Continental Shelf Research 264 (2023) 105055

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Continental Shelf Research
journal homepage: www.elsevier.com/locate/csr

Modal content of typhoon-induced near-inertial waves around the East
China Sea
Anzhou Cao a, b, Shuya Wang b, Akihiko Morimoto b, *, Tetsutaro Takikawa c, Xinyu Guo ba

Ocean College, Zhejiang University, Zhoushan, China
Center for Marine Environmental Studies, Ehime University, Matsuyama, Japanc
Graduate School of Fisheries and Environmental Sciences, Nagasaki University, Nagasaki, Japanb

A R T I C L E I N F O

A B S T R A C T

Keywords:
Near-inertial waves
Modal content
East China Sea
Modal wind forcing
Two-layer-structure stratification

Recent studies show that typhoon-induced near-inertial waves (NIWs) exhibit different modal content in theshallow and deep regions, whereas the underlying mechanism has not been fully understood. Based on a threedimensional numerical model, we simulate the NIWs induced by two typhoons (Songda and Meari in 2011) in the
East China Sea and its adjacent deep waters in the northwest Pacific Ocean. Although the near-inertial kinetic
energy induced by the two typhoons has different intensity and spatial distribution, the modal content of NIWs
induced by them shares a common characteristic: In the shallow regions (water depth smaller than 200 m), the
NIWs are mainly dominated by mode-1; whereas in the deep regions (water depth larger than 200 m), the NIWs
are dominated by higher modes (mode-2 to mode-5). Different mechanisms are found to account for the different
modal content in shallow and deep regions. The dominance of higher-mode wind forcing is the cause for thedominance of higher-mode NIWs in the deep regions. The two-layer-structure stratification is the cause for thedominance of mode-1 NIWs in the shallow regions.

1. Introduction
Near-inertial waves (NIWs) are internal waves with frequency close
to the local Coriolis frequency, which are mainly caused by winds andare ubiquitous in the global ocean. As a predominant peak in the internal
wave spectrum, NIWs make significant contributions to the turbulent
mixing in the ocean (Alford et al., 2016; Mackinnon et al., 2017; Whalen
et al., 2020). The global wind power input to near-inertial motions is0.3–1.5 TW (Alford, 2003, 2020; Jiang et al., 2005; Furuichi et al., 2008;
Liu et al., 2019), which is comparable to that converted from astro­
nomical tides to internal tides (Munk and Wunsch, 1998; Simmons et al.,
2004; Niwa and Hibiya, 2011).
Typhoons are particularly efficient generators of NIWs owing to theirstrong wind stresses and compact size (Alford et al., 2016).
Typhoon-induced NIWs are generally characterized by upgoing phaseand hence downgoing energy (e.g. Alford et al., 2012; Guan et al., 2014;
Le Boyer et al., 2020). Observations have indicated that the verticalscales of typhoon-induced NIWs are approximately ranging from 100 to
600 m (Alford et al., 2012; Cao et al., 2018; Yu et al., 2022).
Typhoon-induced NIWs can persist for several to more than 10 days after
the passage of the typhoon (e.g. Chen et al., 2013; Guan et al., 2014; Caoet al., 2018; Qiao et al., 2022). Furthermore, other ocean dynamical
processes, such as the large-scale circulations and mesoscale eddies, canmodulate the propagation and dissipation of NIWs (Chen et al., 2013;
Jeon et al., 2019a; Kawaguchi et al., 2020; Sanford et al., 2021; He et al.,2022).
Typhoon-induced NIWs are certainly related to the typhoon char­acteristics, such as the maximum sustained wind speed, radius of the
maximum sustained wind speed, typhoon translation speed and typhoon
track (e.g. Chen et al., 2015). The ocean stratification can also influence
their characteristics (Jeon et al., 2019b). Recent studies show that the
typhoon-induced NIWs show apparent differences in shallow and deep
regions. One significant difference is the dominant mode of NIWs. The
NIWs in shallow regions are usually dominated by mode-1 (Yang et al.,2015, 2021; Zhang et al., 2018; de Freitas et al., 2019; Schlosser et al.,2019), whereas higher modes account for more of the total near-inertial
kinetic energy (NIKE) than mode-1 in deep regions (He et al., 2022; Rajaet al., 2022). However, the underlying mechanism has not been fully
understood.
In this study, we choose the East China Sea (ECS) and its adjacent
deep waters in the northwest Pacific Ocean to study the modal content of
typhoon-induced NIWs based on the numerical simulation. Two* Corresponding author.
E-mail address: morimoto.akihiko.cl@ehime-u.ac.jp (A. Morimoto).
https://doi.org/10.1016/j.csr.2023.105055
Received 25 November 2022; Received in revised form 28 May 2023; Accepted 13 June 2023
Available online 14 June 2023
0278-4343/© 2023 Elsevier Ltd. All rights reserved.

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Continental Shelf Research 264 (2023) 105055

Fig. 1. Bathymetry of the domain. The two black dots indicate the locations of two moorings. The black and gray curves represent the tracks of typhoons Songda andMeafi in 2011, respectively. The colored dots indicate the typhoon central pressure. Time is labeled every 6 h.

moorings deployed on the continental shelf of ECS captured the passage
of typhoons Songda and Meari in 2011, which provide the data formodel validation. The paper is organized as follows. The two typhoons,moored observations, model configurations and data analysis methods
are introduced in section 2. The main results are shown in section 3,
including the validation of simulated results, NIKE, and modal content
and wave characteristics of NIWs induced by the typhoons. In section 4,
the mechanisms for different modal content of NIWs in shallow and deep
regions are discussed. Finally, a summary completes the paper in section
5.

ADCPs also measured the bottom pressure at the two moorings, fromwhich the surface elevation can be obtained.
We used percent good which is the ratio of good pings per total pingsfor each ensemble average for data quality control. Velocities more than
90% of percent good were used for analysis. Magnetic north was con­verted to true north using geomagnetic data of Geospatial Information
Authority of Japan.
Due to the poor data quality near the surface, the velocity observa­
tions in the upper layer were discarded. Thereafter, the moored velocity
observations were linearly interpolated at uniform 4-m interval levels.
Linear interpolation was used to fill in the gaps in the temporal domain,
if the raw observations covered more than 95% of the total observation
period at the corresponding depth (Cao et al., 2017). After this pro­cessing, the effective vertical range of velocities at the north (south)
mooring was 28–80 (32− 104) m. In this study, the observed velocities
and surface elevations were used to validate the numerical simulation
results.

2. Data and methodology
2.1. Typhoons Songda and Meari
Songda and Meari were the 2nd and 5th typhoons in the western
Pacific Ocean in 2011. According to the best track data from the China
Meteorological Administration tropical cyclone database (tcdata.
typhoon.org.cn, Ying et al., 2014), Songda entered the domain on May
28 with the central pressure of 960 hPa (Fig. 1). Thereafter, it moved
northeastward and left the domain on May 29. During this period, themaximum sustained wind speed of Songda decreased from 40 to 25 m/s
and the central pressure increased from 960 to 980 hPa. Compared with
Songda, Meari was a little weaker, with the maximum sustained windspeed of approximately 30 m/s. It entered the domain on June 24 andleft the domain on June 25. Unlike Songda which moved northeastward,
Meari’s track was nearly northward.

2.3. Model configuration
The regional ocean modeling system (ROMS) under the frameworkof coastal and regional ocean community model (CROCO, www.crocoocean.org) was used to simulate the NIWs induced by typhoons
Songda and Meari. The simulated domain was 116–134◦ E, 23− 41◦ N
with a uniform horizontal resolution of 1/10◦ . There were 30 unevensigma layers in the vertical direction, with a finer resolution near thesurface. The bathymetry used in the model was obtained from the
ETOPO1 data (Amante and Eakins, 2009) and smoothed to minimize thehorizontal pressure gradient error. To avoid artificial reflection of NIWs
at the open boundaries, a 1◦ sponge layer was used to absorb the bar­oclinic energy.
The numerical simulation started on May 1, 2011 and ended on July
31, 2011. The initial conditions including the water temperature,salinity, sea surface height and background currents on 1 May 2011were obtained from the hybrid coordinate ocean model (HYCOM)
reanalysis results downloaded from the Asia-Pacific Data-ResearchCenter (apdrc.soest.hawaii.edu/data/data.php). At the open bound­aries, the surface elevations and barotropic currents of the eight prin­ciple tidal constituents (K1, O1, P1, Q1, M2, S2, N2 and K2) extracted fromthe Oregon State University global models of ocean tides (TPXO7; Egbert

2.2. Moored observations
Two moorings were deployed on the continental shelf of ECS fromMay 28 to July 2, 2011, which captured the passage of the two typhoons.
The two moorings were located at (126.5155◦ E, 29.0136◦ N) and(126.1568◦ E, 29.7089◦ N), where the water depth was approximately
113 and 87 m, respectively (Fig. 1). At the north (south) mooring, a WHSentinel 600 (300) kHz upward looking acoustic Doppler current pro­filer (ADCP, Teledyne RD Instruments) was equipped at the seafloor tomeasure velocities in the water column. The bin size of each ADCP was
set to 4 m and the sampling time interval was 600 s. The standard de­viation of measured velocities for error was smaller than 0.5 cm/s. The
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and Erofeeva, 2002) were introduced into the model via the Flather
radiative conditions. The daily temperature, salinity and backgroundcurrents from the HYCOM reanalysis results were introduced into themodel via a nudging scheme. The hourly Climate Forecast System
Reanalysis (CFSR) winds downloaded from the Asia-Pacific Data-­
Research Center were used as the surface forcing. Through a comparison
with the maximum sustained wind speed of the two typhoons from thebest track data, we found that the CFSR winds were a little smaller.
Hence, the CFSR winds were amplified by a factor of 1.2 when used in
the CROCO. The wind stress drag coefficient developed by Oey et al.
(2006) was used to calculate the wind stress. The Large/­
McWilliams/Doney K-profile parameterization mixing scheme (Largeet al., 1994) was used for vertical turbulent mixing of momentum andtracers. The lateral viscosity and bottom friction coefficient was set to
10 m2/s and 0.0025, respectively. The simulated results were output
every hour. This experiment was named as “FULL run”.
Because the local Coriolis frequency near 30◦ N is close to those ofdiurnal tidal constituents, we cannot accurately extract typhooninduced NIWs from FULL run (The same problem exists for themoored observations). Hence, another experiment named as “NO-TIDErun” was performed. The settings of NO-TIDE run were the same as thoseof FULL run except that there was no tidal forcing. In this study, theresults of FULL run were used to compare with the moored observations
to validate the numerical simulation, and the results of NO-TIDE run
were used to study the NIWs induced by the two typhoons.

Fig. 2. (a) Buoyancy frequency and (b) the first five baroclinic modes at 128◦ E,
24.8◦ N. Note that the y-axes are in the log form.

modal decomposition was not conducted; For 50 ≤ H ≤ 200 m (H > 200m), the simulated temperature, salinity and near-inertial velocities werefirst interpolated at 20 uniform layers between the surface and seafloor(uniform 10-m layers), and then modal decomposition was conducted.
Following Raja et al. (2022), the first five baroclinic modes wereconsidered in this study. Fig. 2 shows the buoyancy frequency andnormal modes (Πm) at 128◦ E, 24.8◦ N as an example. Note that Πm has
been normalized in this study.
Based on the filtered near-inertial velocities (modal decomposition
results), the NIKE (modal NIKE) can be calculated as:
)
)
1 (
1 (
NIKE = ρ0 u2f + v2f and NIKEm = ρ0 u2fm + v2fm .
(4)2
2

2.4. Data analysis methods
The 4th order Butterworth filtering with cutoff frequency of [0.80,
1.20]f (f is the local Coriolis frequency) was used to extract the nearinertial velocities from the results of NO-TIDE run. The filtering was
also operated twice with once forward and once backward. Thereafter,
modal decomposition was carried out:
⎧
M
M
∑
∑
⎪
⎪
̂
u fm (t)Πm (z)ufm (z, t) =⎪⎨ uf (z, t) =
m=0

m=0

M
M
∑
∑
⎪
⎪
⎪
⎩ vf (z, t) =̂v fm (t)Πm (z)vfm (z, t) =
m=0

,

(1)

The wind power input (WPI) to near-inertial motions is defined as:

m=0

WPI = τ • uf (z = 0),

where z is the depth, t is the time, uf and vf are the filtered zonal andmeridional near-inertial velocities, ufm and vfm are the zonal andmeridional modal near-inertial velocities with respect to mode m (m =v fm
0 for the barotropic mode and m > 0 for baroclinic modes), ̂u fm and ̂
are the corresponding modal amplitudes of ufm and vfm, and Πm is the mth normal mode:Πm (z) = ρ0 c2m

dΦm (z),dz

where τ is the near-inertial wind stress vector and uf is the near-inertial
velocity vector. Following Furuichi et al. (2008) and Raja et al. (2022),
the modal WPI was calculated:
WPIm = τ • uf m (z = 0).

(6)Frequency and wavenumber are important wave characteristics of
NIWs. Based on the Wentzel-Kramers-Brillouin (WKB) scaling and planewave fitting, the frequency and vertical wavenumber in the WKB
stretched depth coordinate can be estimated (Alford et al., 2012; Caoet al., 2018). The WKB stretched depth is calculated as:∫zzWKB =
N(z′) / Ndz′,
(7)

(2)

in which ρ0 is the reference density, Φm(z) is the eigenfunction of
eigenvalue problem for eigenspeed cm:
d2 Φm N 2
+ 2 Φm = 0,
dz2
cm

(5)

(3)

0

where N(z) is the local buoyancy frequency and N is its mean value. In
the WKB stretched depth coordinate, the zonal or meridional nearinertial velocities [Ψ(zWKB,t)] can be fitted with the plane-wave equa­tion based on the least squares method:

subject to boundary conditions Φm(0) = Φm(− H) = 0, in which N is
the local buoyancy frequency and H is the water depth. Based on thesimulated temperature and salinity, the potential density and buoyancy
frequency were easily obtained, and the normal mode Πm was thencalculated according to Equations (2) and (3). Using the least squares
method and filtered near-inertial velocities, ̂u fm and ̂v fm were obtained
according to Equation (1) (e.g. Zhao et al., 2010; Cao et al., 2015; Heet al., 2022). Multiplying ̂u fm (̂v fm ) by Πm, the modal near-inertial ve­
locities were finally obtained. Considering that the water depth varies
significantly in the domain (Fig. 1), we first divided the domain into
shallow (H ≤ 200 m) and deep (H > 200 m) regions and then adopted
the following strategy to conduct modal decomposition: For H < 50 m,

Ψ(zWKB , t) = Re{Ψ0 exp[i(ωt − m0 zWKB − φ)]},(8)

where Ψ0 is the amplitude, ω is the frequency, m0 is the vertical wave­
number, and φ is the phase. Note that only the ω, m0 and φ were fitted inthis study.

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Fig. 3. Comparison between raw observations and simulated results of FULL run at the two moorings: (a, b, e, f) zonal velocities, (c, g) current variance averaged in
the measuring range and (d, h) surface elevations at the (a–d) north and (e–h) south moorings. The vertical dashed lines indicate the time that the two typhoons
passed by.

Fig. 4. Time-averaged (a, b) depth-integrated NIKE and (c, d) WPI for (a, c) Songda and (b, d) Meari. In each panel, the green curve denotes the typhoon track, andthe black dashed and solid curves denote the 50 and 200 m isobaths, respectively.

3. Resultsby the CROCO: The velocities, current variance and surface elevation
show apparent spring-neap tidal cycles, suggesting that the motions at
the two moorings are dominated by tides. After the passage of the two
typhoons, the velocities in the upper layer are enhanced (Fig. 3b and f),
indicating that the ocean dynamical response to the typhoons is suc­cessfully simulated by the CROCO. Given that the FULL run generally
reproduces the motions at the two moorings, it is reasonable to use to

3.1. Validation of simulated results
Fig. 3 compares the raw observations and simulated results of FULL
run at the two moorings. On the whole, the observed velocities, current
variance (Var = u2+v2) and surface elevations are generally reproduced
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3.3. Modal content of typhoon-induced NIWs
Fig. 5 shows the modal decomposition results of zonal near-inertial
velocities as well as the modal NIKE induced by typhoon Meari at
128◦ E, 24.8◦ N as an example. It is clearly shown that the mode-3
dominates Meari-induced NIWs here. The mode-2, mode-4 and mode5 near-inertial velocities are comparable but weaker than the mode-3.
The mode-1 near-inertial velocities are much weaker than othermodes. The proportions of the first five baroclinic modes in the total
NIKE are 0.4%, 12.8%, 44.5%, 16.0% and 13.7%, respectively, and thesum of them exceeds 87%. As a result, the reconstructed near-inertial
velocities (Fig. 5b), which are the superposition of mode-1 to mode-5,
are nearly the same as the raw near-inertial velocities (Fig. 5a). This
result validates the modal decomposition method. The slight deviation
between the reconstructed and raw near-inertial velocities is related tothe modes higher than mode-5, of which the total contribution to thetotal NIKE is smaller than 13%.
The time-averaged depth-integrated modal NIKE as well as thedominant mode of the first five baroclinic modes for Meari-induced
NIWs are displayed in Fig. 6. It is easy to find that the distribution ofmode-1 NIKE is different from those of the higher modes (mode-2 tomode-5). As shown in Fig. 6a, the mode-1 NIKE mainly appears in theshallow regions on the continental shelf of ECS and around the Ryukyu
Islands, and that in the deep regions in the Okinawa Trough andnorthwest Pacific Ocean is too small to be detected. In contrast, highermode NIKE is mainly concentrated in the deep regions, and that in theshallow regions is nearly invisible (Fig. 6b− e). As a result, Meariinduced NIWs are mainly dominated by mode-1 in the shallow regions
but higher modes in the deep regions. To be specific, mode-2 and mode3 are dominant in the Okinawa Trough, and mode-3 to mode-5 aredominant in the northwest Pacific Ocean.
The modal NIKE and dominant mode for Songda-induced NIWs areshown in Fig. 7. Although the intensity and distribution of modal NIKE
induced by Songda (Fig. 7a− e) vary from those induced by Meari(Fig. 6a− e), the distributions of dominant mode of NIWs induced by thetwo typhoons are similar (Fig. 6f and 7f). Combining these results, we
can preliminarily conclude that the modal content of typhoon-induced
NIWs are related to the local water depth. The underlying mechanisms
will be discussed in Section 4.

Fig. 5. (a) Raw zonal near-inertial velocities at 128◦ E, 24.8◦ N and (b) thereconstructed result by superposing (c–g) mode-1 to mode-5 zonal near-inertial
velocities. (h) Depth-integrated NIKE and modal NIKE at this point. In eachpanel, the gray vertical dashed line indicates the time Meari passed by. Notethat the y-axes of subfigures (a–g) are in the log form.

3.4. Wave characteristics of typhoon-induced NIWs
Based on the WKB scaling and plane-wave fitting, we can obtain
more wave characteristics of typhoon-induced NIWs. Fig. 8 shows the
WKB scaling and plane-wave fitting results of Meari-induced NIWs at
128◦ E, 24.8◦ N as an example. According to Equation (7), if the strati­
fication is larger (smaller) than the averaged stratification (Fig. 8a), thecorresponding depth range would be extended (compressed) in the WKB
stretched depth coordinate (Fig. 8b). Hence, transforming the nearinertial velocities from the depth coordinate (Fig. 8c) to the WKB
stretched depth coordinate (Fig. 8d) reduces the influence of varying
stratification in the vertical direction. As shown in Fig. 8e, the fitted
NIWs generally show the same phase pattern as the observed NIWs in the
WKB stretched depth coordinate (Fig. 8d), demonstrating the accuracyof plane-wave fitting. The fitted frequency (ω) and vertical wavenumber(m0) in the WKB stretched depth coordinate of Meari-induced NIWs hereare 6.17 × 10− 5 s− 1 (1.01 times the local Coriolis frequency f) and 1.40
× 10− 3 m− 1. Hence, the vertical wavelength of Meari-induced NIWs is
4488 m in the WKB stretched depth coordinate. This value is generally
consistent with the vertical wavelength of mode-3 (Table 1), the domi­
nant mode here (Fig. 5). According to the dispersion relation of NIWs,()
m2 ω2 − f 2
kh2 = 0,(9)N2simulated results of NO-TIDE run to analyze the characteristics of NIWs
induced by typhoons Songda and Meari.
3.2. Typhoon-induced NIKE
Fig. 4a and b show the time-averaged depth-integrated NIKE induced
by Songda and Meari, respectively. The time range for averaging is from
00:00 on May 28 to 00:00 on June 9 (from 00:00 on June 25 to 00:00 on
July 3) for Songda (Meari). It is clearly shown that large NIKE mainly
appears to the right side of both typhoon tracks, which is consistent withthe rightward biased feature of ocean response to typhoons in the
Northern Hemisphere (Price et al., 1994). Because Songda is stronger
than Meari, Songda-induced NIKE is also larger than that induced by
Meari. The NIKE induced by the two typhoons also shares a common
feature, i.e. the NIKE in the deep regions of the domain is apparently
larger than that in the shallow regions. To be specific, the NIKE in the
Okinawa Trough and northwest Pacific Ocean is much larger than thaton the continental shelf of ECS. Fig. 4c and d illustrate the time-averaged
WPI for Songda and Meari. It is easy to find that the WPI nearly shares
the same pattern as the NIKE for both typhoons, suggesting that the
NIKE is mainly generated locally.

the horizontal wavenumber (kh) of Meari-induced NIWs here is 7.47
× 10− 6 m− 1, corresponding to the horizontal wavelength of 841 km. The
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Continental Shelf Research 264 (2023) 105055

Fig. 6. Time-averaged depth-integrated modal NIKE of (a–e) mode-1 to mode-5 for Meari. (f) Dominant mode among the first five baroclinic modes of Meari-induced
NIWs. The black dashed and solid curves denote the 50 and 200 m isobaths.

Fig. 7. Time-averaged depth-integrated modal NIKE of (a–e) mode-1 to mode-5 for Songda. (f) Dominant mode among the first five baroclinic modes of Songdainduced NIWs. The black dashed and solid curves denote the 50 and 200 m isobaths.

estimated frequency and horizontal wavenumber of NIWs generally
satisfy the following equation (Kundu, 1993):

ω = UT kh ,(2012),
cgz =

(10)

ω2 − f 2
,
m0 ω

(11)

the estimated vertical group speed (cgz) of Meari-induced NIWs hereis 9.53 × 10− 4 m/s (approximately 82 m/day). Note that the afore­
mentioned wave characteristics vary with locations, as the water depth,buoyancy frequency and dominant mode of NIWs are different. In

where UT is the typhoon translation speed. The estimated UT according
to the frequency and horizontal wavenumber of NIWs is 8.25 m/s, andthat calculated from the best track data is 5.2–12.1 m/s during 12:00 on
June 24 to 18:00 on June 25. Moreover, according to Alford et al.
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Fig. 8. (a) Stratification at 128◦ E, 24.8◦ N. (b) The WKB stretched depth according to the stratification. Zonal near-inertial velocities at 128◦ E, 24.8◦ N in the (c) depth
coordinate and (d) WKB stretched depth coordinate. (e) Results of plane-wave fitting. Note that the y-axes of subfigures (a–c) are in the log form.

4. Discussion

Table 1
Theoretical vertical wavelengths (unit: m, in the WKB stretched depth coordi­nate) of mode-1 to mode-5 at 128◦ E, 24.8◦ N.
Mode

Mode-1Mode-2Mode-3Mode-4Mode-5

Wavelength

12000

6000

4000

3000

2400

The simulated results of NIWs induced by typhoon Songda and Mearishow that the typhoon-induced NIWs are mainly dominated by mode-1
in the shallow regions of the domain but higher modes (mode-2 to mode5) in the deep regions. Given that WPI can account for the typhooninduced NIKE (section 3.2), attention is first paid to the modal WPI.
Figs. 9 and 10 illustrate the modal WPI for typhoons Meari and Songda,
respectively. It is clearly shown that the modal WPI almost shares thesame pattern as the modal NIKE for all the first five baroclinic modes andfor both typhoons (Figs. 6 and 7): Mode-1 WPI mainly appears in theshallow regions (on the continental shelf of ECS and around the Ryukyu
Islands) and higher-mode WPI mainly appears in the deep regions (in the

addition, because the NIWs are dominated by mode-1 in the shallow
regions, which exhibit mode-1 rather than beam-like structure, the WKB
scaling and plane-wave fitting cannot be used in these regions.

Fig. 9. Time-averaged modal WPI of (a–e) mode-1 to mode-5 for typhoon Meari. In each panel, the green curve denotes the typhoon track, and the black dashed andsolid curves denote the 50 and 200 m isobaths, respectively.
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Fig. 10. Time-averaged modal WPI of (a–e) mode-1 to mode-5 for typhoon Songda. In each panel, the green curve denotes the typhoon track, and the black dashedand solid curves denote the 50 and 200 m isobaths, respectively.

Okinawa Trough and northwest Pacific Ocean). This result indicates thatthe modal NIKE is also mainly generated locally.
However, the modal WPI is not the real cause for the modal content
of typhoon-induced NIWs. According to Equation (6), the modal WPIequals to the dot product of wind stress and modal near-inertial velocity
at the surface, of which the former is the same for different modes andthe latter is the modal decomposition result. In other words, the modal
WPI represents the energy flux from winds to NIWs of the certain mode,
but it cannot explain why the NIWs of such mode are excited by thewinds.
The theoretical framework developed by Kundu and Thomson(1985) is used to explain the modal content of typhoon-induced NIWs.
The governing equations for the linearized inviscid near-inertial motion
are:

∂u
1 ∂p
− fv = −
+ F,
∂t
ρ0 ∂x

(12a)

∂v
1 ∂p
+ fu = −
+ G,
∂t
ρ0 ∂y

(12b)

∂p
+ ρg = 0,
∂z

(12c)

∂u ∂v ∂w
+ += 0,
∂x ∂y ∂z

(12d)

∂um
1 ∂pm
− fvm = −+ Fm ,∂tρ0 ∂ x(14a)∂ρ ρ0 N 2 w
= 0,
−
∂t
g

(12e)

∂vm
1 ∂pm
+ fum = −+ Gm ,
∂t
ρ0 ∂y

(14b)

Fig. 11. Estimated dominant mode based on the theoretical framework ofKundu and Thomson (1985). The black dashed and solid curves denote the 50
and 200 m isobaths, respectively.

in which,τxτyF=
and G =,hρ0hρ0in which,
(13)

Fm =

are the wind forcing functions acted as a body force in the mixed
layer (h is the mixed layer depth). Expanding the variables into modes,
the horizontal momentum Equation (12a− b) become

ρ0

∫0

τx

Π2m dz− H

and Gm =∫0τyρ0 − H Π2m dz

,

(15)

are the modal wind forcing. If we neglect the slight influence of airpressure, the modal wind forcing is the only cause for the modal NIWs.
Therefore, we can approximately estimate the dominant mode of NIWs
through comparing the wind forcing of different modes [according to8

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Fig. 12. (a) Buoyancy frequency (shading) and potential density anomaly (σ θ, contours, unit: kg/m3) along 30◦ N and vertical profiles of potential density anomaly at(b) 123◦ E, (c) 124◦ E, (d) 125◦ E, (e) 126◦ E, (f) 127◦ E, (g) 128◦ E and (h) 129◦ E along this section. The locations of these profiles are marked by green triangles in (a).
Note that when the water depth is smaller than 50 m, the buoyancy frequency is not calculated and is not shown in (a). Also note that all the y-axes are in thelog form.

∫0
Equation (15), the minimum value of − H Π2m dz corresponds to the
maximum modal wind forcing].
Take the result at 128◦ E, 24.8◦ N as an example. According to the∫0normal modes shown in Fig. 2b, the values of − H Π2m dz for mode-1 tomode-5 are 413, 316, 289, 379 and 458, respectively. Because the value∫0of − H Π2m dz for mode-3 is the smallest among the five modes, thedominant mode of NIWs at 128◦ E, 24.8◦ N is mode-3 according to thetheoretical framework of Kundu and Thomson (1985). This result is
consistent with the modal decomposition result (Fig. 5). Fig. 11 further
shows the dominant mode of NIWs estimated from this theoreticalframework. It is easy to find that in the deep regions of the domain, theestimated dominant mode is generally consistent with the modal
decomposition results for typhoons Meari and Songda (Fig. 6f and 7f), i.
e. mode-2 and mode-3 are dominant in the Okinawa Trough, andmode-3 to mode-5 are dominant in the northwest Pacific Ocean. The
slight deviation between them can be explained, because the advection
and dissipation are not considered in the theoretical framework (Equa­tion (12)), but they do exist in the CROCO. Therefore, the dominance of
higher-mode wind forcing is the cause for the dominance of
higher-mode NIWs in the deep regions.
However, the result of the theoretical framework cannot account forthe dominance of mode-1 NIWs in the shallow regions, as the wind
forcing here is still dominated by higher modes (Fig. 11). Actually, thewind forcing is not the sole factor that determines the NIWs. The strat­
ification also has a crucial influence on the NIWs. Fig. 12 shows thestratification along 30◦ N as an example. It is clearly shown that in theregions where water depth is smaller than 50 m, the density is nearly
uniform in the vertical direction, indicating that no stratification isdeveloped here (Fig. 12b). That’s why we did not conduct modal
decomposition in these regions (section 2). In the shallow regions wherewater depth is between 50 and 200 m, there exists two-layer-structure
stratification (Fig. 12a, c− f), which can only support mode-1 internal
waves in theory. In the deep regions where water depth is larger than
200 m, the two-layer-structure stratification disappears (Fig. 12a, g− h).
Similar stratification can be found at other sections, which are notshown. Based on this result, we believe that the two-layer-structure

stratification is the cause for the dominance of mode-1 NIWs in theshallow regions. Note that such phenomenon (two-layer-structure
stratification and dominance of mode-1 NIWs) also exists on the conti­
nental shelf of the Mid-Atlantic Bight (Zhang et al., 2018; Han and Yu,
2022).
Although this study only focuses on the modal content of NIWs
induced by typhoons Songda and Meari around the ECS, the conclusionsof this study can be extended to other oceans. Actually, NIWs dominatedby mode-1 have been reported in many shallow regions, such as in the
Yellow Sea (Yang et al., 2021), on the continental shelves of South China
Sea (Yang et al., 2015) and Mid-Atlantic Bight (Zhang et al., 2018; Han
and Yu, 2022), and NIWs dominated by higher modes have been foundin the deep regions in the South China Sea (He et al., 2022) and global
ocean (Raja et al., 2022).
5. Summary
In this study, the NIWs induced by typhoons Songda and Meari in the
ECS and its adjacent deep waters are simulated based on the CROCO,
and their characteristics, especially the modal content, are analyzed.
Results indicate that the NIKE induced by the two typhoons showsdifferent intensity and spatial distribution, but shares a common feature,i.e. the NIKE in the deep regions of the domain is apparently larger thanthat in the shallow regions, which is consistent with the WPI, suggestingthat the NIKE is mainly generated locally. With respect to the modal
content, it is found that in the shallow regions, the NIWs induced by thetwo typhoons are mainly dominated by mode-1, whereas in the deep
regions, they are dominated by higher modes (mode-2 to mode-5).
Through analysis, we find that two mechanisms account for this phe­nomenon. In the deep regions, the dominance of higher-mode wind
forcing is the cause for the dominance of higher-mode NIWs. Whereas in
the shallow regions, the two-layer-structure stratification is the cause forthe dominance of mode-1 NIWs. Although this study only focuses on the
NIWs induced by two typhoons around the ECS, the conclusions of thisstudy can be extended to other oceans, as similar phenomenon has beenreported in other oceans.

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Continental Shelf Research 264 (2023) 105055

Declaration of competing interest

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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.
Acknowledgements
The authors would like to deeply thank the two reviewers who
provide constructive suggestions that greatly improve the manuscript.
This study is supported by the Zhejiang Provincial Natural Science
Foundation of China (grant number: LY21D060005) and the China
Scholarship Council (grant number: 202006325025). The authors also
thank the support by Grants-in-Aid for Scientific Research (MEXT
KAKENHI grant numbers: 19H05696/20H04319) and the JSPS Post­
doctoral Fellowships for Research in Japan.
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