Ocean Modelling 186 (2023) 102243

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Ocean Modelling
journal homepage: www.elsevier.com/locate/ocemod

Energetics of the M2 internal tides modulated by typhoons at the Luzon Strait
Anzhou Cao a,b ,∗, Zheng Guo c , Shuya Wang b , Xu Chen d , Jinbao Song a , Xinyu Guo ba

Ocean College, Zhejiang University, Zhoushan, China
Center for Marine Environmental Studies, Ehime University, Matsuyama, Japan
Marine Science and Technology College, Zhejiang Ocean University, Zhoushan, Chinad
Key Laboratory of Physical Oceanography, Ocean University of China, Qingdao, Chinabc

ARTICLEINFO

Dataset link: www.crocoocean.org, apdrc.soest.
hawaii.edu/data/data.php
Keywords:
Internal tides
Typhoon Megi
Luzon Strait
Conversion
Baroclinic energy flux
Dissipation

ABSTRACTThis study investigates the influence of typhoons (a real typhoon, Megi in 2010, and four idealized typhoons)on the energetics of the M2 internal tides (ITs) at the Luzon Strait (LS) based on the numerical simulation.
Results indicate that typhoon Megi caused intense low-frequency currents and stratification variation near theLS, which further induced significant temporal variations in the M2 conversion, baroclinic energy fluxes anddissipation at the LS. With a condition of no background currents, typhoon Megi reduced the M2 conversion at
the LS by 4.5% and weakened the westward M2 baroclinic energy fluxes into the South China Sea by 14.3%.
Typhoon Megi did not significantly change the averaged M2 dissipation at the LS, but it elevated the averaged
local dissipation efficiency to some extent. When background currents were taken into consideration, theinfluence of typhoon Megi on the M2 conversion and baroclinic energy fluxes was weakened, but the influenceon the M2 dissipation was enhanced. Experiments of idealized typhoons indicate that typhoons with different
tracks have different influences on the M2 ITs at the LS. With the same characteristics (radius, maximum windspeed and translation speed), the typhoon that passes over the LS from east to west causes the largest variationin the energetics of the M2 ITs at the LS.

1. Introduction
Internal tides (ITs) are internal waves with tidal frequency, which
are ubiquitous and play an important role in driving the turbulent
mixing in the ocean. According to the estimations of Munk and Wunsch(1998) and Carter et al. (2012), about 2 TW energy is required tomaintain the abyssal ocean stratification with globally averaged diapycnal diffusivity of 10−4 m2 /s, and ITs contribute approximately 1 TW.
Numerical simulations of ITs estimate the global tidal conversion to
be 1.1–1.7 TW (Niwa and Hibiya, 2011; Müller, 2013; Buijsman et al.,2016)), most of which is related to the 𝑀2 ITs (0.6–1.1 TW; (Simmons
et al., 2004; Niwa and Hibiya, 2011, 2014; Müller, 2013). Significant
tidal conversions are usually found over rough topographies, such as
the Aleutians Islands, Hawaiian Ridge and Luzon Strait (LS).
Theoretical studies of ITs indicate that the tidal conversion is related
to the water stratification, topographic features, water depth, Coriolis
frequency as well as the frequency and magnitude of barotropic tidal
currents (e.g. Baines, 1973; Llewellyn Smith and Young, 2003; Pétrélis
et al., 2006; Echeverri and Peacock, 2010; Cao et al., 2014). These studies clarify the factors that influence the tidal conversion, however, theirconclusions cannot be directly expanded to the real ocean, because
they are mainly based on two-dimensional linear IT models. Therefore,
three-dimensional numerical models are widely used when estimating∗

the tidal conversion in the global ocean or marginal seas (e.g. Simmons
et al., 2004; Di Lorenzo et al., 2006; Niwa and Hibiya, 2011, 2014;
Kerry et al., 2013; Kelly et al., 2021).
Previous studies also indicated that other ocean dynamical processes, such as background currents and mesoscale eddies, can influence the tidal conversion as well as the propagation and dissipationof ITs (e.g. Zilberman et al., 2011; Jan et al., 2012; Kerry et al.,2014; Xu et al., 2021; Guo et al., 2023; Zhao and Qiu, 2023). Mooredobservations upon the Kaena Ridge (between the Hawaiian islands of
Oahu and Kauai) showed that the 𝑀2 conversion varies by a factor of
2 (0.5–1.1 W/m2 ) in 6 months, which is partially related to the lowfrequency currents and stratification fluctuation due to two mesoscaleeddies (Zilberman et al., 2011). Using a three-dimensional model with
idealized settings, Jan et al. (2012) found that the generation andpropagation of the 𝑀2 and 𝐾1 ITs at the LS are influenced by thetransport and location of the Kuroshio Current. Based on the year-longnumerical simulation of background currents and the 𝑀2 ITs in thePhilippine Sea, Kerry et al. (2014) found that the 𝑀2 conversion at theLS varies from a minimum of 13.01 GW to a maximum of 19.95 GW
with the time-averaged value of 16.21 GW. Xu et al. (2021) further
pointed out that the Kuroshio in different paths significantly modulate
the energetics of ITs radiated from the LS. The tidal conversion, energy

Corresponding author at: Ocean College, Zhejiang University, Zhoushan, China.
E-mail address: caoanzhou@zju.edu.cn (A. Cao).

https://doi.org/10.1016/j.ocemod.2023.102243
Received 13 April 2023; Received in revised form 11 June 2023; Accepted 19 July 2023
Available online 27 July 2023
1463-5003/© 2023 Elsevier Ltd. All rights reserved.

A. Cao, Z. Guo, S. Wang et al.

Ocean Modelling 186 (2023) 102243

Fig. 1. (a) Bathymetry (shading, unit: m) of the study domain. (b) Sea surface height induced by the mode-1 𝑀2 ITs [shading, unit: cm; cited from Zhao (2019)] and Typhoon
Megi’s track (different colors represent different statuses). Locations of Megi’s center are marked by dots every 6 h and time (00:00) is labeled every 24 h. The black plus denotes
the location of mooring UIB6 in Cao et al. (2018).
Table 1
Design of numerical experiments.

flux divergence and dissipation of both diurnal and semidiurnal ITs under the influence of leaping Kuroshio are greater than those under the
influence of looping Kuroshio. Based on 24-year-long satellite altimetry
measurements, Zhao and Qiu (2023) revealed the seasonal variabilityof the mode-1 𝑀2 ITs radiated from the LS and suggested that the ocean
stratification and Kuroshio Currents were the main driving factors.
Typhoons can also cause low-frequency currents and stratification
variation in the ocean (e.g. Ko et al., 2014), which may have an
impact on the energetics of ITs when passing over the ocean near the
IT generation sites. However, this issue has not been fully studied.
Given that the LS is a typical generation site of ITs (e.g. Alford et al.,2015) and the adjacent waters of the LS are frequently affected bytyphoons (e.g. D’Asaro et al., 2011), we chose the LS to investigate
the energetics of the 𝑀2 ITs modulated by typhoons based on the
numerical simulation (Fig. 1). Typhoon Megi in 2010, which caused
significant ocean response in the South China Sea (Guan et al., 2014;
Ko et al., 2014; Pun et al., 2018; Cao et al., 2018), was taken into
consideration. Moreover, we also designed four idealized typhoons to
discuss the influence of typhoon’s track on the M2 ITs at the LS.
The paper is organized as follows. The model configurations anddata analysis methods are introduced in Sections 2 and 3, respectively.
The low-frequency currents and stratification variation caused by typhoon Megi are shown in Section 4. The energetics of the 𝑀2 ITs at theLS modulated by typhoon Megi is analyzed in Section 5. A discussion iscarried out in Section 6. Finally, the paper is summarized in Section 7.

Experiment

Tidal
forcingWind
forcing

Backgroundcurrents

Initialstratification

Exp-T

TPXO7

No

No

Exp-TW

TPXO7

CFSR

No

Exp-TC

TPXO7

No

HYCOM

Exp-TCW

TPXO7

CFSR

HYCOM

Horizontallyhomogeneous
Horizontallyhomogeneous
Horizontally
inhomogeneous
Horizontally
inhomogeneous

Four numerical experiments were designed in this study (Table 1),
all of which were simulated from October 1 to 31, 2010. In Exp-T,
only the 𝑀2 tidal forcing was added into the model with horizontallyhomogeneous stratification. The 𝑀2 tidal forcing was introduced into
the model at the open boundaries via the Flather radiative conditions,of which the surface elevations and barotropic tidal currents wereobtained from the Oregon State University global models of ocean tides(TPXO7; Egbert and Erofeeva, 2002). The horizontally homogeneous
stratification was obtained from the horizontally averaged temperature and salinity of the HYbrid Coordinate Ocean Model (HYCOM)
reanalysis data (apdrc.soest.hawaii.edu/data/data.php) in the domain
on October 1, 2010. In Exp-TW, the wind forcing was consideredin addition to the tidal forcing. The hourly Climate Forecast System
Reanalysis (CFSR) wind speed data at 10 m height (apdrc.soest.hawaii.
edu/data/data.php) and the wind stress drag coefficient developed by
Oey et al. (2006) were used to calculate the wind stress. The CFSR winddata generally captured the characteristics of typhoon Megi. The effectsof typhoon Megi on the ocean and the 𝑀2 ITs were imposed on thesimulations in terms of wind forcing. The initial stratification in ExpTW was also horizontally homogeneous, which is the same as that in
Exp-T. In Exp-TC, in addition to the 𝑀2 tidal forcing, the backgroundcurrents were taken into consideration while the wind forcing waseliminated. The HYCOM reanalysis data in October 2010 were used as
the initial and boundary conditions. In Exp-TCW, both the influences ofwind forcing and background currents on the 𝑀2 ITs were considered.
Note that the stratification was no longer horizontally homogeneousin Exp-TC and Exp-TCW. In all the four experiments, the simulated
results were output every one hour. The simulated ITs in this region
have been validated by previous studies (Guo et al., 2020a; Cao et al.,2022). The simulated ocean dynamical response to typhoon Megi wasvalidated by comparing the near-inertial currents between observationand simulation (Exp-TCW) at the mooring site (Fig. 1b), which is shownin the supporting material.

2. Modal configurations
In this study, the Regional Ocean Modeling System (ROMS) under the framework of Coastal and Regional Ocean COmmunity model(CROCO, version 1.0, www.croco-ocean.org) was employed to simulate
the 𝑀2 ITs under the influence of typhoon Megi and/or backgroundcurrents. The CROCO has been validated to perform well in different
scenarios including the simulation of ITs in the SCS (e.g. Renault et al.,2017; Marchesiello et al., 2019; Guo et al., 2020a,b; Cao et al., 2022).
The simulated domain was 115.5–126.5◦ E and 15.5–24.5◦ N and thestudy domain was 116–126◦ E and 16–24◦ N (Fig. 1), as four 0.5◦ sponge
layers were used at the four open boundaries. The horizontal resolutionof the model was 1/20◦ (approximate 5 km). There were 30 sigma
layers in the vertical direction. Because the main aim of this study is toinvestigate the influence of typhoon Megi on the energetics of the 𝑀2
ITs at the LS, the sigma layers had finer resolution near the surface. To
be specific, there were nearly 10 sigma layers in the upper 100 m in
the South China Sea Basin. Moreover, other settings of the model were
the same as those in Cao et al. (2022).
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Ocean Modelling 186 (2023) 102243

3. Data analysis methodology

before October 15 (Fig. 2a). Before Megi’s center entered the domain
on October 17, the surface currents were rapidly increased to approximately 0.5 m/s in the Philippine Sea (Fig. 2b). After passing over theLuzon Island, although Megi was weakened from a super typhoon to asevere typhoon (Fig. 1), the surface currents induced by Megi exceeded
1 m/s in the South China Sea (Fig. 2c–f), which are nearly comparable
to the intensity of the Kuroshio Current at the same time (Fig. 2i–l).
Actually, when the study domain was under the influence of typhoon
Megi, the Kuroshio Current was also slightly affected, which can bedetected from Fig. 2o–r.
Fig. 3 illustrates the temporal variations of temperature, low-frequency meridional currents, buoyancy frequency squared (𝑁 2 = −g /𝜌0 ⋅𝑑𝜌/dz, where g is the acceleration of gravity, 𝜌0 is the reference densityand 𝜌 is the water density) and shear squared [𝑠2 =(d𝑢′ /dz)2 +(d𝑣′ /dz)2 ]at 121◦ E, 20◦ N in the four experiments. In Exp-T, the temperature,
stratification and shear showed regular semidiurnal cycles and the lowfrequency meridional currents were nearly invisible (Fig. 3a, e, i, m), as
the only external forcing in this experiment was the 𝑀2 tidal forcing. In
Exp-TW, the temperature, meridional currents, stratification and shear
were significantly changed after the passage of the typhoon: The surface temperature was slightly decreased by 0.9 ◦ C and the subsurface
temperature was slightly increased by 0.1–0.8 ◦ C (Fig. 3b); The lowfrequency meridional currents were enhanced to 0.28 m/s (Fig. 3f); The
stratification in the upper 60 m was significantly decreased (Fig. 3j) andthe shear squared in the upper 100 m was enhanced by 1–2 orders ofmagnitude (Fig. 3n). Because background currents were considered in
Exp-TC and Exp-TCW, the patterns of meridional currents, stratificationand shear in these experiments showed large differences from those in
Exp-T and Exp-TW, which were largely due to the Kuroshio Current.
Although the Kuroshio Current dominated the motion here, typhoon
Megi caused variation of meridional currents, reduction of stratificationand enhancement of shear squared in the upper ocean after October 17,
according to the comparison between the results in Exp-TC and ExpTCW (Fig. 3g, h, k, l, o, p). These results indicate that typhoon Megi
caused significant low-frequency currents and stratification variationnear the LS.

The period-averaged energy budget of the 𝑀2 ITs (e.g. Alford et al.,2011; Kerry et al., 2013; Guo et al., 2020a) is(1)∇ ⋅ 𝐅 = 𝐶 − 𝐷,where F=(𝐹𝑥 , 𝐹𝑦 ) is the depth-integrated baroclinic energy flux, C is thebarotropic to baroclinic tidal conversion rate and D is the dissipation.
The depth-integrated baroclinic energy flux is calculated as⟨ 𝜂⟩𝐅=𝑝′ (𝑧, 𝑡) 𝐮′ (𝑧, 𝑡) d𝑧 ,(2)∫−𝐻where < > denotes the average over a tidal period, z is the depth, tis the time, 𝜂 is the surface elevation, H is the water depth, u′ = (𝑢′ ,𝑣′ ) is the horizontal baroclinic velocity and p′ is the baroclinic pressure
perturbation which is calculated as𝜂𝑝′ (𝑧, 𝑡) =∫𝑧()
𝜌′ 𝑧′ , 𝑡 𝑔d𝑧′ −

𝜂
𝜂
(
)
1
𝜌′ 𝑧′ , 𝑡 𝑔d𝑧′ d𝑧,
𝐻 + 𝜂 ∫−𝐻 ∫𝑧(3)where 𝜌′ is the density perturbation, g is the acceleration due to gravity.
Apparently, the atmospheric pressure is not considered in the pressure
perturbation. The tidal conversion rate is computed as⟨⟩ ⟨⟩𝐶 = 𝑝′ (−𝐻, 𝑡) 𝑤𝑏𝑡 (−𝐻, 𝑡) = 𝑝′ (−𝐻, 𝑡) 𝐮𝑏𝑡 (−𝐻, 𝑡) ⋅ ∇ (−𝐻) ,(4)
where 𝐮𝑏𝑡 and 𝑤𝑏𝑡 are zonal and vertical barotropic velocity. Following
Zilberman et al. (2011) and Cao et al. (2022), the period-averaged
conversion rate and baroclinic energy flux are calculated as
[
]
1
(5)
𝐶 = 𝑃 (−𝐻) 𝑊𝑏𝑡 (−𝐻) cos 𝜃𝑃 (−𝐻) − 𝜃𝑊 (−𝐻) ,
2
𝜂
[
]
1
𝐹𝑥 =
𝑃 (𝑧) 𝑈 (𝑧) cos 𝜃𝑃 (𝑧) − 𝜃𝑈 (𝑧) d𝑧,
(6)
∫−𝐻 2
𝜂
[
]
1
𝐹𝑦 =
𝑃 (𝑧) 𝑉 (𝑧) cos 𝜃𝑃 (𝑧) − 𝜃𝑉 (𝑧) d𝑧,
(7)
∫−𝐻 2
where P, 𝑊𝑏𝑡 , U, V, 𝜃𝑃 , 𝜃𝑊 , 𝜃𝑈 and 𝜃𝑉 are the amplitudes and phases of𝑝′ , 𝑤𝑏𝑡 , 𝑢′ and 𝑣′ , respectively. In this study, the T_tide Matlab package(Pawlowicz et al., 2002) was used to calculate the daily P, 𝑊𝑏𝑡 , U, V,
𝜃𝑃 , 𝜃𝑊 , 𝜃𝑈 and 𝜃𝑉 from October 15 to 30. Hence, the daily conversion
rate and baroclinic energy flux were obtained according to Eqs. (5)–(7).
Following Kerry et al. (2014), the sensitivities of tidal conversion
rate to variations of bottom pressure perturbation, vertical barotropic
velocity and phase difference between pressure perturbation and vertical barotropic velocity (hereafter, phase difference is used for short)
were investigated in this study. According to Eq. (5), it is easy to obtainthe following equations:

5. Energetics of the M𝟐 ITs
5.1. Tidal conversion
Fig. 4 displays the 𝑀2 conversion rates at the LS on October 21
in the four experiments as an example. As shown in Fig. 4a, large
𝑀2 conversion rates mainly appeared upon the eastern flank of thewest ridge and both flanks of the east ridge of the LS, and the total
conversion integrated at the LS (120–122.5o E, 18.5-22o N) was 17.7
GW. This result is generally consistent with previous studies (e.g. Kerryet al., 2013; Xu et al., 2016; Guo et al., 2020a).
Under the influence of typhoon Megi (Exp-TW), the 𝑀2 conversion
rates were significantly decreased on both ridges of the LS (Fig. 4b). As
a result, the 𝑀2 conversion integrated at the LS in Exp-TW was 16.4
GW, which is 1.3 GW smaller than that in Exp-T. In contrast, whenbackground currents were considered in Exp-TC, the 𝑀2 conversion
integrated at the LS was elevated to 19.4 GW. Note that not all the𝑀2 conversion rates at LS were enhanced in Exp-TC (Fig. 4c). Instead,the 𝑀2 conversion rates on the north part of the west ridge and middle
part of the east ridge were mainly increased, whereas those at otherlocations were generally decreased, compared to Exp-T (Fig. 4c). Whenboth typhoon Megi and background currents were considered in ExpTCW, the pattern of the 𝑀2 conversion rates is similar to that in Exp-TC.
The 𝑀2 conversion integrated at the LS in Exp-TCW was 18.9 GW,
larger than that in Exp-T but a little smaller than that in Exp-TC. Basedon these results, we can find that typhoon Megi indeed influenced
the 𝑀2 conversion at the LS. Note that this is only based on the 𝑀2
conversion rates on October 21. In the following, we will show thedaily 𝑀2 conversion integrated at the LS from October 15 to 30, and1
𝜕𝐶= 𝑊𝑏𝑡 (−𝐻) cos (𝛥𝜃) ,(8)𝜕𝑃 (−𝐻)
2
1
𝜕𝐶= 𝑃 (−𝐻) cos (𝛥𝜃) ,(9)𝜕𝑊𝑏𝑡 (−𝐻)2
𝜕𝐶1= − 𝑃 (−𝐻) 𝑊𝑏𝑡 (−𝐻) sin (𝛥𝜃) ,
(10)
𝜕𝛥𝜃
2
where 𝛥𝜃 = 𝜃𝑃 (-H )-𝜃𝑊 (-H ) is the phase difference. Multiplying Eqs.
(8)–(10) by the standard deviations of bottom pressure perturbation(𝜎𝑃 ), vertical barotropic velocity (𝜎𝑊 ) and phase difference (𝜎𝜃 ) respectively, the sensitivities of tidal conversion rate with respect to P(-H ),W 𝑏𝑡 (-H ) and 𝛥𝜃 are obtained:
𝛥𝐶𝑃 =

𝜕𝐶
𝜕𝐶
𝜕𝐶
𝜎 , 𝛥𝐶𝑊 =𝜎 and 𝛥𝐶𝜃 =𝜎 .
𝜕𝑃 (−𝐻) 𝑃
𝜕𝑊𝑏𝑡 (−𝐻) 𝑊
𝜕𝜃 𝜃

(11)

4. Low-frequency currents and stratification variation
Low-frequency surface currents in Exp-TW, Exp-TC and Exp-TCW
are shown in Fig. 3, which were extracted from the raw simulations
through the fourth order Butterworth lowpass filter with the cutoff
frequency of 0.5 cpd (Cao et al., 2022). It is clearly shown that typhoon
Megi caused significant surface currents during its passage. In Exp-TW,
the surface currents were weak and generally smaller than 0.2 m/s
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Ocean Modelling 186 (2023) 102243

Fig. 2. Low-frequency surface currents (magnitude: shading, unit: m/s, direction: quivers) at 00:00 on October (a, g, m) 15, (b, h, n) 17, (c, i o) 19, (d, j, p) 21, (e, k, q) 23 and(f, l, r) 25 in (a–f) Exp-TW, (g–l) Exp-TC and (m-r) Exp-TCW. The magenta curve denotes Megi’s track.

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Ocean Modelling 186 (2023) 102243

Fig. 3. (a–d) Temperature (shading, unit: o C), (e–h) low-frequency meridional currents (shading, unit: m/s), (i–l) buoyancy frequency squared (shading, unit: s−2 , in the log form)and (m-p) shear squared (shading, unit: s−2 , in the log form) at 121◦ E, 20◦ N in (a, e, i, m) Exp-T, (b, f, j, n) Exp-TW, (c, g, k, o) Exp-TC and (d, h, l, p) Exp-TCW. The verticaldashed line denotes 00:00 on October 17.

Fig. 4. (a) Conversion rates (shading, unit: W/m2 ) at the LS on October 21 in Exp-T. Difference of conversion rates at the LS between (b) Exp-TW, (c) Exp-TC, (d) Exp-TCW and
Exp-T on October 21. In each panel, the gray contours denote the 1000, 2000 and 3000 m isobaths, and the domain-integrated value is shown in the title.

explore its sensitivities to the bottom pressure perturbation and verticalbarotropic velocity.
Fig. 5a illustrates the daily 𝑀2 conversion integrated at the LS in
the four experiments, from which it is easy to detect the influencesof typhoon Megi and background currents on the generation of the𝑀2 ITs. In Exp-T with the absence of typhoon Megi and backgroundcurrents, the 𝑀2 conversion was stable at 17.7 GW. In contrast, the 𝑀2
conversion in the other three experiments showed temporal variations.
In Exp-TW, the 𝑀2 conversion was generally smaller than 17.7 GW
except on October 20, suggesting that typhoon Megi reduced the generation of the 𝑀2 ITs at the LS. Actually, the 𝑀2 conversion in Exp-TW
reached the maximum of 17.74 GW on October 20 and the minimumof 16.37 GW on October 21, when typhoon Megi caused intense lowfrequency currents in the South China Sea Basin (Fig. 2). Typhoon Megi
left the South China Sea on October 23, but the 𝑀2 conversion was
still significantly depressed on October 30. This result suggests that the
influence of typhoon Megi on the 𝑀2 conversion at the LS could last
for at least one week after its passage. Moreover, the 𝑀2 conversion in
Exp-TW showed two apparent peaks with one appearing on October 20
and the other on October 24.
Unlike typhoon Megi which reduced the 𝑀2 conversion, the background currents promoted it in October. The 𝑀2 conversion in Exp-TC
reached the maximum of 19.5 GW and the minimum of 18.4 GW,

yielding an average of 19.2 GW which is 1.5 GW greater than that in
Exp-T. As for Exp-TCW, we can detect the influences of backgroundcurrents and typhoon Megi on the 𝑀2 conversion from two different
aspects. On one hand, the 𝑀2 conversion in Exp-TCW was 18.5–
19.6 GW, which is 0.8–1.9 GW greater than that in Exp-T. Given thattyphoon Megi generally reduced the 𝑀2 conversion at the LS (Exp-TW)
but the background currents promoted it (Exp-TC), this result suggeststhat the background currents played a more important role in affecting
the magnitude of the 𝑀2 conversion at the LS than typhoon Megi.
On the other hand, the temporal variation of the 𝑀2 conversion in
Exp-TCW is similar to that in Exp-TW, and the correlation coefficient
between them is 0.55 with a p-value of 0.03, suggesting that they weresignificantly correlated. In contrast, the correlation coefficient and pvalue of the 𝑀2 conversion between Exp-TC and Exp-TCW are 0.41 and
0.12, respectively, suggesting a bad correlation. Moreover, we can also
detect two peaks in the 𝑀2 conversion in Exp-TCW, which also existed
in Exp-TW but were absent in Exp-TC. These results indicate thattyphoon Megi contributed more to the temporal variation of the 𝑀2
conversion than the background currents. In addition, the differenceof the averaged 𝑀2 conversion between Exp-T and Exp-TW is 0.8 GW
whereas that between Exp-TC and Exp-TCW is only 0.2 GW, suggestingthat the background currents weakened the impact of typhoon Megi on
the 𝑀2 conversion at the LS.
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Ocean Modelling 186 (2023) 102243

Fig. 5. (a) Daily conversion and its sensitivities to bottom (b) pressure perturbation, (c) vertical barotropic velocity and (d) phase difference integrated at the LS in the four
experiments. The vertical dashed line denotes 00:00 on October 17.

the results in Exp-T and Exp-TW (Exp-TC and Exp-TCW), we can findthat typhoon Megi did not significantly change the pattern of the 𝑀2
baroclinic energy fluxes, but it changed their magnitude, especiallyfor the westward 𝑀2 baroclinic energy fluxes into the South China
Sea Basin. To clearly demonstrate this point, we integrated the 𝑀2
baroclinic energy fluxes along the four boundaries of the LS, which are
shown in Fig. 7.
In all the four experiments, the eastward and westward 𝑀2 baroclinic energy fluxes were one order of magnitude greater than thesouthward and northward ones. Hence, attention is mainly paid tothe eastward and westward 𝑀2 baroclinic energy fluxes. In Exp-T, thewestward 𝑀2 baroclinic energy flux into the South China Sea wasgreater than the eastward one into the Philippine Sea by approximately
0.8 GW. Compared with Exp-T, the westward 𝑀2 baroclinic energy flux
in Exp-TW was depressed by typhoon Megi by 0.6 GW (14.3% of the
westward 𝑀2 baroclinic energy flux in Exp-T), whereas the eastward
one was less affected. As a result, the averaged westward 𝑀2 baroclinic
energy flux was only 0.2 GW greater than the averaged eastward one
in Exp-TW, which is one quarter of the value in Exp-T. However,when background currents were considered in Exp-TC and Exp-TCW,
the situation was a little different, i.e. typhoon Megi reduced both
westward and eastward 𝑀2 baroclinic energy fluxes. Compared with
Exp-TC, the averaged westward 𝑀2 baroclinic energy flux in Exp-TCW
was reduced by 0.3 GW (7.9% of the averaged westward 𝑀2 baroclinic
energy flux in Exp-TC), whereas the eastward one was reduced by 0.2
GW (5.1% of the averaged eastward 𝑀2 baroclinic energy flux in ExpTC). Combining these results, we can find that typhoon Megi mainly
reduced the westward 𝑀2 baroclinic energy fluxes into the South China
Sea, but it did not significantly change their pattern. The existence of
background currents weakened the influence of typhoon Megi on the𝑀2 baroclinic energy fluxes.

Thereafter, attention is paid to the sensitivities of the M2 conversion
to the bottom pressure perturbation, vertical barotropic velocity andphase difference, which are shown in Fig. 5b–d, respectively. In ExpTW, Exp-TC and Exp-TCW, 𝛥C 𝑃 was apparently greater than 𝛥C 𝑊
and 𝛥C 𝜃 , suggesting that the bottom pressure perturbation played amore important role than the vertical barotropic velocity and phasedifference in determining the M2 conversion in October 2010. Thisis consistent with the result of Kerry et al. (2014) in October 2010,
although in other months, the phase difference played a dominant role[Fig. 7a in Kerry et al. (2014)]. We also note that the 𝛥𝐶𝑃 and 𝛥𝐶𝜃
in this study are smaller than those in Kerry et al. (2014), perhaps
because the 𝜎𝑃 and 𝜎𝜃 in October in this study are smaller than thosein a whole year in Kerry et al. (2014). Moreover, in Exp-TW and ExpTCW, the 𝛥C 𝑃 and 𝛥C 𝑊 were slightly varied, but the 𝛥C 𝜃 showedsignificant variations. This result suggests that the temporal variationof the 𝑀2 conversion at the LS induced by typhoon Megi (Fig. 5a) was
largely due to the variation of phase difference. In contrast, because thebackground currents, especially the Kuroshio Current, were relatively
stable during the simulation (Fig. 2g–l), the 𝛥𝐶𝑃 , 𝛥C 𝑊 and 𝛥𝐶𝜃 wereslightly varied in Exp-TC.
Based on the above results, we can conclude that with the conditionof no background currents, typhoon Megi reduced the generation of the𝑀2 ITs at the LS by 4.5% (0.8 GW to 17.7 GW) and caused significant
temporal variation of the 𝑀2 conversion at the LS. Sensitivity analysis
shows that the bottom pressure perturbation dominated the magnitude
while the phase difference dominated the temporal variation of the𝑀2 conversion at LS under the influence of typhoon Megi. Whenbackground currents were taken into consideration, the influence of
typhoon Megi on the 𝑀2 conversion at the LS was reduced.
5.2. Baroclinic energy fluxes
Fig. 6 shows the daily 𝑀2 baroclinic energy fluxes from October 15
to 25 with an interval of 2 days in the four experiments. The 𝑀2 baroclinic energy fluxes under the horizontally homogeneous stratification(Exp-T and Exp-TW) showed an apparently different pattern from thoseunder the realistic stratification (Exp-TC and Exp-TCW). This difference
is reasonable, which is also found in previous studies (e.g. Kerry et al.,2014; Xu et al., 2016; Guo et al., 2020a; Cao et al., 2022). Comparing

5.3. Dissipation
After obtaining the 𝑀2 conversion and baroclinic energy fluxes,
the dissipation was easily calculated according to Eq. (1). We also
calculated the local dissipation efficiency (q), which is defined as theratio of the 𝑀2 dissipation to the 𝑀2 conversion at the LS (Alford
et al., 2011). Fig. 8 shows the daily 𝑀2 dissipation and local dissipation
6

A. Cao, Z. Guo, S. Wang et al.

Ocean Modelling 186 (2023) 102243

Fig. 6. Daily 𝑀2 baroclinic energy fluxes (magnitude: shading, unit: kW/m, direction: quivers) on October (a, g, m, s) 15, (b, h, n, t) 17, (c, i, o, u) 19, (d, j, p, v) 21, (e, k, q,w) 23 and (f, l, r, x) 25 in (a–f) Exp-T, (g–l) Exp-TW, (m–r) Exp-TC and (s–x) Exp-TCW. In each panel, the magenta curve denotes Megi’s track and the black dashed box indicatesthe LS.

efficiency in the four experiments. The dissipation in Exp-T remained
stable at 9.5 GW. In Exp-TW, the averaged dissipation was 9.4 GW,
which is comparable to that in Exp1, suggesting that typhoon Megi did
not significantly enhance the dissipation of the 𝑀2 ITs at the LS on the
average. However, typhoon Megi modulated the variation of the 𝑀2
dissipation, which reached the maximum (10.3 GW) on October 20 andthe minimum (8.8 GW) on October 21 and shared a similar trend as the𝑀2 conversion in Exp-TW (Fig. 5a). The 𝑀2 dissipation in Exp-TC wassignificantly elevated to 10.3–10.8 GW, with an average of 10.6 GW.
Because the background currents were relatively stable (Fig. 2g–l), the𝑀2 dissipation in Exp-TC did not show large variations. When both typhoon Megi and background currents were considered in Exp-TCW, the𝑀2 dissipation was further elevated to 10.4–11.6 GW, with an averageof 11.0 GW. Moreover, the 𝑀2 dissipation was highly correlated with
the 𝑀2 conversion in Exp-TW, of which the correlation coefficient is

0.92. However, the correlation coefficients between the 𝑀2 conversion
and dissipation in Exp-TC and Exp-TCW were significantly decreased,
which were 0.79 and 0.55, respectively.
Typhoon Megi and background currents had different influences on
the generation and dissipation of the 𝑀2 ITs at the LS (Figs. 5a and8a). However, it is interesting to find that both typhoon Megi andbackground currents enhanced the local dissipation efficiency of the𝑀2 ITs (Fig. 8b): The q was stable at 0.54 in Exp-T. In Exp-TW, ExpTC and Exp-TCW, the q showed temporal variations and the averaged
q was elevated to 0.56, 0.55 and 0.58, respectively. These values are
consistent with the recent estimations of q at the LS (e.g. Guo et al.,2020a; Xu et al., 2021).
Based on the aforementioned results, we can conclude that typhoon
Megi did not significantly change the averaged 𝑀2 dissipation at the7

A. Cao, Z. Guo, S. Wang et al.

Ocean Modelling 186 (2023) 102243

Fig. 7. Daily 𝑀2 baroclinic energy fluxes integrated at the (a) east, (b) west, (c) north and (d) south boundaries of the LS in the four experiments. Positive values denote that
the 𝑀2 ITs are radiated away from the LS.

Fig. 8. Daily 𝑀2 (a) dissipation and (b) local dissipation efficiency at the LS in the four experiments.

LS, but it caused temporal variation on it and enhanced the local dissipation efficiency. With background currents, typhoon Megi enhanced
both the 𝑀2 dissipation and local dissipation efficiency at the LS.

respectively. Note that the tracks of typhoons T1 and T2 are generally
similar to that of typhoon Megi before and after October 20, respectively, and the tracks of typhoons T3 and T4 are directly over the LS.
We can also find similar tracks of the four idealized typhoons from thepast typhoons in this region (Figure S3 in the supporting material). The
wind fields of the four idealized typhoons were prescribed following
Jelesnianski (1965):

6. Discussion
6.1. Influence of typhoon’s track
This study shows that typhoon Megi influenced the energetics of the𝑀2 ITs at the LS. However, the typhoons that passed over this region
had different tracks (Figure S3 in the supporting material). According toprevious studies, typhoon’s track has an important impact on the ocean
response (e.g. Pun et al., 2018; Zhang et al., 2023). Hence, typhoons
with different tracks may have different influences on the 𝑀2 ITs at theLS.
To clarify this point, we designed four idealized typhoons and analyzed the energetics of the 𝑀2 ITs under their influences individually.
As shown in Fig. 9, typhoons T1 and T3 moved westward along 17
and 20◦ N, and T2 and T4 moved northward along 118 and 121◦ E,

( ⇀
)
)
⎧
( )3 ( ⇀⇀⎪ 𝑟⃖⃗ + 𝑊𝑅 1 𝑟 2 𝐴 𝑖 + 𝐵 𝑗 ,
𝑉
𝑖
+
𝑉
𝑗
𝑦
𝑥
𝑟 𝑅
⎪ 𝑅+𝑟
𝑊 (𝑟) = ⎨( ⇀))( )1 ( ⇀
⇀
𝑅
1
𝑅 2
⎪
⃖
⃗
𝑉
𝑖
+
𝑉
𝑗
+
𝑊
𝐴
𝑖
+
𝐵
𝑗
,
𝑥
𝑦
𝑅𝑟
𝑟
⎪ 𝑅+𝑟
⎩
⇀

0<𝑟≤𝑅
,
𝑟>𝑅
(12)

⃗ is the wind speed vector, ⃗𝑖 and 𝑗⃖⃗ are zonal and meridional
where 𝑊
unit vectors, r is the distance from the typhoon center, R is the radius of
the maximum wind speed 𝑊𝑅 , 𝑉𝑥 and 𝑉𝑦 are the zonal and meridional
8

A. Cao, Z. Guo, S. Wang et al.

Ocean Modelling 186 (2023) 102243

Fig. 9. (a) Tracks of four idealized typhoons (T1–T4) and (b–j) the wind field (magnitude: shading, unit: m/s, direction: quivers) of idealized typhoon T1 from Day 15 to 23.
Typhoon Megi’s track is also shown in panel (a) as a comparison.

Fig. 10. Same as Fig. 5a but for the four idealized typhoons. The black dashed line denotes 17.7 GW.

translation speeds of typhoon center, and
{
[(
)
(
)
]
𝐴 = − 𝑥 − 𝑥𝑐 sin 𝜃 + 𝑦 − 𝑦𝑐 cos 𝜃
,
[(
)
(
)
]
𝐵 = 𝑥 − 𝑥𝑐 cos 𝜃 − 𝑦 − 𝑦𝑐 sin 𝜃

was 17.0, 17.3 and 16.8 GW, respectively; whereas the averaged 𝑀2
conversion at the LS under typhoon T4 was 17.7 GW, which is just thesame as that in Exp-T (Fig. 10). These results suggest that comparedwith the northward moving typhoons (T2 and T4), the 𝑀2 conversion
at the LS decreased more under the westward moving typhoons (T1 and
T3). For the two westward moving typhoons (T1 and T3), the peakof the 𝑀2 conversion mainly appeared before October 20 when thedomain was under the influence of the typhoons. However, for thetwo northward moving typhoons (T2 and T4), large 𝑀2 conversion
appeared after October 22 when the typhoons have left the domain.
These results explain the occurrence of the two peaks in the 𝑀2
conversion in Exp-TW and Exp-TCW (Fig. 5a), i.e. one peak was causedby the westward movement of typhoon Megi before October 20 and theother was related to the northward movement thereafter. Moreover,
the typhoons which passed over the LS (T3 and T4) caused larger peakvalues of the 𝑀2 conversion than those away from the LS (T1 and T2).
Because all the four typhoons left the study domain on October 21(Fig. 9), result of Fig. 10 again confirms that the influence of a typhoonon the 𝑀2 conversion at the LS could last for more than a week after
its passage.

(13)

where (x, y) and (𝑥𝑐 , 𝑦𝑐 ) are the coordinates of grid and typhoon center,
respectively, and{20◦ , 𝑟 ≤ 𝑅
𝜃=
.
(14)
15◦ , 𝑟 > 𝑅
For the four typhoons, 𝑊𝑅 = 50 m∕s and 𝑅 = 50 km, which kept
invariant during their passage. Moreover, the center of typhoon T1 (T3)
appeared at 130◦ E on October 14, moving westward with constant 𝑉𝑥 =−3 m/s until reaching 110◦ E. The center of typhoon T2 (T4) appeared
at 10◦ N on October 14, moving northward with constant 𝑉𝑦 = 3 m∕suntil reaching 30◦ N. These parameters are generally consistent withtyphoon Megi’s characteristics (e.g. Guan et al., 2014; Cao et al., 2018).
Thereafter, we repeated Exp-TW by using the four idealized typhoons
individually.
On the average, typhoons T1-T3 reduced the generation of the 𝑀2
ITs at the LS, under which the averaged 𝑀2 conversion at the LS
9A. Cao, Z. Guo, S. Wang et al.

Ocean Modelling 186 (2023) 102243

Fig. 11. Same as Fig. 6 but for the four idealized typhoons.

Analysis in Section 5.2 indicates that typhoon Megi did not significantly change the pattern of the 𝑀2 baroclinic energy fluxes but
modulated their magnitude. Similar results are found for idealized
typhoons T1 and T2 (Fig. 11a–l). But for typhoons T3 and T4 which
passed over the LS, the pattern of the 𝑀2 baroclinic energy fluxes was
remarkably changed (Fig. 11m–x), especially for typhoon T3. Before thecoming of all these typhoons, the 𝑀2 baroclinic energy fluxes shared
the same pattern (Fig. 11a, g, m, s), which is also the same as thosein Exp-T (Fig. 6a) and Exp-TW (Fig. 6g). However, when typhoon
T3 entered into the study domain, the pattern of the 𝑀2 baroclinic
energy fluxes changed (Fig. 11n). After October 19 (Fig. 11o), thepattern of the 𝑀2 baroclinic energy fluxes tended to be stable, withthe westward energy fluxes apparently weakened and the eastward
energy fluxes concentrated to the north of the typhoon track. Evenat 124◦ E, the eastward 𝑀2 baroclinic energy fluxes still exceeded 20
kW/m. This phenomenon was absent for typhoons T1, T2 and T4.
More importantly, this phenomenon could nearly last to the end of thesimulation, although typhoon T3 has left the domain on October 21.
As for typhoon T4, the variation of the pattern of the 𝑀2 baroclinic
energy fluxes mainly appeared between October 17 and 21 (Fig. 11t–v) when it passed over the LS from south to north, with both eastward
and westward 𝑀2 baroclinic energy fluxes decreased. After October 21,
the pattern of the 𝑀2 baroclinic energy fluxes (Fig. 11w–x) changed
back into that before the typhoon (Fig. 11s). These results indicatethat typhoons can influence both the magnitude and pattern of the 𝑀2
baroclinic energy fluxes near the LS, which are related to their tracks.
Like typhoon Megi, idealized typhoons T1 and T2 did not significantly change the 𝑀2 dissipation at the LS (9.6 and 9.4 GW) but slightly
elevated the local dissipation efficiency (0.56 and 0.55), compared to
Exp-T (Fig. 12). However, typhoon T3, which passed over the LS fromeast to west, elevated the averaged 𝑀2 dissipation and local dissipation
efficiency to 10.0 GW and 0.59, respectively. The instantaneous 𝑀2
dissipation and local dissipation efficiency under the influence of typhoon T3 could reach 14.6 GW and 0.75. For typhoon T4 which passed
10

A. Cao, Z. Guo, S. Wang et al.

Ocean Modelling 186 (2023) 102243

Fig. 12. Same as Fig. 8 but for the four idealized typhoons. The black dashed lines in panels (a) and (b) represent the dissipation of 9.5 GW and local dissipation efficiency of0.54, respectively.

over the LS from south to north, the averaged 𝑀2 dissipation and local
dissipation efficiency were 9.9 GW and 0.56, respectively. Comparedwith typhoons T1 and T2, the 𝑀2 dissipation under the influence of
typhoon T4 was elevated, whereas the local dissipation efficiency wasnot. These results indicate that both the distance between typhoon’s
track and the LS and the moving direction of the typhoon influence
the dissipation of the 𝑀2 ITs at the LS: The former contributes moreto the 𝑀2 dissipation, while both are important in the local dissipation
efficiency.
As discussed above, the typhoon that passes over the LS from east to
west (T3) causes the largest variation of the energetics of the 𝑀2 ITs.
Actually, this kind of typhoons has a high possibility of occurrence.
Among the 90 typhoons in the domain from 2011 to 2020 (Figure
S3 in the supporting material), 17 typhoons generally passed over theLS from east to west, yielding a possibility of approximately 19%.
Moreover, other typhoon characteristics, such as the maximum windspeed, the radius of the maximum wind speed and the translation
speed, may also have influences on the energetics of ITs at the LS, which
are not explored in this study.

in which
√
𝑁=

𝑔 d𝜌
,
𝜌 d𝑧

(18)

is the buoyancy frequency and g is the acceleration due to gravity.
According to Eq. (17), it is easy to know that when low-frequency
currents (𝐮) and corresponding stratification (𝜌 and N ) vary, the density perturbation would change accordingly. The variation of density
perturbation further changes the pressure perturbation (Eq. (3)) andfinally influences the conversion rate and baroclinic energy fluxes(Eqs. (5)–(7)). Introducing Eq. (16) into the momentum equationd𝐮
1+ 𝐟 × 𝐮 = − ∇𝑝,
d𝑡
𝜌

(19)

we can obtain the equation for the tidal motion following Kelly andLermusiaux (2016)
)
(
)
𝜕𝐮′ (
1
+ 𝐮 ⋅ ∇ 𝐮′ + 𝐮′ ⋅ ∇ 𝐮 + 𝐟 × 𝐮′ = − ∇𝑝′ .
(20)
𝜕𝑡
𝜌
Note that Eq. (20) is valid whether the stratification exists or not.
Hence, when the stratification is not taken into consideration, Eq. (20)is the equation for barotropic tidal velocity u′ . From this equation, we
can find that the barotropic tidal velocity is modulated by the lowfrequency currents via the nonlinear terms in Eq. (20). The variationof barotropic tidal velocity further influences the conversion rate according to Eqs. (4)–(5). Fig. 13 shows the amplitudes and phases ofbottom pressure perturbation and barotropic vertical velocity at the LS
on October 21 in Exp-T and Exp-TW as an example. It is easy to findthat the low-frequency currents and stratification variation induced bytyphoon Megi in Exp-TW indeed cause variations of bottom pressure
perturbation and barotropic vertical velocity at the LS.
The influences of background currents and typhoons on the ITs
are a little different. The background currents, especially the Kuroshio
Current, are large-scale slowly-varied process, while the typhoons areintermittent weather process. Hence, the long-term variation of theenergetics of ITs at the LS is mainly related to the background currents(Kerry et al., 2014; Xu et al., 2021), and typhoons mainly accountfor the short-term fluctuations (Figs. 5–8, 10–12). In addition, because
the incoherent ITs are characterized by high temporal variability, theshort-term fluctuations in the energetics of ITs caused by the frequent
typhoons near the LS may be an important cause of the incoherent ITs
in this region (e.g. Xu et al., 2014; Pickering et al., 2015; Cao et al.,2017).

6.2. Mechanism
Previous studies have revealed the mechanism through which background currents (as well as the corresponding stratification) affect thegeneration, propagation and dissipation of ITs at the LS (Jan et al.,2012; Kerry et al., 2014; Xu et al., 2021; Zhao and Qiu, 2023). We
believe that typhoons influence the energetics of ITs at the LS throughthe same mechanism, because they also cause low-frequency currents
and stratification variation in the ocean (Figs. 2 and 3). Consider asimple case only containing low-frequency currents and ITs and thedensity equation for the motion is
d𝜌
= 0,
(15)
d𝑡
in which 𝜌 is the density and t is the time. Decomposing the velocity[u=(u, v, w)], pressure (p) and density into two parts with one corresponding to the low-frequency currents (marked by overbar) and theother corresponding to the ITs (marked by prime):𝐮 = 𝐮 (𝑥, 𝑦, 𝑧, 𝑡) + 𝐮′ (𝑥, 𝑦, 𝑧, 𝑡) , 𝑝 = 𝑝 (𝑥, 𝑦, 𝑧, 𝑡) + 𝑝′ (𝑥, 𝑦, 𝑧, 𝑡) ,
𝜌 = 𝜌 (𝑥, 𝑦, 𝑧, 𝑡) + 𝜌′ (𝑥, 𝑦, 𝑧, 𝑡) ,

−

(16)

and introducing them into Eq. (15), it is easy to obtain the equation ofdensity perturbation for ITs:

7. Summary𝜕𝜌′+ 𝐮 ⋅ ∇𝜌′ + 𝐮′ ⋅ ∇𝜌 + 𝑁 2 𝑤′ = 0,
𝜕𝑡Based on a series of numerical simulations, this study investigates
the energetics of the 𝑀2 ITs at the LS modulated by typhoons. Typhoon

(17)
11

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Ocean Modelling 186 (2023) 102243

Fig. 13. Amplitudes (shading, unit: Pa for pressure and m/s for velocity) and phases (shading, unit: ◦ ) of bottom pressure perturbation and vertical barotropic velocity at the LS
on October 21 in Exp-T and Exp-TW. The differences between Exp-T and Exp-TW are also shown.

influence the dissipation of the 𝑀2 ITs at the LS: The former contributes
more to the 𝑀2 dissipation, while both are important in the local
dissipation efficiency.

Megi in 2010 is chosen as the real case, and four idealized typhoons aredesigned to explore the influence of typhoon’s track on the M2 ITs. The
main conclusions of this study are displayed as follows.
(a) With the condition of no background currents, typhoon Megi
caused significant temporal variations in the 𝑀2 conversion at the LS
and decreased the averaged 𝑀2 conversion by 4.5% (0.8 GW to 17.7
GW). Sensitivity analysis indicates that the bottom pressure perturbation dominated the magnitude while the phase difference between
the pressure perturbation and vertical barotropic velocity dominatedthe temporal variation of the 𝑀2 conversion during this process. The
westward movement of Megi before October 20 and the northward
movement thereafter accounted for the two peaks of the 𝑀2 conversion
on October 20 and 24, respectively. Typhoon Megi also reduced thewestward 𝑀2 baroclinic energy fluxes into the South China Sea by
14.3% (0.6 GW to 4.2 GW), but it did not significantly change their pattern. Typhoon Megi elevated the averaged local dissipation efficiency
from 0.54 to 0.56, but it did not significantly change the averaged 𝑀2
dissipation at the LS. Moreover, the influence of typhoon Megi on theenergetics of the 𝑀2 ITs at the LS could last for at least one week after
its passage.
(b) When background currents were taken into consideration, theinfluence of typhoon Megi on the 𝑀2 conversion and baroclinic energy
fluxes was weakened, but the influence on the 𝑀2 dissipation wasenhanced. To be specific, the reduction of the 𝑀2 conversion at the
LS induced by typhoon Megi was decreased from 0.8 GW to 0.2 GW.
The reduction of the westward 𝑀2 baroclinic energy fluxes induced bytyphoon Megi was decreased from 0.6 GW to 0.3 GW. With backgroundcurrents, typhoon Megi elevated the averaged 𝑀2 dissipation at the LSfrom 10.6 GW to 11.0 GW and the averaged local dissipation efficiency
from 0.55 to 0.58.
(c) Typhoons with different tracks have different influences on theenergetics of the 𝑀2 ITs at the LS. Generally, the typhoons that passover the LS cause greater variations of the 𝑀2 conversion, baroclinic
energy fluxes and dissipation than those away from the LS. Comparedwith the northward moving typhoons, the 𝑀2 conversion at the LS
decreases more under the westward moving typhoons. For westward
moving typhoons, the peak of the 𝑀2 conversion appears when they
are still in the domain; whereas for northward moving typhoons, large
𝑀2 conversion appears after they leave the domain. The typhoons
that pass over the LS modulate both the magnitude and pattern of
the 𝑀2 baroclinic energy fluxes, whereas those away from the LS
mainly influence the magnitude. In addition, both the distance between
typhoon’s track and the LS and the moving direction of the typhoon

CRediT authorship contribution statement
Anzhou Cao: Conceptualization, Methodology, Formal analysis,
Funding acquisition, Writing – original draft, Writing – review & editing. Zheng Guo: Methodology, Formal analysis, Writing – originaldraft, Writing – review & editing. Shuya Wang: Methodology, Formal
analysis, Writing – original draft, Writing – review & editing. Xu Chen:
Supervision, Writing – review & editing. Jinbao Song: Supervision,
Writing – review & editing. Xinyu Guo: Supervision, Writing – review& editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared toinfluence the work reported in this paper.
Data availability
The CROCO code and tidal forcing data are available at www.
crocoocean.org. The HYCOM data and CFSR surface forcing data are
available at apdrc.soest.hawaii.edu/data/data.php.
Acknowledgments
This study is supported by the National Natural Science Foundationof China (Grant number: 42176002), the National Key Research andDevelopment Program of China (Grant number: 2021YFC3101603),
and the China Scholarship Council (Grant number: 202006325025).
Appendix A. Supplementary data
Supplementary material related to this article can be found online
at https://doi.org/10.1016/j.ocemod.2023.102243.
12

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Ocean Modelling 186 (2023) 102243

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