Submesoscale Ageostrophic Motions Within and Below the Mixed Layer of the Northwestern Pacific Ocean

Abstract

Submesoscale dynamics below the mixed layer (ML) and their mechanisms are still unclear. By a series of nested simulations in the Pacific Northwest with high horizontal resolution of ∼500 m, this study reveals that there exist strong submesoscale ageostrophic motions in the upper pycnocline of the Kuroshio Extension region. These motions exhibit enhanced lateral buoyancy gradient and vigorous vertical velocity but with weak vertical vorticity distinct from the ML submesoscale activities. The vertical velocity in the high‐resolution simulation reaches tens of meters per day, consistent with recent observations (e.g., SubMESI and OSMOSIS). Our analysis shows that the enhanced vertical velocity is mostly attributed to the along‐isopycnal motions at the Kuroshio front, but in the region nearby the large vertical velocity mostly arises from the wave‐like vertical movement of isopycnals. To understand the mechanisms for the large vertical velocity, this paper further examined the instability of the flow and the frequency‐wavenumber spectra of vertical vorticity, lateral divergence, lateral buoyancy gradient, and vertical velocity. A criterion based on the ratio between divergence and vorticity variance in spectral space is used to roughly identify the upper bound of unbalanced submesoscales. The results suggest that the high‐frequency, high‐wavenumber processes dominate the vertical motions within and below the ML and significantly enhance the net vertical heat transport between the ML and the ocean interior. This study seeks to provide comprehension of the submesoscale ageostrophic motions below the ML and their impacts on the upper ocean.

Full text

1. Introduction
The oceanic flow is known to be highly turbulent and consists of motions on a wide range of scales. With the
great success in satellite altimetry, geostrophic eddies with horizontal scales of a few hundred kilometers can
be routinely observed (Chelton etal., 2007; Fu etal., 2010). The mesoscale features and their impacts on the
transport of oceanic tracers have been well studied in the past decades (e.g., Chelton etal., 2011; Ferrari &
Wunsch,2009; Qiu & Chen,2013; Xu etal., 2016; Zhang etal.,2014). Recently, the physics of submesoscale
turbulence has attracted great attention as it is not well understood due to the difficulty and challenge in observ-
ing submesoscale dynamics (McWilliams, 2016). Recent literature has reported that submesoscale processes
play a crucial role in the forward energy transfer from the geostrophic scale toward dissipation (e.g., Cao
etal.,2021; Capet etal.,2008a; D’Asaro etal.,2011; Jing etal.,2021; Kaneko etal.,2013; Lazaneo etal.,2020;
McWilliams,2016; Thomas etal.,2008; Wang etal.,2018; Zhang etal.,2016) and highlighted their importance
to the vertical transport of heat, salt, and nutrients, which ultimately is important for biological dynamics (e.g.,
Lévy etal.,2012,2001; Mahadevan & Tandon,2006; Rosso etal.,2014; Siegelman etal.,2020; Su etal.,2018).
Abstract Submesoscale dynamics below the mixed layer (ML) and their mechanisms are still unclear. By
a series of nested simulations in the Pacific Northwest with high horizontal resolution of ∼500m, this study
reveals that there exist strong submesoscale ageostrophic motions in the upper pycnocline of the Kuroshio
Extension region. These motions exhibit enhanced lateral buoyancy gradient and vigorous vertical velocity but
with weak vertical vorticity distinct from the ML submesoscale activities. The vertical velocity in the high-
resolution simulation reaches tens of meters per day, consistent with recent observations (e.g., SubMESI and
OSMOSIS). Our analysis shows that the enhanced vertical velocity is mostly attributed to the along-isopycnal
motions at the Kuroshio front, but in the region nearby the large vertical velocity mostly arises from the
wave-like vertical movement of isopycnals. To understand the mechanisms for the large vertical velocity, this
paper further examined the instability of the flow and the frequency-wavenumber spectra of vertical vorticity,
lateral divergence, lateral buoyancy gradient, and vertical velocity. A criterion based on the ratio between
divergence and vorticity variance in spectral space is used to roughly identify the upper bound of unbalanced
submesoscales. The results suggest that the high-frequency, high-wavenumber processes dominate the vertical
motions within and below the ML and significantly enhance the net vertical heat transport between the ML and
the ocean interior. This study seeks to provide comprehension of the submesoscale ageostrophic motions below
the ML and their impacts on the upper ocean.
Plain Language Summary The ocean is usually known as a dynamical system of geostrophic
turbulence. This study uses a high-resolution (∼500m) numerical simulation to investigate the geostrophically
unbalanced motions with horizontal length scales of a few kilometers (submesoscales) in the upper ocean of the
northwestern Pacific. The results show active submesoscale processes (e.g., submesoscale fronts and eddies) at
the surface and even below the mixed layer (ML), which have distinct dynamical features from large-scale or
mesoscale flows. Although these motions are not the primary energy reservoir, they play a significant role in
the energy transfer between scales and can drive much stronger vertical motions than large-scale and mesoscale
processes within and below the ML. This is consistent with the recent observations in the other regional oceans.
Importantly, our results suggest that these motions can drive a significant net heat transport between the ML
and the ocean interior at horizontal length scales much smaller than the baroclinic Rossby deformation radius.
CAO AND JING
© 2022. American Geophysical Union.
All Rights Reserved.
Submesoscale Ageostrophic Motions Within and Below the
Mixed Layer of the Northwestern Pacific Ocean
Haijin Cao1,2 and Zhiyou Jing3
1Key Laboratory of Marine Hazards Forecasting, Ministry of Natural Resources, Hohai University, Nanjing, China, 2College
of Oceanography, Hohai University, Nanjing, China, 3State Key Laboratory of Tropical Oceanography, South China Sea
Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China
Key Points:
• The submesoscale motions below
the mixed layer (ML) show different
features from the mixed-layer
submesoscale processes
• The mechanisms for the enhanced
vertical velocity rely on along-
isopycnal motions and internal waves
• The high-frequency, high-wavenumber
processes dominate the net vertical
heat transport between the ML and the
ocean interior
Supporting Information:
Supporting Information may be found in
the online version of this article.
Correspondence to:
Z. Jing,
jingzhiyou@scsio.ac.cn
Citation:
Cao, H., & Jing, Z. (2022). Submesoscale
ageostrophic motions within and below
the mixed layer of the northwestern
Pacific Ocean. Journal of Geophysical
Research: Oceans, 127, e2021JC017812.
https://doi.org/10.1029/2021JC017812
Received 21 JUL 2021
Accepted 1 FEB 2022
10.1029/2021JC017812
RESEARCH ARTICLE
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Submesoscale flows are characterized by the O(1) Rossby number,
Ro =∕
, and Froude number,
Fr =∕𝑁
.

is the relative vorticity, f is Coriolis frequency, V is a characteristic velocity with a horizontal length scale of
L, N is the buoyancy frequency, and h is the vertical length scale (McWilliams,2016). Physically, submesoscale
processes differ from geostrophic flows by the intensification of ageostrophic motions but are still influenced by
Earth rotation, manifested by the submesoscale horizontal buoyancy gradient, divergence/convergence, straining,
and large vertical vorticity (Capet etal.,2016; Shcherbina etal.,2013).
In the open ocean, it is difficult to capture intermittent and fast-evolving submesoscales through traditional
cruise surveys (McWilliams,2016; Shcherbina et al., 2013). Although surface submesoscale eddies or fronts
are frequently detected from high-resolution remote sensing images (e.g., Liu etal.,2015; Yu etal.,2018; Zeng
etal.,2014; Zheng,2017), the dynamical link between the surface and the oceanic interior is much more complex
for submesoscale flows than larger-scale geostrophic flows. It is a great challenge to reconstruct the submesoscale
features in the ocean interior based on the sea surface height (Qiu etal.,2016,2020). Instead, high-resolution
numerical simulations, together with satellite data, have been widely used to reproduce the submesoscale phys-
ics (e.g., Balwada etal., 2018; Capet etal., 2008b; Gula etal.,2014; Klein etal.,2008; Lapeyre etal.,2006;
Qiu et al., 2014; Rocha etal.,2016) and to explore their generating mechanisms (Fox-Kemper etal.,2008;
McWilliams,2017; McWilliams etal.,2015; Srinivasan etal.,2019).
Previous studies focus mainly on submesoscale processes within the mixed layer (ML). However, recent stud-
ies suggest that the ocean interior is not always in quasi-geostrophic balance with small Rossby number, but
with enhanced vertical motions at submesoscales (Siegelman etal.,2020; Yu etal.,2019a; Zhang etal.,2021).
Case studies investigated the ageostrophic dynamics during restratification (Johnson etal.,2020a,2020b). These
motions are particularly energetic in strong frontal systems (e.g., the Kuroshio front) and can drive considera-
ble vertical flux in the ocean interior. However, to date, their dynamical mechanisms remain unclear. Based on
a series of nested simulations in the eddy-rich northwestern Pacific, this study investigates the submesoscale
features, with a focus on the geostrophically unbalanced scales (high-frequency, high-wavenumber), highlighting
their significant contribution to vertical velocity within and below the ML. Here, submesoscale ageostrophic
motions refer to the motions that can drive large vertical velocity at high frequencies and high wavenumbers (e.g.,
larger than the Coriolis frequency f and the wavenumber of 1×10
−4cpm). The outline of this paper is as follows.
The next section briefly describes the simulations. Section3 compares the submesoscale characteristics (relative
vorticity, divergence, buoyancy gradient, strain field, and vertical velocity) of the simulations at low, middle,
and high resolution (referred to as LR, MR, and HR). In this section, the dynamical regimes of the large vertical
velocity are investigated in detail. Section4 further investigates the scale range of ageostrophic motions and the
dynamical mechanisms for the large vertical velocity. Finally, the results are summarized in Section5.
2. Model Description
A nested simulation suite in the northwestern Pacific was conducted using the Regional Oceanic Modeling
System (ROMS; Shchepetkin & McWilliams,2005). Three-layer offline nesting was applied from a coarse hori-
zontal resolution of ∼7.5km to the intermediate resolution of ∼1.5km and finally to the highest resolution of
∼0.5km (Figure1). The ∼7.5-km simulation covers a large domain from 10°S to 45°N and from 95°E to 170°E
with a 20-year spin-up to reach a statistically steady state before starting the one-way nesting simulations. The
next simulation in the nesting hierarchy (∼1.5km) extends from 28°N to 43.5°N and from 138°E to 162°E and
ran for a whole year to provide boundary and initial conditions for the higher resolution simulation. The final
∼0.5-km simulation is run in a smaller domain: 30°–40°N, 142°–155°E for 6weeks (after 4-week spin-up, the
2-hourly outputs of last 2weeks from April 28 to May 12). Since the resolved submesoscale structures are statis-
tically quasi-steady, we select snapshots at some time instants to focus the analysis. Each of the simulations (LR,
MR, and HR) is run on a curvilinear, latitude-longitude grid, and terrain-following S-coordinates of 60 vertical
levels. The vertical layers are refined with 24 layers over the upper 200m.
The boundary conditions and initial state for the LR simulation are provided by the monthly averaged Simple
Ocean Data Assimilation (SODA) ocean climatology data (Carton & Giese,2008). The surface atmospheric forc-
ing such as wind stress, heat, and freshwater fluxes is provided by the Quick Scatterometer (QuikSCAT) data set
and the International Comprehensive Ocean Atmosphere Data Set (ICOADS; Woodruff etal.,2011). The K-pro-
file parameterization (KPP) is used for the subgrid vertical mixing of momentum and tracers (Large etal.,1994).

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Note that we used the climatological daily wind forcing and did not include tidal forcing in the simulations. The
simulations on regional circulation, ML depth, sea surface temperature, and kinetic energy have been validated
against satellite measurements and available in situ observations (see the Supporting Information file and model
description of Luo etal.(2020), Huang etal.(2020), and Cao etal.(2021). The comparison with the measure-
ments shows that the simulations have reached a steady state after 20-year spin-up and are sufficiently accurate
to characterize the climatological Pacific conditions and delineate local submesoscale features. In the HR simu-
lation, the computational domain shows a shallow ML depth of about 35m using the criteria of a density differ-
ence of 0.03kgm
−3 from the surface layer, consistent with some observations (de Boyer Montégut etal.,2004;
Kara etal., 2003). As such, the simulated period in this study exhibits less active submesoscales compared to
the wintertime (Sasaki etal.,2014). The output shows a robust set of statistics of submesoscale characteristics,
so the randomly selected snapshot can nearly represent the submesoscale features within a narrow time window.
3. Submesoscale Features
3.1. Comparison of Submesoscale Characteristics (LR, MR, and HR)
The submesoscale features in the LR, MR, and HR simulations are compared at depths of z=−10 m, −50m,
and −200m, representing the upper ML, the base of the ML, and the pycnocline, respectively. A comparison
of kinetic energy from different simulations suggests differential meandering shapes (Figure S1 in Supporting
InformationS1), as some of the subgrid processes are parameterized in the LR and MR simulation but resolved
in the HR simulation. The submesoscale eddies can modify the large-scale and mesoscale flows by inverse kinetic
energy cascade (Schubert etal.,2020).
Figure 1. (a) The model surface temperature in domains of the nested models at horizontal resolutions of ∼7.5km (low resolution (LR)), ∼1.5km (middle resolution
(MR)), and ∼0.5km (high resolution (HR)), respectively. The dashed-line box denotes a subregion for the analysis of vertical velocity in Section3.4. (b) Snapshot of
simulated upper-ocean temperature field at HR.

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The O(1) Ro (
∕
) is generally used to characterize submesoscale flows (Bachman etal.,2017; Gula etal.,2014;
Thomas etal.,2008). As shown in Figure2 (a snapshot at a randomly selected time, 10:00 on 30 April), all the
vorticity fields show a horizontally elongated line pattern with large positive/negative values of relative vorticity
along the Kuroshio jet, which is a sign of sharp frontogenetic buoyancy fronts (Hoskins & Bretherton,1972;
McWilliams, 2016). The HR simulation with the highest horizontal resolution compared to the LR and MR
simulations shows a denser population of eddies at the three depths (the right column compared to the left and
middle columns in Figure2). A comparison of the snapshots for different depths (i.e., Figure2, right column)
shows a clearly weaker vorticity field at the 200-m depth than at the 10-m and 50-m depths. The 200-m depth is
mostly below the ML throughout the year. Those small eddies certainly have limited vertical scales and cannot
extend to depth (D'addezio etal.,2020; Liu etal.,2020)—submesoscale eddies are mostly contained in the ML
(Figure 2, right column). This also restrains the development of submesoscale eddies to be local (Boccaletti
etal.,2007; Fox-Kemper etal.,2008). Similar to the vertical vorticity, horizontal divergence,

=

+

, and
Figure 2. Snapshots of relative vorticity normalized by

at different depths (z=−10m, −50m, and −200m) from different simulations (LR, MR, and HR) at a
randomly selected time, 10:00 on 30 April. LR is short for low resolution (left column), MR is short for middle resolution (middle column), and HR is short for high
resolution (right column).

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strain rate,

=
√
(−)2+(+)
2
, are also largely intensified with smaller scales in the HR simulation
than in the MR and LR simulation, which is indicative of the development of ageostrophic motions (Figures S2
and S3 in Supporting Information S1). As shown in Figure S4 in Supporting InformationS1, the divergence
is closely related to the strain-induced frontogenesis (Barkan etal.,2019). Although the strain is reduced with
depth, it remains strong near the Kuroshio jet and can drive ageostrophic motions, suggesting the generation of
ageostrophic motions below the ML.
Figure3 shows the magnitude of lateral buoyancy gradient (
|∇|
), where
=(1−∕0)
is the buoyancy, with
g the gravitational acceleration,

the potential density, and

0
a reference density of 1,025kgm
−3. Compared
with the LR and MR simulation, the HR simulation displays more active fronts at smaller scales. Stronger
submesoscale buoyancy gradients appear more frequently on the north side of the Kuroshio jet (right column
of Figure3). In the ML with weak stratification, the strain-induced frontogenesis can drive sharp density fronts
Figure 3. Snapshots of lateral buoyancy gradient at different depths (z=−10m, −50m, and −200m) from different simulations (LR, MR, and HR) at a randomly
selected time, 10:00 on 30 April. LR is short for low resolution (left column), MR is short for middle resolution (middle column), and HR is short for high resolution
(right column).

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(McWilliams,2016; Thomas etal.,2008). Meanwhile, a part of the fronts/filaments can transform into submesos-
cale eddies through ML baroclinic instabilities (Boccaletti etal.,2007; Fox-Kemper etal.,2008). All of these
submesoscale features can result in large

,

, and

at the 10-m depth. Notice that the submesoscale fronts
captured by sheared flows at z=−50m remain energetic. There still exist strong submesoscale density fronts
well below the ML (e.g., z=−200m). The consequence for the submesoscale fronts is discussed in the following
sections.
3.2. Statistics of Vorticity, Divergence, Strain Rate, and Buoyancy Gradient
This section evaluates the statistics of vertical vorticity, lateral divergence, strain rate, and lateral buoyancy gradi-
ent for different simulations at z= −10 m and for different depth levels from the HR simulation (Figure4).
The probability density functions (PDFs) calculated from the HR domain show that higher horizontal resolu-
tion presents greater submesoscale characteristics. Table1 lists the mean, skewness, and standard deviation of
the vorticity, divergence, and strain rate for the simulations. The HR compared to the MR and LR simulations
presents larger skewness for all quantities (Figure4, upper row), as more submesoscale cyclones are resolved
with higher horizontal resolution. Strong anticyclones are rarely seen because the flow is centrifugally unstable
when
∕

is smaller than −1. The distribution of relative vorticity,
∕

, from the HR simulation is markedly
Figure 4. Probability of density function (PDF) of (a, e) normalized vertical vorticity, (b, f) lateral divergence, (c, g) lateral strain rate, and (d, h) buoyancy gradient for
three simulations (upper row, z=−10m) and for three depth levels (bottom row, the high resolution (HR) simulation), respectively.
∕
∕
∕
Mean Sk ew. St. d. Mean Sk ew. St. d. Mean Skew St. d.
LR 0.000 0.650 0.250 −0.001 −0.167 0.087 0.204 1.691 0.160
MR −0.001 2.952 0.437 0.002 −1.951 0.122 0.312 5.527 0.327
HR −0.005 3.988 0.606 −0.002 −1.522 0.187 0.436 7.021 0.460
Table 1
The Mean, Skewness (Skew.), and Standard Deviation (St. d.) of
∕

,
∕
, and
∕

for the Simulations (z=−10m)

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asymmetric with a large positive skewness of 3.988 and a standard deviation of 0.606, which decreases to 2.952
and 0.437 in the MR simulation, and to 0.650 and 0.250 at the 200-m depth, respectively (Table1).
Table2 compares the mean value, skewness, and standard deviation of the variables for the three depth levels,
where the statistical estimations are based on the HR simulation (Figure4, bottom row). The
∕
ranges from
−1 to 2, −0.8 to 1.2, and −0.8 to 0.9 at z=−10m, −50m, and −200m, respectively. Vertically, the
∕
is more
skewed at the surface compared to the greater depths (skewness of 2.679, 1.904, and 0.932 at the depths of 10, 50,
and 200m, respectively) and shows decreasing standard deviation (0.537, 0.417, and 0.275 for the three depths).
They agree with the result shown in Figure2 that there are more submesoscale eddies in the ML than below
and large vorticity values tend to be cyclonic (the positive tail with
∕
> 1), consistent with the observations
(Rudnick,2001; Shcherbina etal.,2013). Below the ML, the vorticity distribution becomes more Gaussian-like
in the absence of topography. The distributions of lateral divergence are fairly symmetric at all depths and become
less skewed with increasing depth. The PDF of the strain rate is more narrowly distributed, with continuously
decreasing peak modes from
∕=0.175
at z=−10m to
∕=0.1
at z=−200m. Statistically, high values
of
|∇|
greater than 1×10
−7s
−2 appear more frequently at z= −50m compared to z= −10m and −200m
(Figure4h) because of the variation of the ML base. Distinct from the other parameters analyzed here,
|∇|
is
not monotonically decreasing with depth. Similar results were also reported in observation-based studies (e.g.,
Thompson etal.,2016).
3.3. Wavenumber Spectrum of Vorticity, Divergence, Strain Rate, and Buoyancy Gradient
The wavenumber spectrum analysis is an effective approach to identify the features of submesoscales as functions
of scales. Dynamically, the divergent KE is primarily attributed to unbalanced motions including both ageo-
strophic motions and internal gravity waves (hereafter referred to as IGW), while the spectrum of vertical vortic-
ity indicates the enstrophy, known as the geostrophically balanced part of KE. Here, “ageostrophic” motions refer
to the unbalanced part of submesoscale processes. The partition between balanced and unbalanced motions is
illustrated in the theoretical decomposition (Helmholtz decomposition), whereby the KE is decomposed into the
rotational and divergent components (Bühler etal.,2014; Torres etal.,2018) as follows:
=r+d=−+,=r+d=+,
(1)
where

r
is the rotational component and

d
is the divergent component of

,

r
is the rotational component and

d
is the divergent component of

,

is the stream function, and

is the potential. Then, the Laplacian of stream
function and potential is
Δ=−,Δ=+
(2)
Thereby, in the spectral space, the power spectrum of normalized squared vertical vorticity (
RV =2∕2
) can
be regarded as the vortex contribution to KE (
RV
()= 
2

2KEv(
)
, in which k is the wavenumber and
KEv()
is
the vortex component of KE spectrum). The transformation of the isotropic 2D to 1D spectrum can be found in
the Appendix of Cao etal.(2019). Thus, a k
−1 vorticity spectrum corresponds to a k
−3 KE spectrum (geostrophic
prediction). Similarly, the spectrum of lateral divergence (
DIV =2∕2
) signifies the divergent component of
KE (
DIV
()= 
2

2KED(
)
).
Figure5 compares the spectra from different simulations but within the same spatial domain of the HR simulation
(z=−10m for the left column). The HR simulation shows a flattened vorticity spectrum (a slope of ∼−0.5) at
∕
∕
∕
Mean Sk ew. St. d. Mean Sk ew. St. d. Mean Sk ew. St. d.
10m 0.001 2.679 0.537 0.001 −1.041 0.137 0.290 5.172 0.282
50m 0.002 1.904 0.417 0.000 −0.081 0.111 0.215 3.532 0.162
200m 0.002 0.932 0.275 0.000 −0.020 0.091 0.134 3.022 0.103
Table 2
The Mean, Skewness (Skew.), and Standard Deviation (St. d.) of
∕
,
∕
, and
∕
for Different Depth Levels (HR
Simulation)

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high wavenumbers, indicative of submesoscale flows. The slope of the vorticity spectrum indicates the strength
of submesoscale processes (Figure5; right column). The vorticity spectrum for the 10-m depth is flattened to
k
−0.5 at the submesoscale, whereas the spectral slopes are approximately at −1 for the 50-m and 200-m depths,
indicative of geostrophic turbulence (Figure5e). This suggests that submesoscale eddies are mostly generated
in the ML and have limited vertical scales. Interestingly, the LR divergence spectrum shows the highest peak
near 50km (geostrophic divergence) compared to the MR and HR spectra (Figure5b). It suggests that the diver-
gence is redistributed over scales when submesoscales are resolved. Essentially, the generation of submesoscale
horizontal divergence is dynamically complicated, e.g., in turbulent thermal wind balance (Barkan etal.,2019).
Besides, the spectra of horizontal divergence peak at the submesoscale for all the depths (Figure5f), demonstrat-
ing an enhancement of unbalanced motions arising from submesoscale divergence/convergence. The subpeaks
of divergence spectra at the mesoscale indicate the scale of geostrophic divergence. The lateral strain rate is also
reduced at the 50-m and 200-m depths (Figure5g). The spectra of buoyancy gradient at depths (z=−50m and
Figure 5. Wavenumber spectra of (a, e) normalized vertical vorticity, (b, f) lateral divergence, (c, g) lateral strain rate, and (d,
h) horizontal buoyancy gradient for three simulations (left column, at z=−10m) and for three depth levels (right column, the
high resolution (HR) simulation), respectively. PSD is short for power spectrum density.

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z= −200m) are as energetic as that at 10-m depth until 10
−5cpm (100 km) and become less energetic at the
submesoscale (Figure5h). Note that all the spectra experience a dramatic roll-off near the Nyquist wavenumber
(0.075×10
−3, 0.322×10
−3, and 1×10
−3cpm for each simulation respectively), which is a numerical artifact.
3.4. Vertical Velocity and Vertical Heat Flux
Vertical velocity (w) associated with submesoscale flow fields is typically larger than that of the mesoscale fields
(Calil & Richards,2010; Lévy etal.,2012; Mahadevan & Tandon,2006; McWilliams,2016). A comparison of
the vertical velocity between the simulations shows enhanced instantaneous w in the HR simulation, suggesting
that the horizontal resolution is a sensitive parameter for the reproduction of vertical motions driven by ageo-
strophic processes with smaller length scales (Figure6). Here, we zoom into a subregion marked by the dash-line
box in Figure1 for removal of bottom effects like seamounts. Differing from the vertical vorticity or horizontal
divergence, w shows larger amplitude at the 200-m depth instead of at the shallower depths. The w at 10-m
depth concentrates on the filamentary structures that are elongated by the strain along the jet; while the w at the
200-m depth shows larger amplitude and spreads over a wider extent. Some regions of the w exhibit small-scale
crisscross structures which are indicative of internal waves. This implies that the large w could partly result from
the spontaneous emission of inertial gravity waves near the Kuroshio front (Danioux etal.,2012; Plougonven &
Figure 6. Snapshots of vertical velocity at different depth levels (z=−10m, −50m, and −200m) from different simulations (low resolution (LR), middle resolution
(MR), and high resolution (HR)) at 10:00 on 30 April.

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Snyder,2007). While the strong stratification below the ML tends to suppress the growth of submesoscale insta-
bilities but indeed supports the propagation of internal waves.
Unlike the large vertical velocity in the ML which has been shown to be related to submesoscale dynamics such
as ML instabilities and frontogenesis (Fox-Kemper etal.,2008; McWilliams etal.,2017), the mechanism lead-
ing to the large w in the pycnocline of the Kuroshio front is not yet identified. The large w is likely associated
with either internal waves or motions along isopycnals (Klymak etal., 2016). Symmetric instability may also
partly contribute to the vertical motions (Thomas etal.,2013). To better understand the vertical velocity in the
pycnocline, Figure7 shows the 3D snapshots of vertical vorticity, vertical velocity, and temperature field on the
density surface of σθ=25.8. In this way, we can clearly identify the location of the density front and its sharpness.
More importantly, the temperature variances on the isopycnal are also visualized (Figure7b), as an indication
of along-isopycnal motions. The vorticity filed on the σθ=25.8 isopycnal, which extends from near-surface to
Figure 7. (a) Vertical vorticity, (b) temperature, and (c) vertical velocity on the density surface σθ=25.8 for the subregion. (d) Vertical velocity w, (e) the estimated
wiso, and (f) the estimated ratio wiso/w based on the scaling method of Freilich and Mahadevan(2019) at 200-m depth. In (e) and (f), the locations where the scaling
relationship is negative because of the negative buoyancy frequency (N
2) are blanked.

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500-m depth, exhibits a few eddy-like and filamentary structures (Figure 7a). Figure7c shows strong vertical
velocity with small length scales, especially at the sloping front. Note that the interpolation of vertical velocity
to the density surface may not be accurate because of the limited vertical layers of the model output especially at
depth. Additionally, the method presented by Freilich and Mahadevan(2019) is employed to decompose the verti-
cal velocity w into two components: wiso along the sloping isopycnal surfaces and wlift as the lifting of isopycnal
surfaces. The scaling relationship is as follows:

iso
∼
(
2
2


),
(3)
where

2∕

2
is the isopycnal slope with

2
=
|
∇
|
and

2
=

and
∕
is the inverse aspect ratio esti-
mated as

∕=
√
(∕)2+(∕)2∕
√
(∕)2+(∕)
2
. To illustrate, we apply the decomposition to
the vertical field at 200-m depth to examine the contribution of the two components (Figure7, right column).
The wiso dominates the vertical velocity along the Kuroshio front, suggesting that the motions at sloping isop-
ycnal surfaces provide an important pathway for the vertical transport of tracers between the surface and the
ocean interior (Mahadevan etal.,2020). We note that the large vertical velocity, which is observed in the other
parts of the computational domain, is likely high-mode internal waves emitted by frontal processes (Shakespeare
& Taylor, 2015). In Figures7e and 7f, the locations where the scaling relationship is negative are blanked out
because of the negative buoyancy frequency (N
2).
To gain more insight into the dynamical regimes for the large vertical velocity, the spatial correlations of vertical
velocity with normalized vertical vorticity, buoyancy gradient, and frontogenesis function are examined. The
frontogenesis function is defined as

s
=−
⋅
∇𝑏
(4)
where

is the frontogenetic vector that can be expressed as (Hoskins etal.,1978)
𝐐
=
⎛
⎜
⎜
⎜
⎝
𝑢𝑥𝑣𝑥
𝑢𝑦𝑣𝑦
⎞
⎟
⎟
⎟
⎠
⋅
⎛
⎜
⎜
⎝
𝑏𝑥
𝑏𝑦
⎞
⎟
⎟
⎠
.
(5)
Fs indicates the evolution of a buoyancy gradient, i.e., frontogenesis (positive Fs) or frontolysis (negative Fs).
The subscripts, x and y, denote the gradient in the zonal and meridional direction, respectively. In Figure8, we
perform a linear fit between vertical velocity and the normalized vorticity as well as the horizontal buoyancy
gradient and frontogenesis function. We also include the correlation coefficient and 95% confidence interval
to demonstrate the fidelity of the linear relationship. A high correlation coefficient typically indicates the loca-
tions of large |w| correspond well with large |
∕
|,
|∇|
, or Fs. In Figure8a, it is interesting that the |w| shows
a clear trend with
|∕|
at 10-m depth (the blue dots), indicating that the large values of vertical velocity are
Figure 8. Plots showing the trend of |w| against |
∕
|, buoyancy gradient, and frontogenesis function from the subregion of high resolution (HR) simulation. Blue,
red, and green dots indicate different depth levels representing the mixed layer (ML), the base of the ML, and the upper thermocline, respectively. Error bars of 95%
confidence interval are also plotted.

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related to the submesoscale eddies in the ML. The correlation coefficient
at the 50-m depth is 0.54 (weak correlation), much lower than that of the
near-surface layer. However, at the 200-m depth, a negative slope between
|w| and
|∕|
is shown within a limited range of
|∕|
(Figure8a, the green
dots). In contrast, |w| shows a positive correlation with the buoyancy gradient
(
|∇|
) at all three depths (Figure8b). The large vertical velocity events below
the ML correlate better with the large buoyancy gradient than with the large
vertical vorticity, although the error bars for high values of
|∇|
at z=−50m
and −200m are relatively large. The enhanced vertical velocity is a result of
frontal effects. Furthermore, the high correlation between |w| and Fs indi-
cates that the high values of vertical velocity are induced by frontogenesis/
frontolysis at the three depths (Figure8c). The frontogenetic effects tend to
decrease with smaller Fs at depths (Figure8c, the red and green dots) but are
associated with larger vertical velocity |w|. In this context, the frontogenetic
processes are of great importance to the large vertical velocity below the ML,
driving efficient vertical transport especially at the site of the sharp front
(recall Figure7).
Although the results show evidence of large vertical velocity, it is unknown
whether these motions can drive strong net vertical transport. In Figure 9,
the statistics of the HR vertical velocity separates the upward (positive w+)
and downward (negative w−) velocities. To evaluate the contribution of large
vertical velocities (
||
≥
30
m/day), the ratios between the large positive and
negative vertical velocity in Figure9 (w−/w+ within the range of
||
≥
30
m/
day) are calculated to be 1.91 for the 10-m depth, 1.13 for the 50-m depth, and
1.12 for the 200-m depth, respectively. This is consistent with previous stud-
ies that indicate stronger downwelling along ageostrophic secondary circula-
tions (e.g., McWilliams,2017). In addition, this also suggests that the vertical
transport tends to be downward with more asymmetric distribution in the ML
than below, in a way, illustrating the efficiency in vertical transport at differ-
ent depths. Vertical heat flux (VHF) is also estimated as
VHF =0p′′
,
where

p
= 3,985 Jkg −1K
−1 is the heat capacity of seawater, and

′
and

′
refer to the anomalies of vertical velocity and temperature by removing the
domain-averaged values. The positive or negative VHF indicates upward or
downward heat flux, respectively. The time and domain-averaged VHF in the
upper 200m are plotted in Figure10 (the solid lines). The VHF experiences
a quick increase from the surface to the middle of the ML (∼25m), reach-
ing peak values of 86.3W/m
2 (1-day mean), and 83.8W/m
2 (3-day mean),
respectively. Below the ML, the VHF remains positive, illustrating the net
upward vertical heat transport. As linear IGW cannot drive clear VHF, there
should be some other processes contributing to the enhanced net vertical heat
transport. Here, a low-pass filter (>10km) was applied to filter out the effect
of high-wavenumber motions for

′
and

′
. In contrast, the low-pass vertical
profiles show a decrease in the ML and almost reduce by half below the ML
(the dashed lines in Figure 10). It follows that the VHF in the ML mostly
relies on the high-wavenumber submesoscale processes, while below the ML,
it is only partly provided by these processes. Note that the possible impacts of
nonlinear IGW and their interaction with background flows are not excluded.
4. Analysis of Dynamics and Regimes
The above results have shown the submesoscale features characterized by
strong ML eddies with weaker vertical velocity in the ML and by active
fronts/filaments with stronger vertical velocity below the ML. However, the
Figure 9. Probability of density function (PDF) of vertical velocity at three
depths for the high resolution (HR) simulation (blue line for 10-m depth,
red line for 50-m depth, and yellow line for 200-m depth).
||
=30m/day is
marked by the dashed lines.
Figure 10. Time and domain-averaged vertical heat flux (VHF) over the
subregion (Figure6) and 1day (30 April; the blue line) and 3days (30 April
to 2 May, the red line). The dashed lines are the corresponding low-pass VHF
derived with low-pass

′
and

′
(>10km).

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dominant process accounting for the enhanced vertical velocity in the ocean
interior remains unclear. Hence, this section further examines the flow state
with the Okubo-Weiss (OW) parameter and investigates the instability condi-
tions by analyzing the Ertel potential vorticity and the frequency-wavenum-
ber spectrum.
4.1. Okubo-Weiss Parameter
The upper-ocean submesoscale turbulence is generated by strain field
and horizontal buoyancy gradient in the form of interactive submesoscale
fronts/filaments and eddies. For example, filaments can break into a train
of submesoscale vortices by shear instabilities (Gula etal., 2014). In this
section, the OW parameter,
OW
=
2
−
2
, is employed to diagnose the state
of the fast-evolving submesoscale flows. Here, the sign of OW determines
the behavior of a tracer gradient (e.g., buoyancy gradient)—positive OW
indicates a growth of tracer gradient induced by strain rate, while negative
OW suggests that the flow tends to be eddying (Gula etal.,2014; Hua &
Klein, 1998). The joint probability distribution functions (JPDF) of verti-
cal vorticity and lateral strain rate are presented in Figure11. The statistical
result shows that the percentages of positive OW for z=−10m, −50 m,
and −200m are 64.8%, 68.3%, and 69.1%, respectively. This result indicates
that the depths show stronger growth of buoyancy gradient in a straining
flow regime with stronger Fs (Figure8c), which can drive stronger vertical
flux (Nagai etal.,2015). Also, the JPDF at z=−10m shows that the large
Ro (Ro> 1) occurs near the
||
=

(shear flow) line and correlates well
with the strain rate. In the ML, the submesoscale eddies and frontogenesis/
filamentogenesis are of comparable importance, as the weak stratification is
favorable for the ML baroclinic instabilities and strain-induced frontogenesis
(Callies etal., 2016). At z= −200m, both the vorticity and strain rate are
reduced, so the JPDF spreads and more positive OW occurs, indicative of the
growth of tracer gradient by flow strain.
4.2. Ertel Potential Vorticity
The Ertel potential vorticity (PV) is estimated for examining the instabilities
associated with submesoscale processes in the rotational and stratified flow.
In the diagnostic estimations, we assume that the large-scale mean flows are
to the leading order in geostrophic balance. The Ertel PV can be expressed as
=(+)+(×)
⋅
∇h𝑏
(6)
where the horizontal gradients of vertical velocity are negligible. Then the Ertel PV can be decomposed into
two components: the vertical component,

vert
=(+)
, and the baroclinic component,

 =(×)
⋅
∇h
.
The sign of Ertel PV indicates the flow state (negative PV in the northern hemisphere corresponds to instabili-
ties; Thomas etal.,2013). Here, the two components of Ertel PV are analyzed separately. As in Equation6, the
negative

can arise from unstable stratification, anticyclonic lateral shear, or a negative baroclinic component
(Thomas etal.,2013). In comparison, the vertical component tends to be the dominant constituent for the Ertel
PV in most of the computational domains except near the Kuroshio front (Figure11).
The mesoscale and submesoscale features are highly heterogeneous throughout the computational domain, with
denser signatures near the Kuroshio front (Figure11, snapshots of Ertel PV on 30 April for three depth levels).
At z=−10m, the qve rt is small in the southern flank, indicative of reduced PV for ongoing instabilities; while
the strong vertical stratification near 40°N (large positive qvert) increases the Ertel PV, acting to stabilize the flow.
Differently, the baroclinic component, qbc, exhibits stronger and denser filamentous structures in the north than
in the south. In particular, the strong negative qbc along the Kuroshio front makes q<0 at the near-surface layer,
Figure 11. Joint probability distribution functions of vorticity versus strain
rate at three depths. The probability is in logspace (log10).

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which is favorable for instabilities. This pattern coincides with the distribution of lateral buoyancy gradient (recall
Figure3), arising from submesoscale frontogenetic processes. At z=−50m, the qvert is mostly positive indicat-
ing stable stratification (except for the stream region between 33.5°N and 36°N). The ML base is highly varying
especially near eddies, similar to the observational results (Thompson etal.,2016). This could partly explain the
spatial heterogeneity of the qbc field at the ML base (z=−50m). The depth of 50m can be sometimes within
the ML with small qvert or within the pycnocline with large qvert. Additionally, the ML of this region is quickly
shoaling during the springtime (de Boyer Montégut etal.,2004; Kara etal.,2003) when there should be enhanced
ML restratification (Fox-Kemper etal.,2008). The local restratification may cause submesoscale ageostrophic
motions to restore geostrophic balance. All these processes are particularly active near the Kuroshio front, i.e.,
these ageostrophic processes likely stem from the frontal instabilities at mesoscale and submesoscale (Johnson
etal.,2020a) and can extend to the deep along the frontal isopycnals. At the 200-m depth, although submesoscale
instabilities are largely suppressed (mostly positive Ertel PV for stable flow), there still exist negative qbc with
filamentous structures. Compared to the 50-m depth, the 200-m depth shows more pronounced signatures of
mesoscale eddy rings at 142.3°E, 34.2°N and 145.5°E, 38.0°N (Figure12, middle column). Below the ML, the
baroclinicity in the periphery of the mesoscale eddies is enhanced, which is likely the causation of the enhance-
ment of vertical motions.
The frontal instability is further examined using an improved instability criterion (Buckingham etal., 2021a,
2021b), which introduces a nondimensional number Cu into the classical criterion that uses the Ertel PV q multi-
Figure 12. Snapshots (high resolution (HR)) of Ertel PV being decomposed into vertical (qvert, left column) and baroclinic (qbc, middle column) components for
different depth levels (z=−10m, −50m, and −200m) at 10:00 on 30 April. The solid line in the first plot indicates the cross-front section analyzed in Figure13.

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plied by the Coriolis parameter f ((1+Cu)fq<0 as a necessary criterion for instability. Here, we take a cross-
front section between 151.09°E, 37.24°N and 151.47°E, 36.75°N, e.g., to investigate the instability conditions in
the upper ocean (marked by the solid line in the first plot of Figure12). For curved fronts, the discriminant for
possible instability can be described as
′= (1 + Cu)(1 + Ro) − (1 + Cu)2
Ri
−1 <0,
(7)
where Cu, Ro, and Ri are the curvature, Rossby, and Richardson number. 1+Cu is defined as the nondimensional
absolute angular momentum. Cu can be calculated as
Cu
=
2
𝑉
𝑓𝑟 ,
(8)
where
𝑉
is the along-front flow velocity. r is the radius of curvature estimated as
= 1∕
where

=
  𝑥 −  𝑥
(
2
+
2
)
3∕2
(9)
is the geometric curvature, and
 𝐴
,
 𝐴
,
 𝐴
, and
 𝐴
denote the first and second derivatives of zonal and meridional
displacements along the frontal boundary (see Appendix B of Buckingham etal.,2021a for detail). Here, the
smoothed contours of temperature are used to calculate the radius of curvature. In Equation7, the discriminant
would be negative when the parameter (1+Cu) is large for small Richardson number. The
|
∇
|
, Ri, 1+ Cu,
and

′
along the cross-front section are shown in Figure13. The Richardson number at the sharp front remains
small (about 3) even at the 200-m depth (Figure13b). As mentioned above that the Rossby number may not be
an important indicator for submesoscale activities in the ocean interior, the Richardson number still plays an
important role in reducing the stability discriminant

′
(Equation7). In Figure13c, the nondimensional absolute
angular momentum (1+ Cu) tends to be negative along the front, resulting in negative discriminant for insta-
bilities (

′
< 0). In this discriminant, the instability would occur when 1+ Cu is negative even if Ro is small.
Figure 13. (a) Lateral buoyancy gradient (
|∇|
), (b) the estimated Richardson number in logspace (log10Ri), (c) the nondimensional absolute angular momentum
(1+Cu), and (d) the discriminant for possible instability (

′<0
) along the cross-front section.

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According to the definition for instability categories (see Appendix B of Buckingham etal.,2021a), there would
occur symmetric instability at the cross-front section even below the ML, accounting for the large along-isopyc-
nal vertical velocity (Thomas etal.,2016; Yu etal.,2019b).
4.3. Frequency-Wavenumber Spectrum Analysis
Submesoscale and IGW signatures are shown in the simulation. However, these processes (e.g., frontogene-
sis, ML instabilities, and IGW) are usually concurrent with overlapped spatial and time scales and cannot be
disentangled easily in the realistic simulation. In particular, the IGW within the stratified layers can result
in strong horizontal buoyancy gradient and vertical velocity, although the spontaneous IGW are underesti-
mated in this simulation without the forcing of tide and high-frequency wind (Vanneste, 2013). Here, the
frequency-wavenumber spectrum is employed to identify the contribution to vertical vorticity, horizontal
buoyancy gradient, and vertical velocity in different spatial and time scales (Figure14; the dispersion rela-
tion curves of linear IGW are marked in solid curves). The variance spectra of vertical vorticity (

) and
horizontal buoyancy gradient (
|∇|
) for three depths show a similar shape and are predominately contrib-
uted by the high-wavenumber, high-frequency motions. No clear signature of low-mode IGW is shown in
the variance spectra of

and
|∇|
(left and middle column, Figure14). In contrast, the variance of vertical
velocity (w) shows some signatures of IGW at the 200-m depth (Figure14i). Interestingly, the submesoscale
w variance is increased with the increase of depth (Figures14c, 14f, and14i), suggesting enhanced vertical
motions below the ML. However, these motions only lead to a limited enhancement of net vertical heat
transport (recall Figure10). One possible explanation is that the vertical motions at depths partly result
from high-mode IGW, which do not significantly contribute to net vertical transport. The high-mode IGW
near the Kuroshio front should play an important role in vertical motions, though no high-frequency wind
forcing is used in this simulation.
Given the basic definition for balanced and unbalanced KE in the spectra (Section3.3), the frequency-wave-
number spectra can also be used to partition the balanced and unbalanced motions and to identify their scale
range. Here, a ratio between the divergence and vorticity spectrum (
=divergence∕vorticity
) is defined. If
R≪1
, the flow is considered to be rotational (quasi-geostrophic). The frequency-wavenumber spectra of
vorticity and divergence both show variance peaks at submesoscales near the wavelength of 8km (this scale
can be well resolved in the HR simulation). The vorticity at submesoscales is dramatically reduced below the
ML; while the mesoscale vorticity variance does not change much as a result of the mesoscale eddies with a
length scale of ∼100km (Figures15a, 15d, and15g). It is no doubt that submesoscale divergence variance
should be stronger in the ML than below (Figure15b). If we take R= 0.1 as the rationale for partitioning
balanced and unbalanced motions (R > 0.1 means that the unbalanced motions cannot be ignored), the
boundary line is roughly near 10km (Figures15c, 15f, and15i), which is coincidentally consistent with the
wavelength of an effective forward kinetic energy cascade (Cao etal.,2021). Note that this is not to define the
scale of submesoscale eddies but roughly identify the scale range where unbalanced motions become nonneg-
ligible. Again, the simulated IGW should be largely underestimated in the absence of tide and high-frequency
wind forcing. In effect, the inertia-gravity waves in the northwestern Pacific upper ocean were found highly
energetic (Jing & Wu,2014).
Based on the spectral analysis, the schematic diagram diagnostically summarizes the dominant mechanisms
with roughly separated spaces: quasi-geostrophic balanced motions (QBM) at low frequencies and low
wavenumbers, linear IGW (high frequency and low wavenumber), and unbalanced submesoscale motions
(USM) at high frequencies and high wavenumbers (Figure16a). With the partition for QBM, IGW, and
USM, it is possible to diagnose their effects on vertical motions by filtering. Figure16b compares the
vertical profiles of root-mean-square (RMS) vertical velocity in spaces dominated by QBM, IGW, and
USM. Here, the Coriolis frequency f and the wavelength of 10km are used to separate the spaces. The USM
vertical motions are remarkably larger than that by either IGW or QBM, reaching ∼27m/day (RMS) below
z=−100m. The USM is likely overestimated as a part of high-mode IGW are included. In the high-fre-
quency and low-wavenumber space, the IGW-induced w continuously increases with depth, demonstrating
the enhancement of IGW at depths. In contrast, the QBM exhibit the least significant contribution to vertical
exchange in the upper ocean.

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5. Summary
This study investigates the submesoscale ageostrophic motions within and below the ML of the northwestern
Pacific upper ocean using a ∼500-m resolution simulation. The purpose of this work is to improve our under-
standing of the enhanced vertical velocity associated with different processes at submesoscales and its impact on
vertical heat transport. The dynamical features and mechanisms of these ageostrophic motions are diagnostically
analyzed. The scale ranges of these processes are also identified using frequency-wavenumber spectrum analysis.
The results are summarized as follows.
The submesoscale activities within and below the ML display different characteristics, indicating different
dynamical mechanisms. There exhibits strong submesoscale eddies and fronts within the ML, which are clearly
weakened below the ML (Figures2 and3); while the vertical motions are intensified at depths (recall Figure14).
Care is needed to understand the submesoscale processes below the ML because the classical variables (e.g., Ro)
for evaluating submesoscale dynamics are no longer remarkable. The Richardson number is still significant in
diagnosing the instability of the flow.
Figure 14. Frequency-wavenumber spectra of vertical vorticity (left column), horizontal buoyancy gradient (middle column), and vertical velocity (right column)
multiplied by wavenumber and frequency at z=−10m, −50m, and −200m. The dispersion relation curves of linear internal gravity waves (IGW; mode 1 and 10) are
marked, and the Coriolis frequency is indicated by the dashed line.

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The results show that the large vertical velocity below the ML is primarily driven by the USM over the upper
200m. The potential mechanisms for the enhanced vertical velocity arise from frontogenesis, along-isopycnal
motions, and high-mode IGW. These processes are associated with frontal effects near the Kuroshio, known as
ageostrophic frontal dynamics (Siegelman,2020). Importantly, these motions can significantly contribute to the
VHF between the ML and the ocean interior. Since the high-order IGW are not exactly qualified in this study,
classifying these wave motions into the USM would lead to an overestimate of the USM vertical velocity in
Figure16b.
The smaller submesoscales are strongly ageostrophic as shown in the F-K spectra (Figure14). The ratio (R)
between unbalanced and balanced KE can be used to approximately identify the upper bound of unbalanced
motions. The vertical velocity increases with the decrease of length scales. It is interesting that the estimated
bound is close to the length scale where forward kinetic energy transfers occur (Cao etal.,2021; the energy trans-
fers were estimated using the same data). From this perspective, the parameter, R, may also be used as a metric
for the length scales of forward kinetic energy cascade induced by unbalanced submesoscale motions.
Figure 15. Frequency-wavenumber spectra of vertical vorticity (left column) and horizontal divergence (middle column) at z=−10m, −50m, and −200m. The
right column shows the ratio between horizontal divergence and vertical vorticity in the spectral space, where red, white, and blue shadings mean R>0.1, R=0.1, and
R<0.1, respectively. The dispersion relation curves of linear internal gravity waves (IGW; mode 1 and 10) are marked, and the Coriolis frequency is indicated by the
dashed line.

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Essentially, the Kuroshio jet provides the energy source for the mesoscale and submesoscale activities within
and below the ML. The fronts or filaments can be arrested and advected by sheared flows in the ML and below
(Siegelman,2020). Within the ML with weak stratification, the ML eddies should be a dominant mode through
ML instabilities. Below the ML, submesoscale eddies would be clearly weakened, while the lateral buoyancy
gradient could still exist as a consequence of the spatial variation of the ML base. Although the submesoscale
ageostrophic motions are not a significant reservoir of KE (Ferrari & Wunsch,2009), they significantly contrib-
ute to the vertical exchange of tracers between the ML and the oceanic interior, e.g., supplying nutrients to
the euphotic layer (Klein & Lapeyre,2009; Zhang etal., 2019). Recent observations (e.g., Zhang etal.,2021)
investigated the ageostrophic motions at frequencies less than f. However, the processes with smaller length
scales and higher frequencies (>f) shown in this study show a stronger impact on vertical communication. Quan-
tification of these effects from in situ observations remains a great challenge. In addition, the seasonal difference
of these effects should be interesting as the submesoscale processes are seasonally modulated by the ML depth,
flow shear, atmospheric forcing, and so on.
Data Availability Statement
We thank Baylor Fox-Kemper of Brown University for valuable discussions. The authors would like to thank
NASA for the QuikSCAT data, NOAA ICOADS (http://icoads.noaa.gov), and SODA (https://www2.atmos.umd.
edu/∼ocean/) used as the forcing (http://podaac.jpl.nasa.gov). The source data for ROMS simulations are available
at the scientific database of South China Sea Institute of Oceanology (www.scsio.csdb.cn). The model data used
in this study have been uploaded to a public online repository (https://github.com/ROMSKURO/ROMS_KURO/
releases), which has been linked to Zenodo at https://zenodo.org/record/5613405#.YXukpZpBxjU (doi:http://
doi.org/10.5281/zenodo.5613405).
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Acknowledgments
This work was supported by the National
Key Research and Development
Program of China (2017YFA0604104),
the National Natural Science Founda-
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