1 Submesoscale Density Fronts and their Dynamical Impacts ... · - 1 - 1 Submesoscale Density...
Transcript of 1 Submesoscale Density Fronts and their Dynamical Impacts ... · - 1 - 1 Submesoscale Density...
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Submesoscale Density Fronts and their Dynamical Impacts on the 1
Eddy-active Northwest Pacific Subtropical Ocean 2
Zhiyou Jing1,2, Baylor Fox-Kemper3, Haijin Cao4, Ruixi Zheng1,5, and Yan Du1,2 3
1State Key Laboratory of Tropical Oceanography, South China Sea Institute of 4
Oceanology, Chinese Academy of Sciences, Guangzhou, China 5
2Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou), 6
China 7
3Department of Earth, Environmental, and Planetary Sciences, Brown University, 8
USA 9
4College of Oceanography, Hohai University, Nanjing, China 10
5University of Chinese Academy of Sciences, Beijing, China 11
12
Corresponding author: Zhiyou Jing ([email protected]) 13
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Abstract: Submesoscale density fronts and their important dynamical impacts are 14
investigated in the Northwest Pacific subtropical counter-current (STCC) system by a 15
high-resolution simulation and diagnostic analysis. Both satellite observations and 16
realistic simulation show active surface fronts occupying a horizontal scale of ~20 km 17
in the STCC upper ocean, where the submesoscale flows are characterized by O(1) 18
Rossby numbers and marginally constrained by geostrophy. Arising from straining 19
deformation of larger-scale geostrophic flows, frontogenesis-induced buoyancy 20
advection is detected to rapidly sharpen the density fronts. The enhanced lateral 21
buoyancy gradients in conjunction with atmospheric forced surface buoyancy loss are 22
conducive to producing a negative potential vorticity (PV) and exacerbating frontal 23
instabilities. Up to 30% of the upper mixed layer inside a typical eddy has negative 24
PV in the high-resolution simulation. As a result, the cross-front ageostrophic 25
secondary circulations tend to restratify the surface boundary layer by driving a net 26
frontal slumping. The instantaneous vertical velocity is found to reach ~100 m day-1, 27
substantially facilitating the vertical communication of the eddy-active STCC system. 28
With geostrophic adjustment and subsequent slumping of isopycnals, the diagnostic 29
results also indicate that the geostrophic shear kinetic energy and available potential 30
energy stored in the fronts are effectively extracted and transferred downscale towards 31
submesoscale turbulence, enhanced by strain-induced frontogenesis. In this context, 32
these active submesoscale density fronts and their dynamical processes provide an 33
improved physical understanding for the enhanced vertical exchanges (e.g., heat, 34
nutrients and carbon) and forward energy transfer in the eddy-active STCC upper 35
ocean, as well as triggering phytoplankton blooms at the periphery of mesoscale 36
eddies.37
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1. Introduction 38
Surface density fronts and elongated filaments can commonly be detected from 39
high-resolution images of ocean color, sea surface temperature (SST), or synthetic 40
aperture radar (SAR) (e.g., Klein et al. 2008; Zheng et al. 2008; Lévy et al. 2012; 41
Shcherbina et al. 2013; Callies et al. 2015; Mahadevan 2015; McWilliams 2016). 42
These elongated density fronts on a typical lateral scale of O(10) km are characterized 43
by O(1) Rossby and Richardson numbers, implying that they are marginally 44
constrained by the Earth’s rotation and oceanic stratification, and thus, geostrophic 45
and ageostrophic components are both featured (Thomas et al. 2008; D'Asaro et al. 46
2011; Bachman et al. 2017). Theoretical and observational analysis of oceanic fronts 47
associated with strong boundary currents, such as the Gulf Stream and Kuroshio 48
Extensions, indicate that the submesoscale flow timescale is typically O(1) day 49
(Boccaletti et al. 2007; Thomas et al. 2013; McWilliams 2017). It is much faster than 50
the timescale of larger-scale, mostly geostrophic flows (e.g., mesoscale eddies). The 51
observed kinetic energy (KE) spectra at submesoscales tend to have a k-2 slope (Fig. 52
1), suggesting a forward energy cascade from balanced geostrophic flows toward 53
dissipation via intermediate submesoscale processes (D'Asaro et al. 2011; Bühler et al. 54
2014; McWilliams 2016; Qiu et al. 2017). Additionally, submesoscale turbulence in 55
the periphery of strong currents and eddies can induce a large vertical velocity with 56
one order of magnitude higher than the geostrophic motions (Mahadevan and Tandon 57
2006; Thomas et al. 2008; D'Asaro et al. 2011). The large vertical velocities are found 58
to favor the vertical fluxes of heat, momentum, nutrients and carbon between the 59
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surface and oceanic interior (e.g., Taylor and Ferrari 2011; Lévy et al. 2012; Sasaki et 60
al. 2014; Omand et al. 2015; Klymak et al. 2016; Su et al. 2018). 61
Due to the perceived importance of enhanced air-sea communication, nutrient 62
supply for phytoplankton growth, and multiscale interactions, these ubiquitous 63
submesoscale fronts and their associated dynamics have received intense study 64
through simulations and observations, especially in the Gulf Stream and strong frontal 65
zones (e.g., Fox-Kemper et al. 2008; Taylor and Ferrari 2011; Gula et al. 2014; 66
Thomas et al. 2015; Klymak et al. 2016; Sullivan and McWilliams 2018; Warner et al. 67
2018). However, in the subtropical counter-current (STCC) system of the Northwest 68
Pacific (Fig. 2), the active submesoscale density fronts (Fig. 3), and especially their 69
dynamical processes, are rarely investigated because of the rarity of high resolution 70
data. These submesoscale fronts and their dynamics are fundamentally important for 71
understanding the energy dissipation and vertical exchanges of mesoscale eddies in 72
the STCC system, as well as their regional significance on the closes of carbon and 73
energy budgets. 74
As shown in Fig. 2, a high mesoscale variability band (17-26°N) is found in 75
satellite measurements and field campaigns due to the presence of eastward 76
subtropical countercurrents and the westward-flowing North Equatorial Current (NEC) 77
of the wind-driven subtropical gyre (Qiu 1999; Qiu et al. 2008; Kobashi and 78
Kubokawa 2012; Qiu and Chen 2012). Active mesoscale eddies in the STCC band 79
propagate westward carrying vigorous surface thermal fronts enveloping the 80
periphery of eddies (Fig. 3a). The density fluctuations in the weakly stratified upper 81
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ocean are particularly active (Fig. 3b), implying that the flows are potentially affected 82
by the mesoscale and submesoscale processes at different timescales. The geostrophic 83
instabilities that lead to these eddies have been widely investigated in the past 30 84
years, substantially improving the understanding of mesoscale processes (e.g., Qiu 85
and Lukas 1996; Kobashi et al. 2006; Qiu and Chen 2010; Chelton et al. 2011; 86
Kobashi and Kubokawa 2012; Chang and Oey 2014). However, the low-mode 87
mesoscale eddies are highly constrained by the earth’s rotation and approximately in 88
quasigeostrophic balance, so they tend to flux energy toward scales larger than their 89
instability scale rather than toward smaller-scale flows (e.g., Scott and Wang 2005; 90
Ferrari and Wunsch 2009). Therefore, the geostrophic dynamics of the mesoscale does 91
not provide a straightforward path for the energy dissipation of mesoscale eddies 92
aside from large-scale dissipation mechanisms such as bottom drag (D'Asaro et al. 93
2011; McWilliams 2016; Bachman et al. 2017). An important question is whether 94
submesoscale dynamical processes catalyze a downscale energy cascade of these 95
regional geostrophic eddies in the STCC upper ocean; it remains unclear so far. 96
On the other hand, the balanced geostrophic flows of mesoscale eddies are 97
characterized by small Rossby numbers and quasi-two-dimensional vortical motions 98
(Klein et al. 2008). Both rotation and stratification suppress vertical velocities within 99
these flows (Ferrari and Wunsch 2009). Enhanced vertical communication associated 100
with mesoscale eddies is hidden by analysis of balanced geostrophic dynamics alone. 101
Recent studies of both simulations and observations highlight the significant 102
contribution of submesoscale enhanced vertical heat and tracer fluxes, particularly in 103
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the northwest Pacific upper ocean (e.g., Sasaki et al. 2014; Qiu et al. 2017; Su et al. 104
2018; Zhang et al. 2019). A careful analysis of the underlying dynamical processes 105
and generation mechanisms has not been well understood in the eddy-active STCC 106
system. 107
In this paper, a high-resolution model is used to investigate the regional 108
submesoscale density fronts, their evolution, and their potential dynamical impacts on 109
vertical exchange and energy transfer in the STCC upper ocean. Section 2 describes 110
the observational data, realistically-forced nested simulations, and analysis methods 111
based on frontogenesis and quasigeostrophic theory (Charney 1971; Hoskins 1974; 112
Hoskins 1982; Lapeyre and Klein 2006; McWilliams 2017). The model description is 113
extensive to cover both this paper and a companion paper covering spectral energy 114
transfers in these simulations as a function of scale (Cao et al. 2020). In section 3, the 115
observational and diagnostic results of submesoscale fronts associated with 116
frontogenetic straining and frontal instabilities are examined in the STCC system. 117
Section 4 focuses on a single selected and magnified mesoscale eddy and its 118
peripheral fronts, quantitatively evaluating the buoyancy-gradient frontogenetic 119
tendencies and submesoscale processes. Finally, the results are summarized with an 120
additional discussion of future work in section 5. 121
2. Data and Methods 122
a. Satellite data and Argo measurements 123
The satellite data used in this study include high-resolution sea surface 124
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temperature (SST), ocean color, sea surface height (SSH) and sea level anomaly (SLA) 125
data obtained from satellite sensors on different platforms. The SST data are derived 126
from the Group for High-Resolution Sea Surface Temperature (GHRSST) project and 127
merged with in situ, microwave, and infrared satellite SST data (Donlon et al. 2012). 128
These merged data, with a daily resolution of 6×6 km from January 2006 to 129
December 2018, are produced by the UK Meteorological Office and distributed by the 130
National Oceanographic Data Center (NODC) of NOAA. In this study, a 131
gradient-based algorithm (Jing et al. 2016) is utilized for the SST fields and the 132
intensity of surface thermal front is roughly estimated by the SST gradient in each 133
georeferenced grid. The phytoplankton pigment concentration data, with a daily 1×1 134
km grid resolution, are derived from the level-2 chlorophyll products of Moderate 135
Resolution Imaging Spectroradiometer (MODIS) and provided by the Goddard Space 136
Flight Center (GSFC) of NASA. 137
The AVISO daily SSH and SLA datasets are retrieved and merged from the 138
TOPEX/Poseidon (T/P), Jason, ERS-1, ERS-2, and ENVISAT satellites on a 0.25° 139
grid from October 1992 to August 2016. The improved altimetry dataset has low 140
mapping errors and better resolves the spatial and temporal scales of mesoscale ocean 141
circulation (Le Hénaff et al. 2011; Strub et al. 2015). To maximize the signal-to-noise 142
ratio for eddy variability, the daily SSH data are high-pass filtered with a cutoff period 143
of 120 days (Qiu and Chen 2010). Additionally, we use the records of one Argo float 144
(#2901191) travelling in the STCC band from July 2011 through March 2015 to 145
represent the thermohaline variability in the weakly stratified upper ocean. The Argo 146
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data are acquired from the NODC of NOAA. 147
b. High-resolution nested simulation 148
The Regional Oceanic Modeling System (ROMS) with nesting are employed in 149
this study. ROMS is specially designed for the simulation of regional oceanic systems 150
(Shchepetkin and McWilliams 2005, 2011) and has been widely applied to the 151
regional simulation of multiscale processes in the global oceans (e.g., Penven et al. 152
2006; Capet et al. 2008a; Marchesiello et al. 2011; Holmes et al. 2014; Gula et al. 153
2016; Zhong et al. 2017; Cherian and Brink 2018). As shown in Fig. 4, the parent 154
model in this study covers the northwest Pacific Ocean (NWPO) (95°E-170°E, 155
10°S-45°N) with a comparatively coarse horizontal resolution of ~7.5 km and 156
976×788 orthogonal grid points (hereafter ROMS0). An online nesting approach is 157
adopted with successive grid refinements from ~7.5 km resolution in the parent model 158
to ~1.5 km and ~500 m resolutions in the refined child1 and child2 models, 159
respectively. The nested child1 model has 3182×2112 grid points from 117°E to 160
160°E and 5°N to 31°N, covering the subtropical gyre of the western Pacific Ocean 161
(hereafter ROMS1). The refined child2 model has 5858×2192 grid points from 120°E 162
to 150°E and 15°N to 25.5°N, covering the STCC band (hereafter ROMS2). The child 163
simulations are created using one-way nesting from coarser to finer models, without 164
feedback from the child solution to the parent model (Penven et al. 2006). The lateral 165
boundary condition algorithms consist of an improved Flather-type scheme for the 166
barotropic mode (Mason et al. 2010) and an Orlanski-type scheme for the baroclinic 167
mode (Marchesiello et al. 2001; Gula et al. 2014). 168
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There are same 60 levels in the parent and child models with concentrated 169
vertical levels for the surface and bottom layers. Two stretching parameters in the 170
vertical terrain-following S-coordinates (Lemarié et al. 2012) are 7 and 2, controlling 171
the bottom and surface refinements, respectively. The transition depth between the Z 172
levels and terrain-following Sigma levels is 100 m. According to the stretching 173
parameters and transition depth, the refined vertical level thicknesses within the 174
mixed layer range from 0.3 m to 5.0 m in all of the parent and child simulations of 175
this study. The bathymetry for parent and child domains is constructed from the 176
General Bathymetric Chart of the Oceans (GEBCO) dataset with a spatial resolution 177
of 30 arc-seconds, which is produced by the British Oceanographic Date Centre 178
(BODC). To avoid exceeding computational restrictions with respect to the 179
topography steepness and roughness (Beckmann and Haidvogel 1993), the local 180
topography in the model is slightly smoothed when the steepness exceeds a slope 181
parameter of 0.2. The vertical subgrid mixing scheme for tracers and momentum is 182
the K-profile parameterization (KPP; Large et al. 1994) based on a critical bulk 183
Richardson number at the surface and bottom (Lemarié et al. 2012), where the effects 184
of bottom friction are parameterized by a logarithmic law above bottom roughness. 185
For the parent and nested child simulations, the surface atmospheric forcing, 186
including wind stress, heat and freshwater fluxes, and lateral oceanic forcing are 187
climatological, rather than a specific historical forcing. The surface wind forcing data 188
is derived from the daily mean climatology of the Quick Scatterometer (QuikSCAT) 189
wind stress dataset with a 0.25°×0.25° spatial resolution, which is distributed by the 190
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French Research Institute for Exploitation of the Sea. The surface heat and freshwater 191
fluxes are from the monthly climatology of the International Comprehensive 192
Ocean-Atmosphere Data Set (ICOADS) with a coarse resolution of 1°×1° (Woodruff 193
et al. 2011; Freeman et al. 2017) and are distributed by the Asia-Pacific 194
Data-Research Center (APDRC). Based on the linearized bulk formulation of Barnier 195
et al. (1995), a surface flux correction toward the climatological SST is included in 196
the simulations to allow feedback from ocean SSTs to atmospheric conditions. The 197
initial oceanic state and lateral boundary information for the parent model are 198
obtained from the monthly climatology of the Simple Ocean Data Assimilation 199
(SODA) reanalysis dataset with a 0.5°×0.5° spatial resolution (Carton and Giese 200
2008), which is provided by the APDRC at the University of Hawaii. 201
The parent model ROMS0 covering the NWPO is spun up from its initial state 202
for 20 years and then run for an additional 2 years to provide daily boundary 203
information for the nested child simulations. The KE from the parent model tends to 204
have a periodic seasonal variation after a few simulation years and finally reaches a 205
numerically equilibrated state within the 20-year spin-up. Under the atmospheric 206
forcing and consecutive lateral oceanic forcing from the parent domain in the last two 207
years, the successive nested ROMS1 and ROMS2 models are online run for the same 208
two years. The parent and both child simulations have outputs of daily mean and 209
snapshots at 12:00 noon in the last simulation year. These modeling results, including 210
regional circulation, thermohaline structure, mixed layer depth (MLD), and energy 211
level of mesoscale eddies, have been validated against the satellite and reanalysis 212
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datasets, as well as the limited historical in situ observations in the NWPO and 213
adjacent South China Sea (SCS). The comparisons to measurements on multiple 214
platforms show that the simulations are sufficiently accurate to characterize the 215
climatological Pacific conditions. For this paper, the simulation outputs in wintertime 216
are used for diagnostic analysis because the surface density fronts are more active due 217
to the large-scale wind-driven convergence and mixed layer instability in the STCC 218
system (Qiu et al. 2017), which are better resolved in wintertime as well (Dong et al. 219
2020). The estimated linear growth lengthscale of mixed layer instabilities from the 220
ROMS2 simulation is roughly ~7.2 km for 1Ri (e.g., Fox-Kemper et al. 2008, Eq. 221
(2)). The maximum horizontal lengthscale for submesoscale symmetric instability (SI) 222
is approximately ~1.8 km (e.g., Bachman et al. 2017, Eq. (1)). They are much smaller 223
than the scale of balanced mesoscale eddies and can be permitted by the refined 224
ROMS2 simulation adequately with a 500mdx resolution. It is important to note 225
that SI normally acts to reduce negative PV, and that partially resolved SI do such 226
much more slowly (Bachman and Taylor 2014), so it is possible that the large amount 227
of negative PV found in ROMS2 may be lessened in a higher resolution simulation. 228
Shown in Fig. 5, the magnitude of surface Rossby number from the merged 229
AVISO altimeters is universally less than 0.2 in the STCC band (Fig. 5a); this 230
indicates that the ~25 km resolution is far from adequate to resolve submesoscale 231
features distinguished by an order one Rossby number. Increased spatial resolutions in 232
the nested simulations exhibit active submesoscale vorticity filaments on a lateral 233
scale of ~20 km at the surface (Figs. 5c and 5d). The dynamics within these 234
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submesoscale activities are distinct from larger-scale geostrophic motions 235
characterized by small Rossby numbers (Thomas et al. 2008; McWilliams 2016). 236
Comparing the results at different resolution, the local vertical vorticity of ROMS2 is 237
much larger in magnitude and more abundant in spatial distribution than that of 238
ROMS0. The resolution of ~7.5 km in the parent simulation only show the rough 239
meander structures and does not exhibit reliable physical characteristics of O(1) 240
Rossby numbers. The local increased submesoscale activities at the periphery of 241
mesoscale eddy might be important for enhanced vertical fluxes and forward cascade 242
of geostrophic energy (Brannigan 2016; Bachman et al. 2017). 243
c. Diagnostic estimations of potential vorticity and frontogenetic tendency 244
The potential vorticity (PV) is critical for the dynamic stability of frontal flows 245
because the PV distribution strongly affects the hydrostatic and geostrophic balance 246
(Hoskins 1974; Thomas 2005; Molemaker et al. 2005; Capet et al. 2008b; Thomas et 247
al. 2013; Holmes et al. 2014; Haney et al. 2015). A variety of instabilities can develop 248
when the Ertel PV, q , takes the opposite sign to that of the Coriolis parameter 249
(Hoskins 1974). 250
2 , hv
a h h
q b f N b (1) 251
where 0b g is the buoyancy and g is the acceleration due to gravity. and 252
0 denote the potential density and reference density, respectively. f is the 253
Coriolis parameter. 2 N b z is the vertical buoyancy frequency squared. 254
2 , hM b b x b y is the lateral buoyancy gradient. refers to the vertical 255
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component of relative vorticity. The expression k ua f is the absolute 256
vorticity with a vertical component ( ) A f and horizontal component h , in 257
which k is the local vertical unit vector. 258
Accordingly, the full Ertel PV can be decomposed into the vertical component 259
vq and horizontal baroclinic component hq . Here, the lateral velocity shear arising 260
from mean flows, an important contributor to the relative vorticity 261
v x u y , is involved in the vertical component vq . For mesoscale eddies 262
in the subtropical ocean with a typical horizontal scale of a few hundred kilometers, 263
the conservative PV is mostly dominated by the vertical component, as the horizontal 264
component hq is negligible in comparison to vq . However, for the submesoscale 265
fronts characterized by O(1) Rossby number dynamics in the periphery of eddies, the 266
baroclinic component of the PV is nonnegligible and acts as an effective source of 267
anticyclonic vorticity (Thomas 2005), that is, the locally baroclinic processes 268
involving vorticity and buoyancy redistribution in the active surface boundary layer 269
(Bachman et al. 2017). 270
For a density front in hydrostatic and geostrophic balance (neglecting vertical 271
velocity and horizontal Coriolis effects), the thermal wind relation is given by the 272
following: 273
uk .
g
h hb f fz
(2) 274
The baroclinic PV component in the assumption of thermal wind balance can be 275
expressed as follows: 276
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4
, h h h
Mq b
f (3) 277
24 ,hM b (4) 278
where hq , depending on the frontal sharpness ( 4M ), is negative definite in the 279
Northern Hemisphere, indicating that the baroclinicity of the frontal flows always 280
reduces the PV and is conducive to frontal instability such as symmetric instability 281
(SI). SI will arise when the total contributions from atmospheric forcing surface 282
buoyancy loss, oceanic vertical vorticity, stratification and horizontal buoyancy 283
gradient cause the PV to drop below zero (Hoskins 1974; D'Asaro et al. 2011; Thomas 284
et al. 2013; Bachman et al. 2017). 285
In the upper ocean where eddies are most active, elongated surface density fronts 286
and filaments are sharpened by the strain from larger-scale flows that enhance lateral 287
buoyancy gradients via strain-induced frontogenesis (e.g., McWilliams et al. 2009a; 288
Gula et al. 2014). The horizontal strain rate arising from frontogenesis/frontolysis is 289
given by the following expression: 290
2 2,x y x ySt u v v u (5) 291
where ( , )u v are the ( , )x y components of horizontal flow in the Cartesian 292
coordinate system. The subscripts refer to the partial derivative with respect to x or 293
y . The direction of the principal strain axis is defined as the angle p : 294
1a a ,rct n
2y x
px y
u v
u v
(6) 295
along which the balanced frontal flows are subjected to the maximum straining 296
deformation (Holton 1982). The horizontal strain-induced frontogenesis within the 297
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developing stage acts to rapidly sharpen the lateral density gradients at a growth rate 298
given by advective frontogenetic tendency F (Hoskins 1982) and increase the 299
frontal baroclinicity. 300
Q ,hF b (7) 301
where u uQ ,h hb b
x y
is the Q-vector. 302
In addition to the horizontal advective terms, other terms contributing to the 303
frontogenetic tendency are also evaluated to better understand the generation 304
mechanisms of frontogenesis. According to the McWilliams (2017) SCFT (secondary 305
circulation and frontogenetic tendency) theoretical framework, these contributing 306
terms can be explicitly quantified by the following diagnostic equation based on a 307
momentum-balanced approximation and neglecting the ageostrophic acceleration. 308
a
2 2 2a3
2 2
1' [ , ] ' [ ' ](u )
2
( ') ( ') [ ' ] ( ),
wg
v
z g g z gF FF
x y z v z
FF
Db f J N w b b b
Dt
b b b b (8) 309
where 'b is the local buoyancy anomaly. gF is the geostrophic self-straining 310
tendency term. wF and aF combined form the advective tendency of two 311
ageostrophic strain terms associated with vertical velocity and buoyancy advection. 312
The notations F and
vF
refer to the external straining deformation and vertical 313
mixing tendency terms, respectively. These tendency terms have no time derivatives 314
so their evaluation is diagnostic. On the right side of the equation, g is the 315
geostrophic streamfunction, i.e. , g y g g x gu v . J is the horizontal 316
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Jacobian operator, i.e. [ , ] x y y xJ p q p q p q , and a3 au (u , )w refers to the 317
ageostrophic secondary circulation velocity. The local ageostrophic horizontal 318
velocity au can be derived from the total horizontal velocity by subtracting 319
geostrophic velocity u g . The coefficient is the horizontal strain rate associated 320
with the large-scale strain field exterior to the front in question, which has a typical 321
magnitude of 10-5 s-1 for mesoscale eddies (McWilliams 2017). The diffusivity v 322
refers to the vertical mixing coefficient for tracers from the KPP scheme (Large et al. 323
1994). 324
In the presence of frontogenesis and enhanced frontal baroclinicity, 325
submesoscale density fronts tend to have a relatively low PV, so flow configurations 326
are preconditioned for SI in conjunction with atmospheric forced surface buoyancy 327
loss (Thomas and Taylor 2010; Bachman et al. 2017). SI is a type of shear instability 328
within submesoscale range, which can extract KE from larger-scale geostrophic flows 329
at a rate given by the geostrophic shear production (GSP) (Bennetts and Hoskins 1979; 330
Thomas et al. 2013) as follows: 331
uGSP u ' ' ,gw
z
(9) 332
where the overline and primes denote a spatial average and the deviations from the 333
average, respectively, gu refers to the geostrophic flow, and w is the vertical 334
velocity given by the solution of ROMS simulation. Meanwhile, available potential 335
energy (APE) stored in the density fronts can be released by geostrophic adjustment 336
and baroclinic instability at a rate equal to the vertical buoyancy flux (BFLUX) as 337
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follows: 338
'BFLUX ' w b . (10) 339
Theoretical studies indicate that the GSP and BFLUX, two primary energy sources for 340
submesoscale turbulence, can cascade down to dissipative scales through a wide 341
variety of small-scale instabilities (Capet et al. 2008b; Molemaker and McWilliams 342
2010; Thomas et al. 2013; Haney et al. 2015; Bachman et al. 2017). 343
These parameters, along with the geostrophic Richardson number 344
(22 2 g hRi f N b ) and the difference between absolute vorticity and strain ( A St ), 345
are diagnostically evaluated in this study based on the outputs of the 500m-resolution 346
simulation of ROMS2. Only diagnostic PV and energy extraction are examined in this 347
study; discussions on PV change by atmospheric forcing (e.g., down-front wind 348
forcing and surface cooling/heating) or unforced ageostrophic baroclinic instability 349
(e.g., mixed layer instabilities) are not of great interest due to the limitations of 350
climatological and coarse atmospheric forcing data. The modification of PV by 351
frictional and diabatic processes is expected from spatially nonuniform atmospheric 352
forcings and mixed layer eddies in the active surface boundary layer (Fox-Kemper 353
and Ferrari 2008; D'Asaro et al. 2011; Benthuysen and Thomas 2012; Gula et al. 354
2015). Additionally, this analysis of fronts at a typical eddy using the McWilliams 355
SCFT theory and the distribution of Ertel PV is only one of two efforts stemming 356
from the nesting simulation suite. A companion paper covers the energy transfers in 357
these simulations as a function of scale (Cao et al. 2020). 358
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3. Active Submesoscale Fronts in the STCC Upper Ocean 359
a. Submesoscale fronts and enhanced vertical exchange from observations and 360
simulations 361
Aside from satellite observations of thermal fronts (Fig. 3), two fine-resolution 362
ocean color images of exemplar mesoscale eddies are presented to illustrate 363
observational evidence for the objectives in studying submesoscale features in the 364
STCC band (Figs. 6b and 6c). The high chlorophyll concentrations appear at the 365
periphery of the mesoscale eddies and occupy a lateral width of 5-30 km. This result 366
suggests either an enhanced vertical nutrient supply feeding phytoplankton growth in 367
the submesoscale fronts and tail-shaped filaments, or the convergence into such fronts. 368
Similar elongated fronts and filaments are found in the surface vorticity fields of the 369
high resolution simulation (Fig. 6a). The maximum relative vorticity normalized by 370
f exceeds 3 in the periphery of mesoscale eddies and strong currents, indicating a 371
departure from balanced geostrophic dynamics (Molemaker et al. 2005; Thomas et al. 372
2008; McWilliams 2017). 373
Due to the presence of these submesoscale fronts and filaments, the vertical 374
velocity w averaged over the MLD exceeds 60 m day-1 in the frontal zones of 375
ROMS2 (Fig. 7b). The average vertical velocity is an order of magnitude in ROMS2 376
than in ROMS0 (Fig. 7a) where only mesoscales are permitted. Interestingly, applying 377
a horizontal Gaussian filter with a scale of 20 km reduces the vertical velocities 378
dramatically in magnitude, and filaments nearly disappear in the STCC band. The 379
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spatial pattern of the vertical velocity after filtering resembles the 380
mesoscale-permitting ROMS0. Thus, enhanced vertical communication between the 381
surface and oceanic interior seems to be carried out by submesoscale structures, 382
consistent with the observations of density fronts in the Gulf Stream and Kuroshio 383
Extensions (Joyce et al. 2009; D'Asaro et al. 2011; Shcherbina et al. 2015). 384
Additionally, the SSH wavenumber spectrum in the STCC system also shows the 385
different spectral characteristics within the wavelength ranges of mesoscale and 386
submesoscale (Fig. 8). The spectral slope of SSH tends to follow a k-5 power law in 387
the approximate subrange of 50-300 km, implying mostly geostrophic turbulence 388
within this scale. But in the smaller wavelengths, the wavenumber spectrum tends to 389
have a rapid slope flattening close to k-11/3, agreement with the interpretation of 390
submesoscale turbulence by surface quasigeostrophic theory (Lapeyre and Klein 2006; 391
Capet et al. 2008a). These spectral piecewise characteristics are also roughly 392
consistent with the recent analysis of 13-year ADCP measurements in the STCC 393
system (Qiu et al. 2017), which is associated with mixed layer instability and strongly 394
depends on the energy level of local mesoscale eddy activities (Qiu et al. 2014; Sasaki 395
et al. 2014; Qiu et al. 2017). 396
b. Frontogenetic strain and frontal submesoscale instability 397
Frontogenesis has been widely examined as an important mechanism to produce 398
submesoscale buoyancy filaments due to the straining deformation of larger-scale 399
geostrophic flows (Hoskins 1982; McWilliams et al. 2009b; Gula et al. 2014; 400
- 20 -
McWilliams et al. 2015; McWilliams 2016). The strain-induced frontogenesis rapidly 401
sharpens the density fronts by increasing lateral buoyancy gradients and vertical 402
shears (Sullivan and McWilliams 2018). As a result, the frontal sharpness 403
( 24 hM b ) in the eddy-active STCC band presents a conspicuous enhancement at 404
the periphery of eddies and streamers (Fig. 9a). The local principal strain axes (p ) 405
tend to align with the density front, along which the deformation of ambient strain 406
flows causes maximum stretching. The other horizontal perpendicular principal axis is 407
the maximum contraction axis (Holton 1982), so strain-induced frontogenesis acts to 408
strengthen lateral gradients along the axis of maximum contraction. The diagnostic 409
results show the enhanced lateral buoyancy gradients leading to a large negative 410
horizontal component hq from Eq. (1) with a magnitude comparable to vq in the 411
elongated fronts and filaments. The negative Ertel PV features resulting from hq 412
(Figs. 9b and 9d) are preceded by surface buoyancy loss (Fig. 9c). The negative PV is 413
favorable for frontal SI at submesoscale, where the local smaller-scale shear 414
instability is also expected within the surface boundary layers (Hoskins 1974; Taylor 415
and Ferrari 2009; Molemaker and McWilliams 2010). However, in the positive PV 416
zones, only geostrophic baroclinic mixed layer instabilities are present (Boccaletti et 417
al. 2007). 418
Fig. 10 shows the instantaneous fields associated with the frontogenetic strain, 419
including advective frontogenetic tendency F and A St , as well as a vertical 420
section of w along the 20°N transect. The strong horizontal strain (> 0.5 f ) drives 421
convergence of the frontal flows and enhancement of frontal lateral buoyancy 422
- 21 -
gradients. The negative A St at the fronts and filaments tends toward loss of 423
geostrophic balance, and the local flows are primarily dominated by the unbalanced 424
submesoscale mode (McWilliams et al. 1998). As expected, large advective 425
frontogenetic tendency corresponds to sharp fronts (Fig. 9a). Thus, as a byproduct of 426
active mesoscale eddies in the STCC system, the frontogenetic strain enhances 427
buoyancy gradients of submesoscale fronts by buoyancy advection and redistribution. 428
This enhanced frontal baroclinicity together with surface buoyancy loss due to 429
atmospheric forcing (Fig. 9c) can effectively contribute a negative PV (Figs. 9b and 430
9d), preconditioning the frontal flows to SI. 431
In response to the frontogenetic straining and frontal instability at submesoscale, 432
diagnostic results show that these density fronts undergo a cross-front ageostrophic 433
secondary circulation (ASC) that drives large vertical velocities in the upper mixed 434
layer (Figs. 10c and 10d). This secondary circulation for an isolated front is an 435
overturning cell with strong upwelling on the light side and downwelling on the dense 436
side. The instantaneous vertical velocity from the refined ROMS2 simulation reaches 437
~100 m day-1 (Fig. 10c), significantly in favor of the vertical exchanges of heat, 438
momentum and tracers, especially within the mixed layer but still strongly tied to 439
large velocities below. Meanwhile, the ASC tends to restratify the water column and 440
restore the geostrophic balance through driving a positive buoyancy flux and 441
downgradient momentum flux (Lapeyre et al. 2006; Bachman et al. 2017). In this 442
process, SI and submesoscale turbulence can trigger frontal smaller-scale instabilities, 443
such as Kelvin-Helmholtz shear instability (e.g., Thomas and Lee 2005; D'Asaro et al. 444
- 22 -
2011), although these smaller secondary instabilities are not resolved in ROMS2. 445
c. Potential contribution to downscaling energy transformation 446
These elongated submesoscale fronts are frequently susceptible to the straining 447
of ambient larger-scale flows and surface buoyancy loss driven by atmospheric 448
forcing. In the presence of a negative PV, the frontal SI at submesoscale also acts as a 449
downscale energy pathway for geostrophic flows (D'Asaro et al. 2011; McWilliams 450
2016; Bachman et al. 2017). With fronts weakening by ASCs, the geostrophic KE can 451
be extracted from the frontal jets at a rate of GSP. A subsequent slumping of 452
isopycnals arising from geostrophic adjustment is expected to lead to a release of APE 453
stored in the fronts at a rate given by BFLUX. As shown in Fig. 11, both the 454
diagnostic GSP and BFLUX, two primary energy sources for the submesoscale, are 455
particularly large in the fronts and filaments, implying that the fronts and frontal 456
submesoscale instabilities effectively facilitate large energy conversion rates from 457
balanced mesoscale flows to submesoscale turbulence in the STCC upper ocean. 458
These energies extracted from geostrophic flows by the intermediate 459
submesoscale processes will be transferred to three-dimensional turbulent kinetic 460
energy (TKE) and cascade down to dissipative scales via a wide variety of small-scale 461
instabilities that are parameterized rather than resolved in ROMS2 (e.g., 462
Kelvin-Helmholtz shear instability) (Capet et al. 2008b; Taylor and Ferrari 2009; 463
Molemaker and McWilliams 2010; Hamlington et al. 2014). Enhanced local mixing 464
and energy dissipation triggered by submesoscale SI has been observed at the frontal 465
- 23 -
zones of the Kuroshio Extension and SCS (D'Asaro et al. 2011; Yang et al. 2017). 466
Accordingly, the submesoscale processes and frontal instabilities in the STCC system 467
are a sink of geostrophic energy of mesoscale eddies, which involve more than 90% 468
of the KE of the ocean circulation (Ferrari and Wunsch 2009). 469
4. Submesoscale Density Fronts at a Mesoscale Eddy 470
a. Unbalanced eddy flows and baroclinic fronts 471
Satellite-derived surface color images have revealed the chlorophyll fronts at the 472
periphery of mesoscale eddies (Fig. 6). To further illustrate frontal submesoscale 473
processes, the magnified three-dimensional structures of a representative eddy case 474
are presented in this section and Figures 12 to 16. As shown in Fig. 12a, both the 475
temperature and flow inside the 200 km mesoscale eddy are horizontally 476
heterogeneous in the upper ocean. Lateral buoyancy gradients are common along the 477
periphery of the mesoscale eddy (Fig. 12b). The diagnostic results from the ROMS2 478
simulation indicate that the relative vorticity is increased along the elongated 479
density fronts of the eddy and has a magnitude comparable to that of f (Fig. 13a), 480
as a response to the enhanced horizontal straining and velocity shears of ambient 481
larger-scale flows. The averaged relative vorticity in the frontal zones is 1.5-2 times 482
that of f , suggesting both geostrophic and ageostrophic flows coexisting in the 483
submesoscale fronts. As a result of increased horizontal velocity shears and buoyancy 484
advection, the frontal sharpness is dramatically enhanced at the periphery of the eddy 485
with a lateral scale of ~20 km, where the vertical velocity reaches O(10-3) m s-1 (Fig. 486
- 24 -
13b) and is favorable to the vertical transport of tracers within the eddy. According to 487
the high-resolution simulation, up to approximate 30% of the upper mixed layer 488
volume inside the mesoscale eddy has enhanced density fronts (Fig. 12b) and negative 489
PV (Fig. 14b) in winter. This result is roughly in line with the satellite observations 490
(Fig. 6) and idealized simulations of Brannigan et al. 2015. 491
b. Frontogenetic tendency 492
Strain-induced frontogenesis can rapidly sharpen density fronts by increasing 493
lateral buoyancy and velocity gradients within a timescale of less than a day (Hoskins 494
1982; Gula et al. 2014; McWilliams 2016; Sullivan and McWilliams 2018). In the 495
present case, the diagnostic results clearly show a negative baroclinic PV component 496
arising from enhanced lateral buoyancy gradients along the periphery of the eddy (Fig. 497
13b), which always reduces the total Ertel PV and is favorable to frontal instability. In 498
conjunction with atmosphere forced surface buoyancy loss, the enhanced baroclinicity 499
of the density fronts preconditions the frontal flows unstable to SI. The advective 500
frontogenetic tendency (Fig. 14a) is roughly coincided with the increased frontal 501
sharpness (Fig. 12b) and low Ertel PV (Fig. 14b) at the periphery of the mesoscale 502
eddy. This result suggests that in this eddy the direct straining effect is a primary 503
influence on the buoyancy-gradient frontogenetic tendency and frontal baroclinic PV 504
enhancement, rather than other potential mechanisms such as sharpening by Turbulent 505
Thermal Wind (e.g., Sullivan and McWilliams 2018). The positive tendencies indicate 506
that the present fronts developing and intensifying. The negative tendency in the 507
eastern periphery of the eddy shows frontolysis where local straining flows are acting 508
- 25 -
to weaken the buoyancy gradients. 509
Fig. 15 shows the different buoyancy-gradient frontogenetic terms for the eddy 510
according to the SCFT solutions (McWilliams 2017), which further support the 511
dominant role of strain-induced frontogenesis in this case. For the present case, both 512
frontal geostrophic self-straining term gF and ageostrophic horizontal strain term aF 513
are effective in sharpening (positive tendency) or weakening (negative tendency) the 514
frontal buoyancy gradients. The vertical straining effect, wF , is much smaller 515
compared to the gF and aF . In addition to the tendency terms by fronts themselves, 516
the external straining deformation arising from horizontal velocity shears of 517
larger-scale flows also has an important contribution to the total buoyancy-gradient 518
frontogenetic tendency (Figs. 15d and 15f). The external deformation term aF 519
approximately contributes 50% of positive totalF in the present case. The regions of 520
positive tendency term F correspond to a strong total frontogenetic tendency totalF 521
for the eddy fronts, explicitly showing that the external larger-scale straining effect is 522
a dominant contributor to the frontogenetic processes. In terms of the diagnosed 523
results, the vertical mixing tendency vkF has a relatively small contribution to the 524
total frontogenetic tendency (i.e., the Turbulent Thermal Wind mechanism) and does 525
not seem to be clearly important in the situation of present case. As yet, not much is 526
known about how common different mechanisms of frontogenesis might be globally, 527
and thus which interactions lead most often to submesoscale flows. 528
c. Cross-front secondary circulation 529
- 26 -
Under the impact of strain-induced frontogenesis, these weakly stratified fronts 530
with low PV are particularly active at the submesoscale and involve a range of 531
instabilities through competing with geostrophy and stratification (Taylor and Ferrari 532
2009; Callies et al. 2016). A zoom view of a front segment with positive frontogenetic 533
tendency is shown in Fig. 16. The local principal strain axes (Fig. 16b) tend to be 534
along the density front due to moderate frontogenesis, causing maximum stretching of 535
the ambient flows and intensifying the frontal baroclinicity. As a result, the 536
enhancement of lateral buoyancy gradients in the present case contributes a large 537
negative baroclinic component of frontal PV. Atmospheric forcing here is driving 538
nonconservative processes that destroy frontal PV by driving a surface buoyancy loss 539
(Figs. 16b and 16d). These dynamically coupled processes at submesoscale 540
effectively create favorable conditions for SI in the peripheral fronts of the eddy (Figs. 541
16c and 16d). Both of the frontal flow configurations and a positive frontogenetic 542
tendency will further contract the horizontal scale and increase Rossby number, 543
becoming more prone to ageostrophic dynamics and growing frontal instabilities 544
(McWilliams 2017). Only geostrophic modes are unstable where PV is positive 545
although smaller-scale shear instabilities are expected within the mixed layer 546
(Boccaletti et al. 2007). 547
Due to frontal submesoscale instabilities, an overturning ASC develops across 548
the front (Fig. 16c). The enhanced vertical velocity of the ASC increases the vertical 549
exchange but mostly within the mixed layer here rather than between the surface layer 550
and the oceanic interior. The overturning ASC tends to restratify the surface boundary 551
- 27 -
layer and restore geostrophic balance. As shown schematically in Fig. 17, the 552
cross-front ASC is conducive to driving a net frontal slumping and release of 553
geostrophic energy (e.g., Thomas and Lee 2005; Lapeyre et al. 2006; Taylor and 554
Ferrari 2010; Bachman et al. 2017). With the front weakening and geostrophic 555
adjustment, the geostrophic shear KE and frontal APE can be effectively extracted and 556
transferred into submesoscale turbulence. The diagnosis of this feature shows large 557
GSP and BFLUX in the frontal zone (not shown, similar to Fig. 11), suggesting an 558
effective downscale energy transformation from geostrophic flows to submesoscales. 559
The geostrophic KE and frontal APE extracted may provide an interpretation for the 560
energy dissipation of mesoscale eddies in the STCC upper ocean. Seasonal variations 561
in frontogenetic tendencies, nonlinear cascades, and instability rates and scales are 562
present and expected (Fig. 18; Dong et al. 2020, 2020a), although these changes are 563
not the focus of this paper which has emphasized wintertime conditions. 564
5. Summary 565
This paper examined the submesoscale processes of frontogenesis-related density 566
fronts in the eddy-active STCC upper ocean and revealed their important dynamical 567
impacts on the vertical exchange and energy transfer, using satellite observations, 568
high-resolution simulation and diagnostic analysis. Both of observations and 569
simulations indicate that the STCC submesoscale fronts characterized by a typical 570
lateral scale of O(10) km are marginally constrained by rotation and stratification, and 571
play important roles in the enhanced vertical communications and downscale energy 572
- 28 -
cascade of mesoscale eddies. As a result of the straining deformation of larger-scale 573
flows, the strain-induced frontogenesis and buoyancy advection are explicitly detected 574
to rapidly sharpen the peripheral density fronts of geostrophic eddy and conducive to 575
a PV destruction by atmospheric forced surface buoyancy loss. In the conditions 576
studied here, frontogenesis was dominantly induced by strain, rather than induced by 577
vertical mixing through the turbulent thermal wind mechanism or other forcing, as 578
verified through the McWilliams (2017) SCFT diagnostic theory. The enhanced 579
baroclinicity and nonconservative atmospheric forcing create favorable conditions for 580
frontal instabilities within the submesoscale range through sharpening fronts and 581
causing negative potential vorticity. As a response, the diagnostic results suggest these 582
density fronts undergoing an overturning ageostrophic secondary circulation (ASC), 583
which tends to restratify the surface boundary layer by driving a net frontal slumping 584
and restore geostrophic balance. By this process, the enhanced vertical velocity 585
induced by the ASC, reaching ~100 m day-1, substantially increase the vertical 586
exchanges of the STCC upper ocean. 587
As a byproduct of mesoscale eddies, the analysis results also indicate that these 588
submesoscale density fronts and their instabilities can facilitate a downscale energy 589
transfer from geostrophic flows. Both diagnostic geostrophic shear production (GSP) 590
and buoyancy production (BFLUX) are particularly large at the submesoscale fronts 591
and implicate an effective energy transformation from balanced geostrophic flows 592
toward submesoscale turbulence in the STCC system. These energies extracted from 593
larger-scale geostrophic flows finally will be dissipated by a wide variety of 594
- 29 -
small-scale instabilities and lead to an enhanced local mixing (Capet et al. 2008b; 595
Taylor and Ferrari 2009; Thomas et al. 2013; Bachman et al. 2017), although these 596
processes are only parameterized in the present simulations. Thus, these active density 597
fronts and their submesoscale processes (Figs. 17 and 18) can partly explain the 598
forward energy cascade of balanced geostrophic flows and enhanced fluxes in the 599
STCC upper ocean (e.g., Qiu et al. 2017; Su et al. 2018; Zhang et al. 2019), as well as 600
increased chlorophyll concentrations around the periphery of eddies (Fig. 6). 601
Further investigations and fine-resolution field campaigns, together with the 602
forthcoming Surface Water Ocean Topography (SWOT) mission, should be expected 603
to quantitatively discuss the complicated submesoscale behaviors and their seasonal 604
variations, as well as their contributions on the physical and biogeochemical budgets 605
of the oceans. Also, a physics-based parameterizations for submesoscales, such as for 606
some of these mechanisms (e.g., Fox-Kemper et al. 2008; Fox-Kemper et al. 2011; 607
Bachman et al. 2017), will reproduce aspects of these dynamics in climate and coarse 608
resolution ocean models. 609
- 30 -
Acknowledgements 610
We would like to thank Ruixin Huang of WHOI, who improved this manuscript 611
with helpful comments and fruitful discussions. The authors would also like to thank 612
GHRSST-PP (http://ghrsst-pp.metoffice.com/), GSFC of NASA 613
(http://oceancolor.gsfc.nasa.gov), NODC/NOAA (http://data.nodc.noaa.gov), 614
NCDC/NOAA (http://www.ncdc.noaa.gov), AVISO (http://www.aviso.altimetry.fr), 615
IFREMER (http://www.ifremer.fr), BODC (https://www.bodc.ac.uk), and APDRC 616
(http://apdrc.soest.hawaii.edu) for providing a suite of new satellite data and 617
reanalysis products. The records of Argo floats are acquired from the NODC of 618
NOAA (https://www.nodc.noaa.gov/argo/). Source data for ROMS simulations are 619
available at scientific database of South China Sea Institute of Oceanology 620
(www.scsio.csdb.cn). 621
This work is supported by the Original Innovation Project of Basic Frontier 622
Scientific Research Program of Chinese Academy of Sciences (CAS) 623
(ZDBS-LY-DQC011). Zhiyou Jing is sponsored by the Talents Team Project of 624
Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou) 625
(GML2019ZD0303), the National Natural Science Foundation of China (41776040, 626
NORC2020-07) and the Guangzhou Science and Technology Project (201904010420). 627
Baylor Fox-Kemper is supported in part by NSF 1350795 and in part by NOAA 628
NA19OAR4310366. Haijin Cao is supported by the National Natural Science 629
Foundation of China (51709092). Yan Du is supported by the National Natural 630
Science Foundation of China (41830538). 631
- 31 -
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- 46 -
Figure Caption List 922
FIG. 1. Schematic diagram of typical horizontal wavenumber spectra of upper ocean 923
kinetic energy (heavy black lines) at different spatial scales (color shading). The thin 924
gray lines denote k-2 and k-3 reference spectra at mesoscale and submesoscale ranges, 925
respectively. 926
FIG. 2. Root mean square (RMS) SSH variability (color shading and white contours) 927
in the Northwest Pacific Ocean based on high-pass filtered satellite altimeter data 928
from 1993-2016. Short black lines across the 137°E dashed-dotted transect demarcate 929
the boundaries of the Kuroshio, eastward-flowing Subtropical Countercurrent (STCC), 930
westward-flowing North Equatorial Current (NEC) and the wind-driven North 931
Equatorial Countercurrent (NECC) bands. The dark gray rectangular box with 932
relatively high eddy variability denotes the research domain of this paper. 933
FIG. 3. (a) Satellite-derived surface thermal fronts (color shading in 10-2 °C km-1) and 934
sea level anomalies (SLA) (white contours in m) from the daily GHRSST and AVISO 935
altimetry data on 24 January 2013. The black line with dots is the trajectory of Argo 936
float #2901191 travelling in the STCC band from July 2011 through March 2015. (b) 937
Vertical profiles of in situ temperatures measured by the Argo float #2901191 in the 938
upper ocean. The heavy black lines and thin gray lines represent the mixed layer depth 939
(MLD) and isothermals, respectively. The MLD is defined as the depth at which 940
potential density is different from the sea surface density by 0.03 . 941
- 47 -
FIG. 4. (a) A snapshot of SST (color shading in °C) in the West Pacific Ocean from 942
the parent ROMS0 simulation (~7.5 km resolution). Two boxes inside with 943
boundaries delineated by the heavy black lines and dotted lines denote the successive 944
nested domains for the child ROMS1 (~1.5 km resolution) and child ROMS2 (~500 m 945
resolution) simulations, respectively. 946
FIG. 5. Snapshots of surface Rossby number derived from (a) AVISO daily SLA data 947
(~25 km resolution), (b) parent ROMS0 simulation (~7.5 km resolution), (c) child 948
ROMS1 nesting simulation (~1.5 km resolution), and (d) child ROMS2 nesting 949
simulation (~500 m resolution) in winter. The successive refinement of spatial 950
resolution exhibits an increased submesoscale activities characterized by order one 951
Rossby numbers at the surface. 952
FIG. 6. (a) A snapshot of surface relative vorticity obtained from the highest 953
resolution ROMS2 simulation (~500 m). (b, c) Images of satellite-derived 954
phytoplankton pigment concentrations representing mesoscale eddies in August 19, 955
2014, and May 26, 2014, respectively. The fine structures of the ocean color images 956
show high chlorophyll concentrations at the periphery of mesoscale eddies with a 957
lateral scale of 5-30 km, which can be inferred from the AVSIO sea surface height 958
anomaly (black contours). 959
FIG. 7. Maps of real vertical velocity (color shading in m s-1) averaged over the MLD 960
from (a) parent ROMS0 (~7.5 km resolution) and (b) nested ROMS2 (~500 m 961
resolution) simulations. (c) Component of vertical velocity contributed by the motions 962
of a wavelength > 20 km, which is calculated from the ROMS2 simulation (shown in 963
- 48 -
panel (b)) by Gaussian filtering to cut off the contribution of the horizontal scale at < 964
20 km. The black contours in each panel show the SSH anomalies. The attached each 965
panel on the right side denotes the zonal mean of frontal vertical velocity w (m s-1). 966
FIG. 8. Wavenumber spectra of SSH from the simulations of different resolutions 967
(~7.5 km, ~1.5 km, and ~500 m). The gray line segment marked on the top axis 968
denotes the scale of 2π times the local first-mode deformation radius. As a reference, 969
the spectral slopes of k-5 and k-11/3 are shown as the heavy gray lines. The dashed lines 970
roughly show the slope transitions. 971
FIG. 9. (a-b) Snapshots of diagnostic parameters averaged over the MLD for (a) 972
frontal sharpness ( 4M ) (color shading in s-4) and Ertel PV ( hq ) (color shading in s-3). 973
(c) Atmospheric forced surface buoyancy loss ( 0B ) (W kg-1) along the representative 974
20°N transect. (d) Vertical section of Ertel PV (color shading in s-3) along the 20°N 975
transect. The blue line segments shown in panel (a) are the local principal strain axes 976
( p) of density fronts. The SSH anomalies are shown as the black contours in panels 977
(a-b). The heavy black line and thin gray contours in panel (d) denote the MLD and 978
isopycnal surfaces with a spacing of 0.3 kg m-3, respectively. 979
FIG. 10. (a-b) Snapshots of diagnostic parameters associated with frontogenetic strain 980
for (a) advective frontogenetic tendency ( F ) (color shading in s-5) and (b) the 981
difference between absolute vorticity and strain rate magnitude ( A St ) (color shading 982
in s-1). (c) The mean of vertical velocity over the MLD of 20°N transect (m s-1). (d) 983
Vertical section of vertical velocity (color shading in m s-1) along the 20°N transect. 984
The parameters in panels (a-b) are vertical averages over the MLD, similar to FIG. 9. 985
- 49 -
The black contours in panels (a-b) show the SSH anomalies. The heavy black line in 986
panel (d) refers to the MLD of the 20°N transect, where the meridional geostrophic 987
currents are shown as the solid gray contours (northward) and dashed gray contours 988
(southward), respectively. 989
FIG. 11. Snapshots of diagnostic parameters associated with downscaling energy 990
transformation for (a) GSP (color shading in W kg-1) and (b) buoyancy flux (BFLUX) 991
(color shading in W kg-1). Both parameters are vertical averages over the MLD. The 992
black contours shown in each panel denote the SSH anomalies from the 993
high-resolution ROMS2 simulation, similar to FIG. 9 and FIG. 10. 994
FIG. 12. Three-dimensional images of a single mesoscale eddy from the 995
high-resolution ROMS2 simulation. (a) Temperature at the upper surface and along 996
the side boundaries (color shading in °C); (b) frontal sharpness in the upper surface 997
(color shading in s-4) and vertical velocity along the side boundaries (color shading in 998
m s-1). The gray vectors in the upper surface of panels (a) and (b) show the surface 999
currents. The thin gray contours with arrows along the side boundaries in each panel 1000
indicate streamlines. The black contours along the side boundaries of panel (b) denote 1001
isopycnal surfaces with a spacing of 0.2 kg m-3. 1002
FIG. 13. Different aspects of submesoscale features in the eddy shown in FIG. 12. (a) 1003
relative vorticity ( ) (color shading in s-1); (b) baroclinic component of Ertel PV 1004
( hq ) in the upper surface (color shading in s-3) and vertical velocity at the side 1005
boundaries (color shading in m s-1). The vectors in the upper surface of panels (a) and 1006
(b) show the surface currents. The thin gray contours with arrows along the side 1007
- 50 -
boundaries in each panel indicate streamlines. The black contours along the side 1008
boundaries of panel (b) denote isopycnal surfaces with a spacing of 0.2 kg m-3, similar 1009
to FIG. 12. 1010
FIG. 14. Different aspects of the eddy shown in FIG. 12. (a) Advective frontogenetic 1011
tendency ( F ) at the upper surface (color shading in s-5) and Ertel PV along the side 1012
boundaries (color shading in s-3); (b) full three-dimensional Ertel PV (color shading in 1013
s-3). The gray vectors in the upper surface of each panel show the surface currents. 1014
The green contours at the upper surface of panel (b) denote the value of 0.3 for gRi . 1015
The thin gray contours with arrows along the side boundaries of each panel depict 1016
streamlines. 1017
FIG. 15. Different terms of buoyancy-gradient frontogenetic tendency (s-5) at the 1018
upper surface of the eddy shown in FIG. 12. (a) Geostrophic self-straining tendency 1019
term ( gF ); (b) ageostrophic vertical straining tendency term ( wF ); (c) ageostrophic 1020
buoyancy advection tendency term ( aF ); (d) external straining deformation tendency 1021
term ( F ); (e) vertical mixing tendency term (v
F ); and (f) total buoyancy-gradient 1022
frontogenetic tendency ( totalF ). 1023
FIG. 16. Magnified structure of a front segment in the mesoscale eddy of FIG. 12. (a) 1024
Surface density (color shading in kg m-3) and currents (vectors); (b) frontal sharpness 1025
( 4M ) (color shading in s-4), where the blue lines refer to the local principal strain axis 1026
and green contours show the contours of atmosphere forced surface buoyancy loss 1027
along the front; (c) density distribution along a cross-front transect (black dashed line 1028
in panel (a)), where the pink and blue contours show the positive/negative vertical 1029
- 51 -
velocities in the left/right sides of the front. The red ellipse with arrows schematically 1030
delineates the overturning cell driven by cross-front ageostrophic secondary 1031
circulation with upwelling ( +w ) on the light side ( - ) and downwelling ( -w ) on the 1032
dense side ( + ) of the front; (d) frontal Ertel PV (color shading in s-3). The black 1033
contours in panels (a) and (d) denote the sea surface height anomalies. 1034
FIG. 17. Schematic diagram of a typical submesoscale density front and cross-front 1035
ageostrophic secondary circulation that tends to slump isopycnals and restratify the 1036
surface boundary layer by submesoscale instabilities. With geostrophic adjustment 1037
and subsequent slumping of isopycnals, the geostrophic KE and APE can be 1038
effectively extracted and downscale transferred towards submesoscale turbulence at 1039
rates of GSP and BFLUX, respectively. 1040
FIG. 18. (a) Maps of surface relative vorticity from successive nested simulations at 1041
different resolutions (~7.5 km, ~1.5 km, and ~500 m) in the Western Pacific Ocean. 1042
Active submesoscale fronts and filaments with increased surface relative vorticity can 1043
be detected in the black boxes inside; (b) Time series of RMS advective frontogenetic 1044
tendency, vertical velocity, GSP, and BFLUX averaged over the MLD of ROMS2. 1045
Two boxes inside of panel (a) with boundaries delineated by the heavy black lines and 1046
dotted lines denote the nested domains for the child ROMS1 (~1.5 km resolution) and 1047
child ROMS2 (~500 m resolution) simulations, respectively. 1048
1
1
1
1
1
1
Fig1050
1051
FIG1055
kine1056
gray1057
resp1058
gures
G. 1. Schem
etic energy
y lines deno
pectively.
matic diagram
(heavy blac
ote k-2 and k
m of typica
ck lines) at
k-3 reference
- 52 -
al horizonta
different sp
e spectra at
l wavenumb
patial scales
t mesoscale
ber spectra
s (color sha
and subme
of upper o
ading). The
esoscale ran
cean
thin
nges,
1
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1
1
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1
1056
FIG1063
in t1064
from1065
the 1066
wes1067
Equ1068
rela1069
G. 2. Root m
the Northw
m 1993-201
boundaries
stward-flow
uatorial Co
atively high
mean square
est Pacific
6. Short bla
of the Kuro
wing North
untercurren
eddy variab
e (RMS) SS
Ocean bas
ack lines ac
oshio, eastw
Equatorial
nt (NECC)
bility denote
- 53 -
SH variabili
sed on high
cross the 13
ward-flowin
l Current
bands. Th
es the resea
ity (color sh
h-pass filter
7°E dashed
ng Subtropic
(NEC) and
he dark gr
arch domain
hading and w
red satellite
d-dotted tran
cal Counter
d the wind
ray rectang
n of this pap
white conto
e altimeter
nsect demar
rcurrent (ST
d-driven N
gular box
per.
ours)
data
rcate
TCC),
North
with
1
1
1
1
1
1
1
1
1
1064
FIG1072
sea 1073
altim1074
floa1075
Vert1076
upp1077
(ML1078
pote1079
G. 3. (a) Sat
level anom
metry data
at #2901191
tical profile
per ocean. T
LD) and is
ential densit
ellite-derive
malies (SLA)
on 24 Janua
1 travelling
es of in situ
The heavy bl
othermals,
ty is differe
ed surface t
) (white con
ary 2013. T
in the STC
u temperatur
lack lines an
respectively
nt from the
- 54 -
thermal fron
ntours in m)
The black li
CC band from
ures measure
nd thin gray
ly. The ML
sea surface
nts (color sh
) from the d
ine with dot
m July 201
ed by the A
y lines repre
LD is defin
e density by
hading in 10
daily GHRS
ts is the traj
1 through M
Argo float #
esent the mi
ned as the d
y 0.03 .
0-2 °C km-1)
SST and AV
ajectory of A
March 2015
#2901191 in
ixed layer d
depth at w
) and
VISO
Argo
5. (b)
n the
depth
which
1
1
1
1
1
1
1073
FIG1078
the 1079
bou1080
nest1081
reso1082
G. 4. (a) A s
parent RO
undaries deli
ted domains
olution) sim
snapshot of
OMS0 sim
ineated by t
s for the chi
mulations, re
f SST (color
mulation (~
the heavy b
ild ROMS1
espectively.
- 55 -
r shading in
~7.5 km re
black lines a
(~1.5 km r
n °C) in the
esolution).
and dotted l
resolution) a
e West Paci
Two boxe
lines denote
and child RO
ific Ocean f
es inside
e the succes
OMS2 (~50
from
with
ssive
00 m
1
1
1
1
1
1
1
1079
FIG1085
(~251086
ROM1087
simu1088
reso1089
Ros1090
G. 5. Snapsh
5 km resolu
MS1 nestin
ulation (~5
olution exhi
ssby number
hots of surfa
ution), (b)
ng simulati
500 m reso
ibits an inc
rs at the sur
ace Rossby
parent ROM
ion (~1.5 k
olution) in
creased sub
rface.
- 56 -
number de
MS0 simul
km resoluti
winter. Th
bmesoscale
erived from
lation (~7.5
ion), and (
he success
activities c
(a) AVISO
5 km resolu
(d) child R
ive refinem
characterized
daily SLA
ution), (c) c
ROMS2 nes
ment of sp
d by order
data
child
sting
patial
one
1
1
1
1
1
1
1
1
1093
FIG1094
reso1095
phy1096
2011097
show1098
later1099
anom1100
G. 6. (a) A
olution RO
ytoplankton
4, and May
w high chl
ral scale of
maly (black
A snapshot
OMS2 simu
pigment co
y 26, 2014,
lorophyll co
f 5-30 km,
k contours).
of surface
ulation (~5
oncentration
respectivel
oncentration
which can
- 57 -
e relative
500 m).
ns represen
ly. The fine
ns at the p
be inferred
vorticity o
(b, c) Im
nting mesos
e structures
eriphery of
d from the
btained fro
mages of s
cale eddies
of the ocea
f mesoscale
AVSIO sea
om the hig
satellite-der
s in August
an color im
e eddies wi
a surface he
ghest
rived
t 19,
mages
ith a
eight
1
1
1
1
1
1
1
1
1094
FIG1101
from1102
reso1103
of a1104
pan1105
20 k1106
pan1107
G. 7. Maps
m (a) paren
olution) sim
a wavelengt
el (b)) by G
km. The bla
el on the rig
of vertical
nt ROMS0
mulations. (c
th > 20 km,
Gaussian filt
ack contour
ght side den
velocity (c
(~7.5 km
c) Compone
which is ca
tering to cu
s in each pa
notes the zon
- 58 -
color shadin
m resolution
ent of vertic
alculated fr
ut off the co
anel show t
nal mean of
ng in m s-1
n) and (b)
al velocity
rom the RO
ontribution o
the SSH ano
f frontal ver
) averaged
nested RO
contributed
MS2 simula
of the horiz
omalies. Th
rtical veloci
over the M
OMS2 (~50
d by the mot
ation (show
zontal scale
he attached
ity w (m
MLD
0 m
tions
wn in
at <
each
s-1).
1
1
1
1
1
1
1102
FIG1107
(~7.1108
den1109
the 1110
roug1111
G. 8. Waven
.5 km, ~1.5
otes the sca
spectral slo
ghly show t
number spe
5 km, and
ale of 2π tim
opes of k-5 a
the slope tra
ectra of SS
~500 m). T
mes the loc
and k-11/3 are
ansitions.
- 59 -
SH from the
The gray l
cal first-mod
e shown as t
e simulation
ine segmen
de deformat
the heavy g
ns of differ
nt marked o
tion radius.
ray lines. T
rent resolut
on the top
As a refere
The dashed l
tions
axis
ence,
lines
1107
F1108
(1109
s1110
E1111
a1112
c1113
a1114
FIG. 9. (a-b
( 4M ) (colo
surface buo
Ertel PV (co
are the local
contours in
and isopycn
b) Snapshot
or shading
yancy loss
olor shading
l principal s
panels (a-b
nal surfaces
ts of diagno
in s-4) and
( 0B ) (W kg
g in s-3) alo
strain axes (
b). The heav
with a spac
ostic parame
Ertel PV (
g-1) along th
ong the 20°N
( p) of den
vy black lin
cing of 0.3 k
- 60 -
eters averag
( hq ) (colo
he represent
N transect.
nsity fronts.
ne and thin
kg m-3, resp
ged over th
or shading
tative 20°N
The blue li
The SSH a
gray contou
pectively.
e MLD for
in s-3). (c)
N transect. (
ine segment
nomalies ar
urs in panel
(a) frontal
Atmosphe
(d) Vertical
nts shown in
re shown as
l (d) denote
sharpness
eric forced
section of
n panel (a)
s the black
e the MLD
1115
F1116
a1117
v1118
o1119
s1120
s1121
i1122
s1123
FIG. 10. (a
advective fr
vorticity and
over the ML
s-1) along th
similar to FI
in panel (d)
shown as th
a-b) Snapsh
rontogenetic
d strain rate
LD of 20°N
he 20°N tra
IG. 9. The b
refers to th
he solid gray
hots of dia
c tendency (
e magnitude
N transect (m
ansect. The
black conto
he MLD of
y contours (
agnostic par
( F ) (color
e ( A St ) (c
m s-1). (d) V
parameters
urs in panel
f the 20°N tr
northward)
- 61 -
rameters as
shading in
color shadin
Vertical sect
s in panels
ls (a-b) sho
transect, wh
and dashed
ssociated w
s-5) and (b)
ng in s-1). (
tion of verti
(a-b) are v
w the SSH
here the mer
d gray conto
with frontog
the differen
c) The mea
ical velocity
vertical aver
anomalies.
ridional geo
ours (southw
genetic stra
nce betwee
an of vertica
y (color sha
rages over
The heavy
ostrophic cu
ward), respe
ain for (a)
n absolute
al velocity
ading in m
the MLD,
black line
urrents are
ectively.
1
1
1
1
1
1
1125
FIG1130
tran1131
(col1132
blac1133
high1134
G. 11. Snap
nsformation
lor shading
ck contour
h-resolution
pshots of d
for (a) GSP
in W kg-1)
rs shown
n ROMS2 si
diagnostic p
P (color sha
. Both para
in each p
imulation, s
- 62 -
parameters
ading in W k
ameters are
panel deno
similar to FI
associated
kg-1) and (b
vertical ave
ote the SS
IG. 9 and F
with down
b) buoyancy
erages over
SH anoma
IG. 10.
nscaling en
y flux (BFL
r the MLD.
alies from
nergy
UX)
The
the
1
1
1
1
1
1
1
1
1
1131
FIG1139
high1140
the 1141
(col1142
m s1143
curr1144
indi1145
isop1146
G. 12. Th
h-resolution
side bound
lor shading
s-1). The gra
rents. The t
icate stream
pycnal surfa
hree-dimens
n ROMS2 s
daries (color
in s-4) and
ay vectors i
hin gray co
mlines. The b
aces with a s
ional imag
simulation.
r shading in
vertical vel
in the uppe
ontours with
black conto
spacing of 0
- 63 -
ges of a
(a) Temper
n °C); (b) f
locity along
er surface o
h arrows alo
ours along th
0.2 kg m-3.
single me
rature at th
frontal sharp
g the side bo
f panels (a)
ong the side
he side boun
esoscale e
e upper sur
pness in the
oundaries (c
) and (b) sh
e boundarie
ndaries of p
eddy from
rface and a
e upper sur
color shadin
how the sur
es in each p
panel (b) de
the
along
rface
ng in
rface
panel
enote
1
1
1
1
1
1
1
1
1
1140
FIG1148
rela1149
( hq1150
bou1151
(b) 1152
bou1153
bou1154
to F1155
G. 13. Differ
ative vortici
h ) in the u
undaries (co
show the s
undaries in
undaries of p
FIG. 12.
rent aspects
ity ( ) (co
upper surfa
lor shading
surface cur
each panel
panel (b) de
s of submes
olor shading
ce (color s
in m s-1). T
rrents. The
l indicate s
enote isopyc
- 64 -
soscale featu
g in s-1); (b
shading in
The vectors
thin gray
streamlines.
cnal surface
ures in the e
b) baroclini
s-3) and ve
in the uppe
contours w
. The black
es with a spa
eddy shown
ic compone
ertical veloc
er surface o
with arrows
k contours
acing of 0.2
n in FIG. 12
ent of Ertel
city at the
of panels (a)
along the
along the
2 kg m-3, sim
2. (a)
l PV
side
) and
side
side
milar
1
1
1
1
1
1
1
1
1149
FIG1156
tend1157
bou1158
s-3).1159
The1160
The1161
stre1162
G. 14. Diffe
dency ( F )
undaries (co
. The gray
e green cont
e thin gray
amlines.
rent aspects
) at the uppe
lor shading
vectors in t
tours at the
contours w
s of the edd
er surface (
in s-3); (b)
the upper s
upper surfa
with arrows
- 65 -
dy shown in
(color shadi
full three-d
surface of e
face of pane
along the
n FIG. 12. (
ing in s-5) an
dimensional
each panel
el (b) denot
side bound
a) Advectiv
nd Ertel PV
Ertel PV (c
show the su
e the value
daries of eac
ve frontogen
V along the
color shadin
urface curr
of 0.3 for
ch panel de
netic
side
ng in
ents.
gRi .
epict
1
1
1
1
1
1
1
1157
FIG1163
upp1164
term1165
buo1166
term1167
fron1168
G. 15. Diffe
per surface o
m ( gF ); (b)
oyancy adve
m ( F ); (e)
ntogenetic te
ferent terms
of the eddy
ageostroph
ection tende
vertical mi
endency ( F
s of buoyan
y shown in
hic vertical
ency term (
ixing tenden
totalF ).
- 66 -
ncy-gradien
FIG. 12. (a
straining t
aF ); (d) ex
ncy term ( F
nt frontogen
a) Geostroph
tendency te
xternal strain
vF ); and (
netic tenden
hic self-stra
rm ( wF ); (c
ning deform
(f) total buo
ncy (s-5) at
aining tende
c) ageostro
mation tende
oyancy-grad
t the
ency
ophic
ency
dient
1
1
1
1
1
1
1
1
1
1
1
1
1175
FIG1176
Surf1177
( M1178
and 1179
alon1180
in p1181
velo1182
deli1183
circ1184
den1185
cont1186
G. 16. Magn
face density
4 ) (color sh
green cont
ng the front
panel (a)), w
ocities in th
ineates the
culation with
se side ( +
tours in pan
nified struct
y (color sha
hading in s-4
tours show
t; (c) density
where the p
e left/right
e overturni
h upwelling
+) of the fr
nels (a) and
ture of a fro
ading in kg
4), where th
the contou
y distributio
pink and bl
sides of the
ng cell d
g ( +w ) on th
ront; (d) fro
(d) denote
- 67 -
ont segment
m-3) and cu
he blue lines
urs of atmo
on along a c
lue contour
e front. The
driven by
he light side
ontal Ertel
the sea surf
in the meso
urrents (vec
s refer to the
osphere forc
cross-front
rs show the
red ellipse
cross-front
e ( - ) and
PV (color
face height a
oscale eddy
tors); (b) fr
e local princ
ced surface
transect (bl
e positive/ne
with arrow
ageostrop
d downwelli
shading in
anomalies.
y of FIG. 12
rontal sharp
cipal strain
e buoyancy
lack dashed
negative ver
ws schematic
phic secon
ing ( -w ) on
s-3). The b
2. (a)
pness
axis
loss
d line
rtical
cally
ndary
n the
black
1
1
1
1
1
1
1
1176
FIG1182
ageo1183
surf1184
and 1185
effe1186
rate1187
G. 17. Schem
ostrophic se
face bounda
subsequen
ectively extr
es of GSP an
matic diagr
econdary ci
ary layer b
nt slumping
racted and
nd BFLUX,
ram of a typ
irculation th
by submeso
g of isopy
downscale
, respectivel
- 68 -
pical subme
hat tends to
oscale instab
ycnals, the
transferred
ly.
esoscale de
o slump iso
bilities. Wi
geostrophi
d towards su
nsity front
opycnals an
th geostrop
ic KE and
ubmesoscal
and cross-f
nd restratify
phic adjustm
d APE can
le turbulenc
front
y the
ment
n be
ce at
1
1
1
1
1
1
1
1
1
1183
FIG1191
diffe1192
Act1193
be d1194
tend1195
Two1196
dott1197
chil1198
G. 18. (a) M
ferent resolu
ive submes
detected in t
dency, verti
o boxes insi
ted lines den
ld ROMS2 (
Maps of surf
utions (~7.5
oscale front
the black bo
ical velocity
ide of panel
note the nes
(~500 m res
face relative
5 km, ~1.5
ts and filam
oxes inside;
y, GSP, and
l (a) with bo
sted domain
solution) sim
- 69 -
e vorticity f
km, and ~5
ments with i
; (b) Time s
d BFLUX
oundaries d
ns for the ch
mulations, r
from succes
500 m) in th
ncreased su
series of RM
averaged o
elineated by
hild ROMS
respectively
ssive nested
he Western
urface relativ
MS advectiv
ver the ML
y the heavy
1 (~1.5 km
y.
d simulation
n Pacific Oc
ive vorticity
ve frontogen
LD of ROM
y black lines
resolution)
ns at
cean.
y can
netic
MS2.
s and
) and