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

qq

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

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Fig1050

1051

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k-3 reference

- 52 -

al horizonta

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l wavenumb

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- 53 -

SH variabili

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ward-flowin

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- 54 -

thermal fron

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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

1 submesoscale density fronts and their dynamical impacts ... · - 1 - 1 submesoscale density...

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