For interpretation of the references
to color in this figure legend, the reader is referred to the web version of this article.)further illustrate their seasonal variations (Fig. 9). On the whole, theintegrated semidiurnal energy conversion in the Bungo Channel is much
lower than that at the shelf break (Fig. 9a). In the Bungo Channel, thetotal energy converted into semidiurnal internal tides is nearly zero inJanuary and April but exceeds 25 MW in July. However, at the shelf
break, semidiurnal internal tides exhibit a different seasonal cycle. Theirgeneration is strongest in October but weakest in April, since the totalenergy conversion in October is almost twice as large as that in April.
Moreover, the energy conversion in January and July is basically com­parable, which is about 20 % lower than that in October.
The energy dissipation of semidiurnal internal tides in the Bungo
Channel shares a similar seasonal cycle with the energy conversion(Fig. 9b), which is also intensified in July and October. Here, the dissi­
pated energy is comparable to or even larger than locally converted
energy from barotropic tides due to external energy input from the shelf
break, implying that the Bungo Channel could be an energy sink of in­
ternal tides. In contrast, the energy dissipation around the shelf break is
not strictly correlated with the energy conversion, as internal tidal en­ergy dissipated in January and April is generally comparable despite thelarge difference in energy conversion in the two months (Fig. 9b). In
addition, note that only half of the energy is dissipated locally at theshelf break, while the remainder is radiated into the Pacific Ocean,
especially in October (Fig. 8d and 9b).
5. Discussion
5.1. Influence of Kyucho
The Kyucho usually occurs in summer and exhibits short-term tem­poral variation (Takeoka and Yoshimura, 1988; Takeoka et al., 1993;
Isobe et al., 2010). Here, the influence of the Kyucho on the semidiurnalinternal tides in the study region is explored. Fig. 10 shows the daily
averaged temperature at z = –14 m, and the variations of energy con­version of semidiurnal internal tides are presented in Fig. 11. During thefour spring tides (stages 1–4 in Fig. 11a) in July and August, the baro­
tropic tidal currents are comparable in strength. However, the inte­
grated energy conversion in the Bungo Channel shows large differencesin the four stages (Fig. 11b). In contrast, the energy conversion inte­
grated at the shelf break does not change considerably during the four
spring tides (Fig. 11c).
Such modulation on the spring-neap cycle of semidiurnal internal
tides could be attributed to the Kyucho. During stage 1, the Kyucho did
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Progress in Oceanography 222 (2024) 103229

Fig. 12. Monthly-averaged squared buoyancy frequency (shadings, unit: s− 2) along the vertical transect denoted by red dashed line in Fig. 5a-5d. (For interpretationof the references to color in this figure legend, the reader is referred to the web version of this article.). (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

not occur; and the water temperature in the Bungo Channel is nearly 5℃
lower than that of the warm Kuroshio water in the Pacific Ocean(Fig. 10a-10b). In this situation, the squared buoyancy frequencies at theshelf break and in the Bungo Channel are basically equal (Fig. 11d).
Whereas, the warm Kuroshio water intruded into the Bungo Channel on
July 22, causing a significant increase in water temperature in the Bungo
Channel on July 23 (Fig. 10c-10d). Correspondingly, the stratification in
the Bungo Channel is greatly intensified during stage 2 when comparedwith that at the shelf break (Fig. 11d), resulting in the enhancement ofenergy conversion (Fig. 11b). In August, a similar event was found; i.e.,
the intrusion of warm water during stage 4 led to the intensification ofstratification once again. This could explain the obvious difference inenergy conversion in stages 3 and 4. The above results indicate that the
Kyucho influences the short-term (intraseasonal) variation of semi­
diurnal internal tides by changing the local stratification. Note that asimilar phenomenon was also observed by Kawamura et al. (2006), who
revealed occasional enhancement of semidiurnal internal tides in the
Bungo Channel affected by the Kyucho.

generated there and have a smaller seasonal variation than that in the
Bungo Channel. Based on the above results, we can conclude that theseasonal variation of stratification in the Bungo Channel is the cause of
the seasonal variation of semidiurnal internal tides.
Tsutsumi and Guo (2016) analyzed the water temperature data in the
Seto Inland Sea, the Bungo, and Kii Channels, and found that the sea­sonal heat content in the upper ocean is larger determined by air-sea
heat flux. This implies that the seasonally varying stratification in the
Bungo Channel could be mainly controlled by surface heating andcooling, which further influences the seasonal variation of semidiurnalinternal tides. At the shelf break, although the stratification shows asimilar seasonal cycle to that in the Bungo Channel, the coastal circu­
lation also varies in different seasons (Isobe et al., 2010), which affects
the generation of internal tides (Masunaga et al., 2018).
5.3. Refraction of internal tides
As the semidiurnal internal tides generated at the shelf break prop­
agate southward into the Pacific Ocean, they are refracted and therefore
exhibit different radiation patterns (Fig. 8). For investigating therefraction of internal tides, we use the following wave front tracing
model (Park and Watts, 2006; Park and Farmer, 2013)

5.2. Influence of seasonal stratification
In shelf seas, the stratification usually exhibits more significant
seasonal variation than that in the open ocean because of the shallow
water depth (e.g., Chang et al., 2009; Tsutsumi and Guo, 2016; Yu andGuo, 2018). As a result, it can lead to seasonal variation of internal tides.
We calculate the squared buoyancy frequency using the JCOPE-T data.
Here, the seawater in the Bungo Channel is well mixed in January and
April (Fig. 12a-12b). Such weak stratification cannot support the exis­
tence of internal tides. This explains why semidiurnal internal tides in
the Bungo Channel are weak during that period (Figs. 7 and 9). In
contrast, stratified seawater exists around the shelf break and in the
Pacific Ocean throughout the year. Therefore, internal tides are always

Δd = Cp Δt(6)where Δd is the traveling distance of wave front in one time step Δt, and
Cp is the phase speed calculated byωCp = √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅Cn
ω2 − f 2(7)Here, we use the M2 tidal frequency ω = 1.405 × 10-4 s− 1. The eigen­speed Cn is obtained by solving the Sturm–Liouville equation (Gill,
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Progress in Oceanography 222 (2024) 103229

Fig. 13. (a and b) Phase speed obtained by solving Equations (7) and (8) (shadings, unit: m/s). (c and d) Difference between the phase speeds without and withbackground currents (shadings, unit: m/s). Black arrows denote surface currents. (e and f) Results for wave front tracing excluding (blue lines) and including
background currents (red lines), respectively. Bathymetry is indicated by gray contours. (For interpretation of the references to color in this figure legend, the reader
is referred to the web version of this article.)

1982)
2

W(z)zz +N (z)W(z) = 0
Cn2

pattern) by background currents as Duda et al. (2018).
Fig. 13 shows the results calculated by the wave front tracing model.
It is easy to find that the Kuroshio path considerably affects the refrac­tion of southward semidiurnal internal tides. As the Kuroshio axis is far
from the shelf (Fig. 13c), the wave front is broadened quickly as theinternal tides propagate southward from the continental shelf break(Fig. 13e). This result generally agrees with that shown in Fig. 8a, since
the energy fluxes are divergent around the shelf break, despite thedifferent intensities of the southwestward and southeastward beams. In
addition, the results with and without background currents only show
slight differences near the coast of Shikoku Island. This implies a weakeffect of background currents on the propagation of internal tides, as theKuroshio axis is a bit far from the continental slope (Fig. 13a and 13c).
When the Kuroshio axis becomes close to the shelf, the calculated wave
front shows an obviously different pattern (Fig. 13f), which could belargely due to the different spatial distribution of eigenspeed controlled(8)with monthly averaged stratification from JCOPE-T, where W(z) is the
eigenfunction. Note that the effect of background currents is notconsidered in Equation (8). For waves propagating in background cur­rents, the eigenspeed is calculated with the Taylor-Goldstein equation(Kundu and Cohen, 2002)
W(z)zz −U(z)zzN 2 (z)W(z) +
W(z) = 0
U(z) − Cn[U(z) − Cn ]2(9)Note that this model does not consider the anisotropic wavenumbers(the difference between the phase propagation direction and the ray
direction). Hence, it cannot fully simulate the blocking of rays (loop-like
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Progress in Oceanography 222 (2024) 103229

Fig. 14. Monthly-averaged surface currents in (a) July and (b) October, with magnitude indicated by shadings (unit: m/s) and directions by black arrows. (c) Resultsof wave front tracing model using the background field in summer (blue curves) and autumn (red curves). (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

Figure A1. (a) Zonal and (b) meridional barotropic tidal currents at the moored ADCP station from JCOPE-T (blue curves) and observations (red curves). Meridional
components of semidiurnal baroclinic velocity (shadings, unit: m/s) from (c) observations and (d) JCOPE-T results. (e) Depth-averaged kinetic energy for semidiurnalinternal tides derived from JCOPE-T results (blue curve) and observations (red curve).

by background stratification (Fig. 13b). On the eastern side, the waves
propagate almost southward into the Kuroshio region rather thanturning eastward. Correspondingly, southward energy fluxes in the
Kuroshio region are found in Fig. 8c, which confirms the wave front
tracing results. Moreover, the semidiurnal internal tides are refracted

more eastward when the background currents are considered in thecalculation. The effect of background currents on the propagation ofinternal tides gradually becomes stronger as the semidiurnal internal
tides are radiated away from the shelf break to the Kuroshio region.
In addition to the Kuroshio axis, the Kuroshio strength also
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Progress in Oceanography 222 (2024) 103229

Figure A2. Same as Fig. A1 but for comparison with ADCP observations at (132.18◦ E, 33.17◦ N).

influences the propagation of semidiurnal internal tides. The Kuroshio isstrong in July with current speeds higher than 1.2 m/s (Fig. 14a), but
weak in October with current speeds lower than 0.9 m/s (Fig. 14b). The
two different background fields are used in wave front tracing to explore
the influence of the Kuroshio strength on the refraction of internal tides.
As shown in Fig. 14c, intense Kuroshio in July causes stronger advection
effects, resulting in the eastward refraction of the offshore propagating
semidiurnal internal tides. Additionally, the wave front becomes wider
as it propagates into deep water when compared to that under the weak
Kuroshio.

break south of the Bungo Channel are identified. The latter makes
a major contribution to the observed semidiurnal internal tides.
Northward internal tides generated at the shelf break are super­
posed with those generated at the Hayasui Strait, causing acomplex interference pattern in the channel. Additionally, a large
amount of internal tidal energy is radiated into the Pacific Ocean
from the shelf break.
(3) Several factors influence the temporal variation of semidiurnalinternal tides in the Bungo Channel. The intraseasonal variationof semidiurnal internal tides can be modulated by the Kyucho.
During summer, the occurrence of Kyucho leads to the variationof stratification in the channel and therefore affects the energy
conversion of internal tides. Seasonal variation of semidiurnalinternal tides in the Bungo Channel is determined mainly by
seasonally varying stratification; while those generated at theshelf break are under the combined influence of seasonal strati­
fication and background currents. As semidiurnal internal tides
propagate southward into the Pacific Ocean from the shelf break,they are refracted due to the spatially varying stratification andbackground currents. The changes of Kuroshio in path andstrength considerably modulate the refraction of southward
semidiurnal internal tides.

6. Summary
The Bungo Channel is the main gate for water exchange between the
Seto Inland Sea and the Pacific Ocean. Based on moored observations
and JCOPE-T results, semidiurnal internal tides in the Bungo Channel
are investigated in this study. Their characteristics, energetics, andseasonal variation are analyzed. The main conclusions are outlined asfollows:(1) Intense semidiurnal internal tides in the Bungo Channel arecaptured by moored observations during 2016/07–2016/10,
associated with baroclinic velocities of about 0.3 m/s. Their en­
ergy shows an obvious spring-neap cycle, which is generally
correlated with the local barotropic tidal forcing. By adopting the
EOF analysis, it is found that the observed semidiurnal internal
tides are mainly dominated by the first two baroclinic modes.
(2) By analyzing the JCOPE-T results, two generation sites of semi­
diurnal internal tides located at the Hayasui Strait and the shelf

CRediT authorship contribution statement
Shuya Wang: Conceptualization, Investigation, Methodology,
Visualization, Writing – original draft, Writing – review & editing.
Xinyu Guo: Conceptualization, Funding acquisition, Supervision,
Writing – review & editing. Akihiko Morimoto: Data curation. Anzhou
13

Progress in Oceanography 222 (2024) 103229

S. Wang et al.

Cao: Conceptualization, Writing – review & editing. Eisuke Tsutsumi:
Conceptualization, Validation. Yasumasa Miyazawa: Data curation.
Sergey M. Varlamov: Data curation, Resources.

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Declaration of competing interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Data availability
Data will be made available on request.
Acknowledgments
The authors deeply thank the editor and two anonymous reviewers
for their constructive suggestions, which greatly improved this paper.
This study was supported by a Grant-in-Aid for Scientific Research(MEXT KAKENHI, grant number: 20H01972, 22H05206). S. Wang
thanks the support from JSPS Postdoctoral Fellowships for Research inJapan (grant number: 23KF0056). A. Cao thanks the support from the
China Scholarship Council (grant number: 202006325025).
Appendix:. Validation of the JCOPE-T results
The JCOPE-T results are validated by comparison with moored ob­
servations. First, Fig. A1 shows the comparison of barotropic tidal cur­rents between JCOPE-T results and moored observations. The
meridional component of barotropic tidal currents from JCOPE-T is ingood consistency with observations (Fig. A1a), while the zonal one
shows some differences from the observations (Fig. A1b). The rootmean-square error (RMSE) and correlation coefficient (r) are 0.03
(0.07) m/s and 0.91 (0.97) for the zonal (meridional) component,
respectively.
Second, the results for semidiurnal internal tides from JCOPE-T andobservations are presented in Fig. A1c-A1d. On the whole, the JCOPE-T
reproduces the observed semidiurnal internal tides in the Bungo Chan­nel. The semidiurnal baroclinic velocities from the JCOPE-T results andobservations are in comparable strength and intensified near the surface
and bottom regions. Also, both of them exhibit obvious spring-neap
cycles and basically coincide with the local tidal forcing. Moreover,temporal variation of the kinetic energy of semidiurnal internal tides
from JCOPE-T also agrees with that from observations (Fig. A1e), with
RMSE = 3 J/m3 and r = 0.6. The appearance of some biases may be
attributed to the lack of data assimilation in JCOPE-T in shallow regions.
Moreover, we also compare the JCOPE-T results with observations
from another moored ADCP at (132.18◦ E, 33.17◦ N), which was
deployed in July 2016. Because the observational period only lasted nolonger than one month, the data is not shown in the main text for theinvestigation of internal tides. The results shown in Fig. A2 also suggest
good consistency between the JCOPE-T and observations. Hence, basedon the above validations, we believe that the JCOPE-T results arereasonable and can be used in corresponding investigations.
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