1. Introduction

The transfer of mixed layer water into the pycnocline, referred to as subduction, sets the flux of heat and tracers from the surface mixed layer into the stratified ocean interior. Previous numerical studies (Samelson and Chapman 1995; Spall 1995; Wang 1993) find that frontogenesis at a meandering density front can induce a three-dimensional (3D) ageostrophic cross-front circulation that subducts surface water into or below the pycnocline, which can result in the formation of weakly stratified submesoscale lenses with anticyclonic vorticity. Such lenses have been observed in the proximity of ocean fronts (e.g., Pollard and Regier 1992; Aoki and Akitomo 2007), suggesting that subduction due to frontal meandering (referred to as frontal subduction) could play a role in generating subsurface eddies.

Subducted water found below the seasonal pycnocline can generally be traced back to the wintertime mixed layer. For example, in the Japan/East Sea waters with properties of the wintertime mixed layer, that is, with low potential temperature (1°–3°C) and high dissolved oxygen (>6.5 ml l⁻¹), have been observed in the salinity minimum (<34.05 psu) layer in the lower pycnocline (Kim and Chung 1984). This example suggests that “wintertime” subduction can contribute to the transfer of surface water into the ocean interior, a process that could play an important role in setting the decadal variability of the ocean–atmosphere climate system (e.g., Latif and Barnett 1994). However, severe wintertime sea and atmospheric conditions make direct observations of winter frontal subduction difficult, and hence our knowledge of the process is limited.

Recently, despite such severe conditions, extensive wintertime surveys of the subpolar front of the Japan Sea have been conducted (Lee et al. 2006). In these surveys, submesoscale lenses of mixed layer water were found beneath the front and were interpreted as direct evidence of frontal subduction. The observations were made during periods of intense atmospheric forcing (where mean wind stress magnitudes exceeded 0.25 N m⁻² and mean surface heat loss was larger than 300 W m⁻²), suggesting that subduction at the subpolar front was likely affected by the atmospheric conditions.

The influence of wind forcing on frontal subduction has been investigated in several studies. Lee et al. (1994) and Thompson (2000) showed that winds can intensify 2D ageostrophic cross-front circulation. Thomas and Lee (2005) investigated a generation mechanism for secondary cross-front circulations by downfront (i.e., oriented along the frontal jet) wind forcing in which convergence/divergence of nonlinear Ekman transport (i.e., modified by the vorticity of the frontal jet) and mixing due to Ekman transport of denser water over light play critical roles. Mahadevan and Tandon (2006) performed 3D numerical experiments of an ocean front forced by downfront winds and found that the formation of strong frontal downdrafts could be explained by convergence of nonlinear Ekman transport.

Frontal subduction under surface cooling was investigated by Yoshikawa et al. (2001) using a 3D numerical model. In this study it was found that convection driven by heat loss intensifies the ageostrophic circulation and frontal subduction by reducing the potential vorticity (PV) and enhancing the geostrophic forcing (i.e., a driving force for frontal vertical circulation associated with shear/strain of the geostrophic flow). Nagai et al. (2006) examined the effect of diapycnal mixing on the 2D secondary circulation at an ocean front using the semigeostrophic omega equation and showed that the secondary circulation is intensified by vertical mixing.

The aforementioned studies considered the effects of winds and cooling on the ageostrophic vertical circulation and frontal subduction separately. In the present study, 3D nonhydrostatic numerical experiments of an ocean front forced by both cooling and winds are performed to explore whether both types of forcing simultaneously reinforce the frontal ageostrophic flow and subduction and to quantify the relative contributions of wind and cooling to the generation of ageostrophic motions and the transfer of surface waters to the ocean interior.

The paper is outlined as follows. In section 2, the nonhydrostatic model and its configuration is described. Frontal subduction simulated with and without atmospheric forcing is presented in section 3. The effects of wind and cooling on the ageostrophic vertical circulation and on frontal subduction are examined in sections 4 and 5. In section 6, a comparison of the results from the numerical experiments with observations from the Japan Sea is discussed. Finally, concluding remarks are stated in section 7.

2. Model configuration

A rectangular domain with coordinates (x, y, z) denoting the zonal, meridional, and vertical directions, respectively, is considered (Fig. 1). The dimensions of the model domain are 500 km (L_x), 250 km (L_y), and 500 m (D) in the x, y, and z directions. The initial conditions used in the experiments are characterized by an intense upper-ocean density front with water of low temperature, low salinity, and high density on its northern side (referred to as subpolar water) and water of high temperature, high salinity, and low density (referred to as subtropical water) to its south. Experiments with and without wintertime atmospheric forcing (southeastward wind stress and/or cooling) are performed. Although the hydrographic structure and atmospheric forcing are meant to represent those of the Japan Sea, the main results of the experiments should be applicable to frontal subduction in other regions.

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A schematic of the model configuration: contours and gray shading represent the initial density and velocity profiles.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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The governing equations used in the model are the nonhydrostatic momentum equations, the continuity equation, advection–diffusion equations for temperature (T) and salinity (S), and the equation of state for seawater (Bryden 1973):

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where u = (u, υ, w) is the velocity vector, ρ is the in situ water density, p is pressure, and is the vertical unit vector. The fluid is assumed to be incompressible and Boussinesq. The reference frame rotates about the vertical axis, with the corresponding Coriolis parameter (f = 10⁻⁴ s⁻¹) being constant for simplicity. The reference density (ρ₀ = 1027 kg m⁻³), gravitational acceleration (g = 9.8 m s⁻²), and horizontal eddy viscosity (ν_H = 10 m² s⁻¹) and diffusivity (κ_H = 5 m² s⁻¹) are constant. Differing forms for the eddy viscosity and diffusivity were used for the forced and unforced experiments. In the unforced experiments, small vertical eddy viscosity (ν_V = 10⁻⁴ m² s⁻¹) and diffusivity (κ_V = 5 × 10⁻⁵ m² s⁻¹) were used to avoid artificially smoothing the gradients of the initial pycnocline. However, using such a small eddy viscosity in the forced experiments produces an unrealistically thin surface boundary layer. To avoid this, the vertical eddy viscosity and diffusivity was set to increase linearly in z from 50 m depth to the surface by a factor of 100 in the forced experiments. Increasing the eddy viscosity and diffusivity near the surface is a crude parameterization for subgrid turbulence driven by atmospheric forcing. Increasing the eddy diffusivity corresponds to external cooling (buoyancy loss) applied at subsurface grid levels as a parameterization of thermal boundary layer (e.g., Jones and Marshall 1993). A viscosity that increases in the vertical has not been widely implemented in the past but is not inconsistent with recent estimations from observed wind-driven flows (Chereskin 1995; Yoshikawa et al. 2007) and large-eddy simulations of the wind-driven Ekman flow (Zikanov et al. 2003). The thickness of the simulated surface boundary layer estimated from vertical profiles of temperature is about 50 m in the forced experiments.

The initial potential temperature (simply referred to as temperature hereafter) and salinity distributions are given by

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and are shown in Fig. 2. A random perturbation is also added to the initial temperature field to excite instabilities. The subpolar front is centered at Y_j = L_y/2, with a characteristic width W_j = 20 km. The temperature and salinity differences across the front at the surface (T_m and S_m) are 6°C and 0.2 psu. At the center of the front, temperature decreases from 10°C (T_υ + T_b) at the surface to 0.5°C (T_b) at the bottom, while salinity is kept constant at 34.06 psu (S_b). The subpolar (subtropical) water is thus identified as water with salinity less (more) than 34.06 psu. The pycnocline depth (h) is 125 m. The initial velocity field consists of an eastward, geostrophically balanced frontal jet that is calculated using the bottom as the level of no motion. These initial conditions are determined from the climatological hydrography of the subpolar front of the Japan Sea.

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Cross-front section of the initial potential temperature [solid contours, contour interval (CI) = 1.0°C], zonal velocity (dashed contours, CI = 5 cm s⁻¹), and salinity anomaly (color shadings). The salinity anomaly is defined as salinity −S_b (34.06 psu).

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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No-normal flow, stress, and constant-flux boundary conditions are used on lateral boundaries at the surface and bottom:

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where (τ_x, τ_y) is the wind stress, H is heat flux at the surface, and C_w (=3900 J kg⁻¹ °C⁻¹) is the specific heat of water. Cyclic boundary conditions are applied in the zonal direction. At the northern and southern edges of the domain (y = 0, L_y) there are walls with free-slip and zero-flux boundary conditions. In the experiments with wind stress, however, using walls at y = 0, L_y would drive vertical motions near the boundaries that would significantly modify the temperature and salinity fields. To avoid this undesirable effect, in the wind-forced experiments the north–south extent of the domain is doubled and periodic boundary conditions are applied at y = 0, 2L_y. The initial temperature and salinity fields in the extended region (L_y ≤ y ≤ 2L_y) are a mirror image of those between y = 0 and L_y. By including two fronts with currents of opposite direction, the effect of wind direction relative to frontal orientation on subduction can be investigated as well.

To better characterize subduction of mixed layer water, the time evolution of a passive tracer of concentration C is calculated by solving an equation of the same form as (3). At t = 0, C is zero everywhere, but subsequently it is set to one at the surface for the duration of the experiment. On all other boundaries the flux of C normal to the boundary is zero. Thus, water with high tracer concentration corresponds to fluid originating from the surface, whereas water with low tracer concentration originates in the interior. For both forced and unforced experiments the eddy diffusivity of C is equal to the diffusivities of temperature and salinity used in the forced runs.

Integration of the governing equations is performed using the numerical model of Yoshikawa et al. (2001), which has been used to simulate convective motion and frontal updrafts and downdrafts under surface cooling. The model uses the SMAC scheme of Amsden and Harlow (1970). Derivatives are approximated by second-order finite differences except for the tracer advection term for which a first-order upwind scheme is partially mixed with a second-order central difference scheme. As in previous studies (e.g., Haine and Marshall 1998), a small grid size (Δx = Δy = 244 m, Δz = 15–50 m) and a short time interval (Δt = 108 s) are used to resolve convective plumes. The integration is continued until the front develops meanders and becomes fully three-dimensional and the initial frontal structure is completely distorted.

3. Results

Four experiments are performed: a reference experiment without surface forcing (R-EXP), an experiment driven by surface cooling only (C-EXP), an experiment forced by only wind stress (W-EXP), and an experiment with both surface cooling and wind stress (CW-EXP). The surface heat loss, H = −300 W m⁻², and southeastward wind stress of magnitude 0.25 N m⁻² used to force the simulations are based on the time-mean atmospheric forcing measured during a winter survey of the subpolar front of the Japan Sea (Lee et al. 2006).

The southeastward wind stress has a downfront (upfront) component relative to the eastward (westward) flowing frontal jet in the region between y = 0 and y = L_y (y = L_y and y = 2L_y). At the front with the westward jet, the upfront wind drives Ekman flow in a layer ~50 m thick that transports water from the lighter to denser side of the front, releasing available potential energy and, hence, reducing the energy source for baroclinic instability. As a result, frontal meandering, ageostrophic circulation, and subduction are suppressed at this front (not shown). Therefore, the focus of the analysis in this paper will be on the dynamically more interesting front with the eastward flowing frontal jet.

In the next subsection, the results of the unforced experiment (R-EXP) are described. In the following subsection, these results are compared with those of the cooling and wind-forced experiment (CW-EXP) to highlight the effects of surface forcings. Finally, the results of the cooling-forced experiment (C-EXP) and the wind-forced experiment (W-EXP) are described to isolate the respective effects of surface cooling and wind stress.

a. Unforced experiment (R-EXP)

In the unforced experiment, finite-amplitude baroclinic waves with wavelengths 80–100 km develop by day 40 (Fig. 3a). Later on in the experiment, frontal meanders pinch off to form cyclonic cold-core and anticyclonic warm-core eddies that propagate to the south and north, respectively (Fig. 3b). These eddies are surface intensified and can be identified in the surface temperature or density fields. Subsurface vortices, on the other hand, are easily identified using the salinity field at 200-m depth. For example, to the south of the front, subsurface anticyclonic eddies (SSACEs) are easily identified as coherent structures with anomalously low salinity. Such eddies typically form on the upstream side of surface cyclonic eddies (SCEs). To the north of the front, saline subsurface cyclonic eddies are found on the upstream side of surface anticyclonic eddies. An interaction between surface and subsurface eddies propels such vortex pairs away from the front and induces eddy fluxes of heat and tracers in the meridional direction (Spall 1995).

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Surface temperature (contours, CI = 1°C), surface horizontal velocity (vectors), and salinity anomaly at 200-m depth (color shadings) evaluated at (a) day 40 and (b) day 50 of R-EXP.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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As the baroclinic waves grow, updrafts and downdrafts are formed along the meandering front (Fig. 4). Downdrafts (updrafts) are found on the upstream (downstream) side of meander troughs (which are marked by a southward excursion of the subpolar water) where the cross-front velocity is directed from the denser (lighter) to the lighter (denser) side of the front. A vertical section of a frontal downdraft is shown in Fig. 5a. Water from the denser side of the front is transported to the south across the front and subducted into and below the pycnocline by the frontal downdraft. The vertical motion in the downdraft drives vortex squashing, which generates anticyclonic vorticity and leads to the formation of the SSACE shown in Fig. 3b. A patch or lens of less saline subpolar water that originated near the surface can be found in the lower pycnocline at the top of the SSACE (Fig. 5b). Note that not all of the subpolar water near the downdraft descends into the lower pycnocline, but some of it is instead transported along the front and entrained in the upper portion of the SCE (Fig. 5b). In the region of the updraft, the saline subtropical water is upwelled, transported northward, and entrained into both the surface anticyclonic eddy and the lower part of the SCE (Fig. 5b). This 3D advection of tracers can be seen in the temperature–salinity relation of water in the SCE and SSACE (Fig. 6). In the SSACE, the upper and lower parts of the water column are composed of subtropical and subpolar waters respectively. In the SCE, the top and bottom of the eddy comprises the subpolar and the upwelled subtropical waters, respectively. A schematic illustrating the processes involved in this 3D advection of water masses driven by frontal meandering is shown in Fig. 7. Note that this process induces both subduction of surface mixed layer water and an upward transfer of interior water: the latter of which has the potential to enhance primary productivity through the upwelling of nutrient-rich waters.

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Vertical velocity (color shadings), potential density (contours, CI = 0.1 kg m⁻³), and horizontal velocity (vectors) at z = −50 m on day 40 of R-EXP. Dashed lines with solid circles and triangles at the ends denote locations of the vertical sections shown in Figs. 5 and 14, respectively.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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(a) Temperature (contours, CI = 1.0°C), salinity anomaly (color shadings), and meridional and vertical velocities (vectors) on day 40 of R-EXP taken along a section that intersects a frontal downdraft (the section along the dashed line with solid circles in Fig. 4). (b) Vertical section of the temperature (contours, CI = 1.0°C) and salinity (color shadings) on day 50 of R-EXP along the transect denoted by the dashed line with solid triangles in Fig. 3b that slices through a surface cyclonic eddy (SCE) to the east and a subsurface anticyclonic eddy (SSACE) to the west.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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The T–S relations for waters in the SCE and SSACE and the subpolar and the subtropical waters on day 50. The water in the SCE and SSACE is sampled at the points shown by dotted line in Fig. 5b. The subpolar and subtropical waters are sampled at the northern and southern boundaries, respectively. The solid circle, triangle, and diamond denote sampling depths of 0, 100, and 200 m, respectively.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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Schematic illustration of frontal subduction.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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b. Cooling and wind-forced experiment (CW-EXP)

The surface temperature field and horizontal velocity and the salinity at 200-m depth on days 10 and 20 of the cooling and wind-forced experiment (CW-EXP) are shown in Fig. 8. Wind stress generates Ekman flow in the top 50 m of the fluid as well as near-inertial internal gravity waves. At the front the denser subpolar water is advected over the lighter subtropical water due to the southwestward Ekman transport. This differential advection combined with the surface cooling destabilizes the water column, triggering convection that both mixes density and results in a translation of the front to the south (Thomas and Lee 2005). Vertical mixing reduces the stratification (and hence Richardson number) at the front, which would tend to enhance the growth rate of baroclinic instability. The mixing also tends to decrease the length scale of the most unstable disturbance (Stone 1966; Stone 1970; Yoshikawa et al. 2001). In addition, convection and gravity waves act as large initial perturbations for baroclinic instability and, as a result, the baroclinic unstable waves reach finite amplitude within a relatively short period of time. As the experiment progresses, restratification due to finite-amplitude baroclinic instability quickly occurs (e.g., Boccaletti et al. 2007) and the wavelength of frontal meanders increases accordingly. Frontal meanders pinch off to form cyclonic and anticyclonic eddies (e.g., SCEs and SSACEs), which move away from the front by the same self-propagation mechanism described above for the unforced experiment (R-EXP).

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As in Fig. 3 but for CW-EXP at (a) day 10 and (b) day 20.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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Figure 9 shows the vertical velocity at 50-m depth and tracer concentration at 150-m depth on day 17. In the region away from the front, roll-like structures with widths of a few kilometers and aligned in the direction of surface wind-driven flow are found. These are associated with convection as their vertical motions are correlated with density anomalies in the sense to release potential energy. In the frontal region intense updrafts and downdrafts 2–3 km wide are found along the meandering front. High tracer concentration at 150-m depth coincides with the intense downdrafts. Thus, subduction in CW-EXP is largely determined by the vertical circulation whose typical horizontal scale is 2~3 km, associated with frontal meanders with wavelengths of 70~80 km.

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(a) The vertical velocity at z = −50 m, (b) the tracer concentration at z = −150 m, and (c) the vertical velocity at z = −400 m evaluated at day 17 of CW-EXP. The potential density (contours, CI = 0.1 kg m⁻³) and horizontal velocity (vectors) are also shown.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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Several processes can drive vertical circulations at fronts: frontogenesis, nonlinear Ekman pumping/suction, internal gravity waves, and upright or slantwise convection. Thomas and Lee (2005) and Mahadevan and Tandon (2006) emphasized the importance of nonlinear Ekman pumping/suction in the induction of secondary circulations at wind-forced fronts. Thomas et al. (2010) further suggests the importance of time-dependent nonlinear Ekman transport in generating vertical circulation. To evaluate these effects in the experiment, the time-dependent nonlinear Ekman transport (M_x, M_y) is estimated. The equations governing the time-dependent nonlinear Ekman transport are obtained by decomposing the flow into geostrophic and ageostrophic components and vertically integrating the horizontal momentum equations for the wind-driven ageostrophic flow over the surface Ekman layer (−50 m ≤ z ≤ 0 m). In deriving the equations, it is assumed that the advection of ageostrophic momentum by the ageostrophic flow is negligibly small and that the vertical variation of the geostrophic flow across the Ekman layer is negligible. With these assumptions, the governing equations for (M_x, M_y) are

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where (U_g, V_g) is the vertically averaged geostrophic velocity and

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is the rate of change following the geostrophic flow. Damping terms have been added to (5) and (6) and are meant to parameterize the radiation of near-inertial waves out of the mixed layer into the ocean interior. Our choice of a damping coefficient of γ = 0.15f is consistent with values inferred from observations (e.g., Alford 2003) and from diagnostics of the vertical component of kinetic energy flux from the CW-EXP (not shown). In the limit of two dimensions, steady flows, and γ = 0 the nonlinear Ekman transport varies inversely with the absolute vorticity (e.g., Stern 1965; Niiler 1969). If these conditions are not met, however, a simple analytical solution for (M_x, M_y) does not exist, and (5) and (6) must be solved numerically.

To solve Eqs. (5) and (6), we put particles at every u and υ grid points on day 17 and traced their position backward from day 17 to day 0 using the vertically averaged geostrophic velocity over the Ekman layer. Equations (5) and (6) were then integrated following the particle from day 0 to day 17 with the initial condition (M_x, M_y) = 0 to obtain (M_x, M_y) at day 17. The pumping/suction velocity due to the time-dependent nonlinear Ekman transport w_Ek was finally estimated using the continuity equation,

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As shown in Fig. 10, w_Ek is large in magnitude near frontal meanders where the total vertical velocity (w) is also strong (Fig. 9a). The horizontal scale and magnitude of w_Ek are similar to those of w. These results suggest that the time-dependent nonlinear Ekman effects play an important role in shaping the vertical circulation.

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The nonlinear Ekman pumping/suction velocity w_Ek, evaluated at day 17.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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In CW-EXP, internal waves are excited below the surface Ekman layer. At z = −400 m where the fluid is stably stratified, strong fluctuations in the vertical velocity are observed beneath the prominent meanders of the front (Fig. 9c). In these regions rotary spectra of profiles of the horizontal velocity (not shown) reveal that clockwise rotary motions (as viewed from above) capture a greater amount of variance than anticlockwise rotary motions. This suggests that the fluctuations in w at depth are associated with downward-propagating internal waves (Leaman and Sanford 1975).

Differences between w and w_Ek are also ascribed to other ageostrophic processes caused by cooling at the front. As in the unforced experiment, frontal meanders are generated whose shear and strain can be frontogenetic and hence conducive to driving vertical motions. Indeed, comparing vertical sections of frontal downdrafts from R-EXP and CW-EXP (Figs. 5a and 11a, respectively) reveals a similar flow structure. The temperature–salinity relation of waters near the front in CW-EXP (Fig. 12) are also similar to those in R-EXP (Fig. 6), showing evidence for the subduction of low salinity, low PV surface water from the north down into the pycnocline south of the front.

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(a) Vertical section of salinity anomaly (color shadings), potential density (black contours, CI = 0.1 kg m⁻³), and meridional and vertical velocities (vectors) on day 17 of CW-EXP along a transect (the dashed line with solid circles in Fig. 9a) that runs through a frontal downdraft. The red line denotes the contour of zero potential vorticity (q); the region enclosed by the line or the region above the line corresponds to zero or negative potential vorticity. (b) The vertical velocity (color shadings) and (c) potential vorticity (color shadings) along with potential density (solid contours, CI = 0.1 kg m⁻³) and absolute momentum υ + fx (dashed contours, CI = 0.5 m s⁻¹) on the same day along a zonal transect across the downdraft (the dashed line with solid triangles in Fig. 9a).

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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The T–S relation from the CW-EXP (solid lines) for waters to the south of the front (denoted by S), at the front (denoted by F), and to the north of the front (denoted by N) on day 17. These waters are sampled at the points shown by solid triangles in Fig. 11a. Dotted lines represent the T–S relation from wintertime observations of the subpolar front of the Japan Sea for waters to the north of the front (N), at the front (F), and to the south of the front (S). These waters are sampled at the points shown by solid triangles in Fig. 19. The PV is denoted by the colored circles (CW-EXP) and triangles (observations).

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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Note that strong frontal downdrafts in CW-EXP are found in regions where surfaces of constant absolute momentum are nearly aligned with isopycnals, corresponding to zero PV (Figs. 11b,c). This suggests that symmetric instability may contribute to the frontal vertical motion (e.g., Haine and Marshall 1998). It should also be noted that frontogenesis and vertical convective mixing both act to make the front symmetrically unstable (Yoshikawa et al. 2001); frontogenesis makes the flow and density fields approximately 2D (e.g., ∂/∂x ≫ ∂/∂y for the downdraft along x = 225 km in Figs. 9a and 11) and intensifies the geostrophic shear, while convective mixing reduces density stratification so that the potential vorticity q,

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tends to be large negative (i.e., symmetrically unstable). (The thermal wind relation was used in deriving the last equation.)

A frontal downdraft driven by frontogenesis is intensified when q = 0—that is, when the fluid is marginally stable to symmetric instability (Yoshikawa et al. 2001; Thomas et al. 2008). Thus, the combined effect of mixing and frontogenesis intensifies the ageostrophic vertical circulation by inducing slantwise convection and strengthening frontogenetically driven downdrafts. Here we have presented a qualitative description of the distinct agents that induce vertical motions at an atmospherically forced front. An analysis aimed at quantifying the various driving mechanisms for frontal vertical circulation will be discussed in section 4.

c. Cooling-forced experiment (C-EXP) and wind-forced experiment (W-EXP)

The vertical velocity and density for the cooling-forced experiment (C-EXP) and the wind-forced experiment (W-EXP) are shown in Fig. 13. In both experiments the locations of intense downdrafts and updrafts in the frontal region are determined by the structure of the frontal meanders, and the magnitude of the updrafts and downdrafts is amplified. In C-EXP, this amplification is induced by the combined effect of frontogenesis and convective mixing. In W-EXP, mixing caused by Ekman advection of denser water over lighter water by the downfront winds, nonlinear Ekman pumping/suction and near-inertial internal gravity waves combine to drive strong vertical motions. Thus, the area of intense vertical motions in the frontal region is larger in W-EXP than in C-EXP. This is more evident at greater depths: at z = −400 m for example, the averaged magnitude of vertical velocity is 1.1 × 10⁻⁷ m s⁻¹ in W-EXP and 0.5 × 10⁻⁷ m s⁻¹ in C-EXP. Note that the effective buoyancy (b = −gρ/ρ₀) flux due to Ekman advection of denser water over lighter water [∂b/∂y(τ_x/ρ₀f); e.g., Thomas and Lee 2005] in W-EXP amounts to −1.5 × 10⁻⁷ m² s⁻³ in the frontal region, whereas the buoyancy flux due to the surface heat flux in C-EXP (αgH/ρ₀C_w, where α is thermal expansion coefficient) is −1.1 × 10⁻⁷ m² s⁻³. Thus, the larger effective buoyancy flux is partly responsible for larger vertical velocity in W-EXP. However, even in an experiment (not shown) where the surface cooling is intensified by 50% so that the surface buoyancy loss almost equals to the effective buoyancy flux of W-EXP, the averaged magnitude of vertical velocity at z = −400 m is only 0.8 × 10⁻⁷ m s⁻¹. Thus, wind stress, which effectively induces near-inertial gravity waves, has a larger effect on the vertical velocity of frontal regions than surface cooling.

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As in Fig. 4 but for (a) C-EXP on day 30 and (b) W-EXP on day 15.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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4. Quantification of the driving mechanism for the ageostrophic vertical motions

In all of the experiments subducted water with high tracer concentration at depth is associated with downdrafts in the frontal region (e.g., Fig. 9), suggesting that it is these features in the flow that are primarily responsible for subduction of surface waters. These frontal downdrafts have a horizontal scale on the order of kilometers, which is much larger than their O(100 m) vertical penetration depth. The small aspect ratio of the frontal vertical circulation indicates that the dynamics of these ageostrophic motions is hydrostatic. Using this fact an analysis for quantifying the driving force of hydrostatic ageostrophic motions will be performed for each of the four experiments and is described in this section. The analysis uses the governing equations for hydrostatic ageostrophic motions derived by Thomas et al. (2010). To apply these equations to solutions from the numerical experiments, which also include nonhydrostatic small-scale motions, the velocity and buoyancy (b = −ρg/ρ₀) from model output are decomposed as follows:

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where the overbar represents a horizontal average and the prime denotes a departure from this average. Nonhydrostatic phenomena are contained within the primed quantities and affect the hydrostatic ageostrophic circulation through convergences/divergences of Reynolds fluxes, which are formulated below. Because the width of convective upwelling and downwelling is 1–1.5 km while the width of frontal downdraft (updraft) is 2–3 km, the horizontal average is taken over an area with dimensions 3.9 km × 3.9 km (16 × 16 grids). (Note that the following results do not qualitatively change even if the average is taken over 1.9- or 7.8-km squares.)

The equations governing the smoothed hydrostatic motions are

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where

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R_x, R_y, and R_b are the convergences of Reynolds fluxes of momentum and buoyancy associated with explicitly resolved small-scale processes and F_x, F_y, and F_b represent the convergences of momentum and buoyancy fluxes by parameterized turbulent processes. In the analysis, the buoyancy is calculated using the in situ rather than potential density. The hydrostatic pressure estimated using (11) and the smoothed pressure field from the numerical solutions is highly correlated, indicating that the coarse-grained flow can be described using hydrostatic dynamics.

The velocity is further decomposed into geostrophic and ageostrophic components:

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Eliminating time derivatives of the geostrophic velocity and buoyancy using the thermal wind relation yields the governing equations for hydrostatic ageostrophic flows:

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The overbar has been omitted in (13) and (14) for simplicity. The left-hand side (lhs) of (13) and (14) are linear functions of the ageostrophic flow; therefore, given knowledge of the spatial structure of the various terms on the rhs of the equations and appropriate boundary conditions for the ageostrophic flow, the ageostrophic vertical circulation can be found by inverting the equations (Thomas et al. 2010). Consequentially, the terms on the rhs of Eqs. (13) and (14) can be thought of as the driving force for the ageostrophic circulation. The various rhs forcing terms represent different physical processes: geostrophic forcing associated with frontogenetic or frontolytic geostrophic shear (GSF), the Lagrangian rate of change of the ageostrophic shear following the geostrophic flow (LTC), vertical variation in ageostrophic advection of the ageostrophic flow (ADV), spatial variations in Reynolds fluxes (REY) and parameterized turbulent processes (EXF), and an error due to the use of in situ density (ERR). Note that ∂/∂x(13) −∂/∂y(14), when (13) and (14) are written in their quasigeostrophic (QG) form and the rhs is equal to GSF yields the QG omega equation (Hoskins et al. 1978; Thomas et al. 2010).

In this study, LHS, GSF, ADV, REY, and EXF are evaluated using the numerical solutions and LTC + ERR is estimated as a residual of these terms: that is, LTC + ERR = LHS − (GSF + ADV + REY + EXF). Note that ERR is expected to have a similar magnitude in all of the experiments since the ranges of T, S, and p are nearly equal for these experiments.

Vertical sections of each of the terms in (13) for all of the experiments are shown in Fig. 14. The sections, whose locations are indicated in Figs. 4, 9a, and 13a,b, slice through intense frontal downdrafts. Term balances of rhs in (14) are basically the same as those in (13) and hence are not shown.

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Vertical section of terms in Eq. (13) for each experiment. The vertical velocity is also contoured (CI = 0.25 × 10⁻³ m s⁻¹), with dashed contours denoting negative values. This section is indicated by the dashed line with solid triangles in Figs. 4, 9b, and 13.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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In the unforced experiment (R-EXP) the strongest vertical motions are found where there are large gradients in the lhs (as expected from the omega equation). The lhs is largely balanced by GSF, indicating that the ageostrophic circulation is mainly forced by frontogenetic processes. Relatively large LTC + ERR is found near the surface. In the upper part of the water column, ERR is small owing to the small difference between the potential and in situ density so that LTC + ERR ~ LTC. Time variability of the ageostrophic flow, which is not considered in QG or semigeostrophic theory, is the second largest driving force for ageostrophic motions next to GSF in the unforced experiment. ERR is a minor term in R-EXP and is small in all of the other experiments as well.

In CW-EXP and W-EXP, LTC + ERR is much greater in magnitude than GSF, while the magnitude of LTC + ERR in C-EXP is similar to that of GSF. Large LTC near the surface (z ≥ −50 m) in CW-EXP and W-EXP mainly corresponds to near-inertial oscillations. Large LTC at greater depths (where fluid is stable in gravitational and symmetric sense) is associated with internal gravity waves. It should be noted that LTC at greater depths is larger in CW-EXP and W-EXP than in C-EXP. This indicates that the ageostrophic motion (internal gravity waves) at greater depths is affected more by wind than by cooling. In CW-EXP and W-EXP, ADV and REY as well as EXF are large in the upper 50 m. Because these terms are not large in R-EXP and C-EXP, they represent wind-induced processes that are strongest in the upper, frictionally influenced layer. On the other hand, at depth (z ≤ −50 m) GSF is larger than ADV, REY, and EXF for all experiments. This indicates that the ageostrophic circulation at greater depths is also forced by frontogenetic processes even when surface forcing is imposed. It should be noted that GSF in the forced experiments are larger in magnitude than that in the unforced experiment. Therefore, surface forcing intensifies frontogenetic processes by changing the hydrography of the front and its velocity field.

5. Effects of forcing on subduction

In 2D experiments (i.e., invariant in the x direction) with initial and boundary conditions identical to the 3D experiments described above, no subducted lenses of surface water are formed (not shown). This suggests that the zonally varying component (referred to as the eddy component) of the velocity and density fields associated with finite-amplitude baroclinic instability is key to frontal subduction. In this section, the eddy-driven transport and the distribution of a tracer tagging surface waters are used to quantify frontal subduction and the role that the deformation fields and eddies play in the process.

a. Eddy-driven transport

The zonally averaged volume transport in the meridional direction in an isopycnal layer of thickness , referenced by index k, and bounded by densities ρ_k ± Δρ/2 is

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where is the meridional velocity in the layer, the overbar denotes a zonal mean, and the prime is the deviation from the zonal mean. The isopycnal volume transport in the meridional direction can be induced from a zonal mean velocity, such as associated with the mean Ekman transport, and an eddy-driven circulation or bolus velocity, that is, the second term in brackets in (15), arising from correlations between thickness and velocity anomalies. It is the bolus velocity that is primarily responsible for frontal subduction at a meandering front (Marshall 1997) and, hence, it is a quantity of interest that will be evaluated from the solutions of the 3D numerical simulations so as to quantify the subduction rate. It is convenient to write the eddy-driven transport in terms of a streamfunction:

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where the streamfunction is set to zero at the bottom of the domain (the layers are ordered in decreasing density; i.e., k = 1 corresponds to the densest layer and larger values of k represent layers of smaller density) and the sign convention is such that a southward eddy transport corresponds to an increase of Φ_k with increasing k (i.e., decreasing density). To calculate (16) from the z-coordinate model output, the domain is split into isopycnal layers separated by a density difference (Δρ) of 0.1 kg m⁻³ and, at each point in the horizontal, the layer thickness and isopycnal meridional velocity (i.e., the meridional flow averaged in the vertical over each layer) are evaluated. For simplicity, in this calculation density profiles with unstable stratification were made neutrally stable by replacing the density of the unstably stratified layer with the density below. This approximation does not greatly affect the calculation owing to the relatively small area covered by regions with unstable stratification (e.g., Fig. 11).

The streamfunction of the eddy-driven transport is shown in Fig. 15 at the time when it attains its maximum magnitude in each of the four experiments. In all of the experiments, the circulation is thermally direct, reflecting the manner in which the baroclinic instabilities responsible for the eddy-induced transport release the available potential energy of the front. The overturning cells in CW-EXP and W-EXP are shifted to the south and are elongated in the meridional direction due to the modulation of the frontal structure by the wind.

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Streamfunction of the eddy-driven transport (solid contours, CI = 1.0 m² s⁻¹) and zonally averaged potential density (dotted contours, CI = 0.1 kg m⁻³) for (a) R-EXP (day 60), (b) CW-EXP (day 35), (c) C-EXP (day 39), and (d) W-EXP (day 36). The horizontal axis is the meridional distance y and the vertical axis is height z.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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The strength of the streamfunction is weakest in R-EXP, demonstrating how surface forcing intensifies the eddy-driven transport. The streamfunction is largest in CW-EXP, indicating that frontal subduction is most intensified when both wind stress and surface cooling are applied. Comparing the amplitude in C-EXP and W-EXP, it can be seen that cooling leads to a greater enhancement of the eddy-driven transport than wind stress. Consequently, cooling is more effective at driving subduction even though wind stress affects the ageostrophic vertical circulations more greatly (section 3). This suggests that part of the ageostrophic circulation that is intensified by wind stress (such as internal gravity waves) does not contribute to net subduction.

b. Tracer analysis

The analysis of the eddy-driven transport quantifies the effect of surface forcings on subduction at every instance. To assess the integrated effect of the forcing on subduction, an analysis of the distribution of a passive tracer is performed in this subsection. The analysis follows the method of Yoshikawa et al. (2001) in which the difference between tracer concentrations from 2D and 3D versions of the same experiments is calculated,

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where is the zonally averaged tracer concentration from the 3D experiment and C₂ is the tracer concentration in the corresponding 2D experiment. Larger values of ΔC denote elevated levels of surface water at depth in the 3D experiment than in 2D experiment and highlight the locations where subduction by deformation fields and eddies has occurred.

In Fig. 16, ΔC and a tracer-based definition for the mixed layer depth is shown for all of the experiments. The tracer-based mixed layer is defined as a layer with C₂ > 0.5. The tracer-based mixed layer base corresponds well with the density-based mixed layer base, except in R-EXP in which the vertical diffusivity of density (i.e., temperature and salinity) and tracer is different. Positive ΔC is found below this layer, while negative ΔC is found within it. This tracer distribution is a consequence of the exchange of water between the mixed layer and pycnocline by deformation fields and eddies.

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Tracer concentration difference (ΔC, color shadings), potential density from the 2D experiment (solid thin contours), and the depth of the tracer-based mixed layer (thick solid line) for (a) R-EXP (day 60), (b) CW-EXP (day 50), (c) C-EXP (day 50), and (d) W-EXP (day 50). Positive ΔC (blue) represents more tracer concentration in the 3D experiment than in the 2D experiment.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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Comparing the density fields from the cooling-forced experiment (C-EXP) and the wind-forced experiment (W-EXP) (e.g., Figs. 16c,d), it can be seen that isopycnals from the lower pycnocline outcrop in C-EXP whereas isopycnals of lesser density, from the middle of the pycnocline, outcrop in W-EXP. As a result, surface water is subducted to greater depths in C-EXP than in W-EXP. When both wind and cooling force the front (CW-EXP), part of the water subducted into the midpycnocline by the wind-forced eddy-driven circulation is re-entrained into the mixed layer via convection (Fig. 16b). Note that the positive values of ΔC are larger in magnitude and can extend to greater depths in C-EXP, W-EXP, and CW-EXP relative to those in R-EXP, indicating that surface forcing affects the isopycnal layers along which downwelling of surface waters occurs and enhances the subduction rate.

The total amount of water subducted into the stratified interior is estimated by calculating the volume integral of ΔC below the tracer-based mixed layer on separate isopycnal layers:

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where V_k is a control volume bounded by densities ρ_k ± Δρ/2 on its sides and the base of the tracer-based mixed layer on its top. The meridional limits of integration are set to 0 < y < L_y in R-EXP and C-EXP and −V_Dt < y < L_y − V_Dt in the wind-forced experiments to account for the southward drift of the front (where V_D (=0.035 m s⁻¹) represents the drift speed and t is the integration time). The total volume of subducted fluid is estimated as

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and its time series for each of the experiments is plotted in Fig. 17a. As can be seen in the figure, both wind and cooling advance the onset of subduction and enhance its rate. Comparing Sub in experiments C-EXP and W-EXP, it can be seen that cooling leads to a greater amount of subduction than wind. Note that wind sets up subduction more rapidly, even though cooling ultimately produces more subduction. In the case of time-dependent forcing, such as cold-air outbreaks, the difference in setup time could result in the two forcings playing more equal roles.

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(a) The temporal evolution of the total volume of subducted fluid Sub(t) estimated from the tracer distribution. Note the difference in the horizontal axis between R-EXP and the other experiments. (b) The volume of subducted fluid as a function of potential density at day 60 in R-EXP and day 50 in the other experiments.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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The isopycnal distribution of subducted water, Sub_k, calculated at times near the end of each experiment is illustrated in Fig. 17b. In C-EXP, subduction primarily occurs on the 26.9–27.2 kg m⁻³ isopycnal layers, whereas, in the wind-forced experiment, W-EXP, surface waters are downwelled along shallower isopycnals with densities ranging from 26.6 to 27.0 kg m⁻³. Thus, the experiments suggest that wind and cooling tend to drive subduction into different parts of the pycnocline: namely, the mid- and lower pycnocline, respectively. When both cooling and wind forcing are applied (CW-EXP) the amount of subducted water is larger than when they are applied separately. However, the volume of subducted water in CW-EXP is less than the sum of the volumes in C-EXP and W-EXP because a portion of the water that is subducted into the midpycnocline by wind is re-entrained into the mixed layer deepened by cooling.

6. Comparison of numerical experiments to in situ observations of the subpolar front of the Japan Sea

Spring surveys of the subpolar front of the Japan Sea (Lee et al. 2006) reveal details of the 3D features characteristic of subduction under weak atmospheric forcing. The observed 3D structure of potential density and chlorophyll fluorescence (Fig. 18) reveals downward extensions of high-chlorophyll waters along isopycnals that are more prominent near the upstream side of the meander’s trough (west of 134.5°E) than on its downstream side (east of 134.5°E). This is similar to the structure of subduction found in the reference experiment (R-EXP, Fig. 7) in which geostrophic forcing induces downwelling in the upstream side of a meander trough. This suggests that, under weak atmospheric forcing, frontal subduction at the subpolar front is primarily driven by geostrophic forcing.

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Three-dimensional view of vertical sections of (a) potential density and (b) chlorophyll fluorescence for the Japan Sea spring survey 1 (Lee et al. 2006). The black line in (a) denotes the axis of the surface density front.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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As mentioned in section 1, the wintertime surveys of the subpolar front of the Japan Sea taken during cold-air outbreaks revealed the presence of lenses in the midpycnocline, just beneath the surface mixed layer, in the vicinity of the front with properties characteristic of water that had recently been subducted (Thomas and Lee 2005; Lee et al. 2006). Vertical sections of PV, zonal absolute momentum, and potential density (Fig. 19) observed across the subpolar front under the cold-air outbreaks [sections 4 and 5 of survey 2, see Fig. 1 of Thomas et al. (2010) for the locations of the sections] reveal lenses of low PV water with absolute momentum and isopycnal surfaces aligned in the region above the lenses (X = 20 km in Fig. 19b). These features are very similar to those in Fig. 11c. The observed temperature–salinity relation (Fig. 12) suggests that low PV surface subpolar water on the northern side of the front (X = 35 km) in section 4 (Fig. 19a) had been subducted beneath the front (X = 20 km) on section 5 (Fig. 19b) to form a lens of water with low salinity and PV. Thomas et al. used an inverse method based on Eqs. (13) and (14) to estimate the frontal vertical circulation and its driving force and inferred that there were submesoscale frontal downdrafts along these sections with vertical velocities O(100–200 m day⁻¹) that tended to coincide with plumes with low PV and salinity (Fig. 4 of Thomas et al. 2010). Such features are seen in CW-EXP (Fig. 11a), suggesting that the observed subduction is forced by processes similar to those simulated in CW-EXP.

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Vertical sections of potential vorticity (color shading), zonal absolute momentum surfaces (blue contours, CI = 0.125 m s⁻¹), and potential density (black contours, CI = 0.1 kg m⁻³) observed across the subpolar front under a cold-air outbreak. (a) Section 4 and (b) section 5 (about 22 km downstream from section 4) of survey 2. The horizontal axis represents the meridional distance from 39.5°N. The solid triangles with N, F, and S indicate the sampling positions of temperature and salinity used in Fig. 12.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-0154.1

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Note that Thomas et al. (2010) concluded that, over the entire frontal region, geostrophic forcing played a relatively minor role in generating the frontal vertical circulation and that wind forcing and time-dependent near-inertial motions were critical to the formation of ageostrophic flow at the front. The present numerical experiments corroborate the observational analysis in that they highlight the importance of time-dependent ageostrophic motions such as near-inertial internal gravity waves in generating vertical circulation. In addition, the experiments suggest that these motions can extend into the lower pycnocline. The results described in this study, namely, that wind stress plays a significant role in the dynamics of the ageostrophic circulation and leads to subduction into the midpycnocline, are also consistent with these observational findings. It is further worth noting that, although the present numerical experiments suggest that the geostrophic forcing generates weaker vertical velocities than winds, it can lead to stronger and deeper net subduction at preferred locations along the front.

Isopycnals from the lower pycnocline of the Japan Sea, with potential temperatures ranging from 1°–3°C, outcrop to the north of the survey area of Lee et al. (2006). These outcropping isopycnals are known to form a density front (Volkov and Danchenkov 2004) at the surface. Water properties in the salinity minimum layer in the lower pycnocline are similar to those in the mixed layer surrounding this front to the north, suggesting that these waters are subducted into the interior at this northern location. It is expected from the present experiments that surface cooling as well as wind stress enhance the subduction of low salinity water into the lower pycnocline in this region.

In contrast to the steady atmospheric forcing used in the numerical experiments, winds and heat fluxes observed during the wintertime surveys were highly episodic, peaking during periods of cold-air outbreaks when the wind stress and heat loss reached values that exceeded those used in the numerical simulations (Lee et al. 2006). The atmospheric forcing used in the experiments was based on the time-mean wind stress and heat flux from the surveys. Therefore, time variability in the ageostrophic vertical circulation at the subpolar front is likely to be underestimated in the numerical experiments, and consequently the numerical solutions should be used to mainly interpret the integrated effects of atmospheric forcing on frontal subduction.

7. Concluding remarks

Numerical experiments were performed using a nonhydrostatic model to understand the dynamics of the ageostrophic vertical circulation and associated subduction at a density front modeled after the subpolar front of the Japan Sea. The emphasis of the study is on the role of atmospheric forcing, specifically wind stress and surface cooling in driving wintertime subduction of surface waters into the permanent pycnocline.

Both wind and cooling were found to intensify frontogenesis, the geostrophic forcing, and the ageostrophic circulation at the front. The combined effect of frontogenesis and vertical mixing also enhances frontal downdraft. In the wind-forced experiments, advection of the ageostrophic momentum by the ageostrophic flow and Reynolds fluxes ascribable to small-scale nonhydrostatic motions contributed to forcing the ageostrophic secondary circulation. In addition, it was found that time-dependent ageostrophic motions such as internal gravity waves were strongest in the wind-forced experiments. These motions extended the region of strong vertical motion from the surface down to the lower pycnocline, where the stratification is weak. Thus, there were more mechanisms for generating ageostrophic circulation by wind stress than cooling; therefore the region of intense vertical motions was larger in the wind-forced experiments than in the cooling-forced experiments.

When the wind stress is oriented downfront, Ekman flow advects surface waters from the denser to lighter side of the front, resulting in gravitational instability and vertical mixing and a gradual migration of the front to the south where the fluid is more stratified. This process forces isopycnals from the middle of the pycnocline to outcrop at the front. It is along these isopycnals where surface waters are transferred into the interior, and hence downfront winds preferentially induce subduction to relatively shallow depths limited to the midpycnocline. Cooling, on the other hand, by energizing convection and deep mixing can uplift isopycnals from even greater depths to the mixed layer for the particular parameters used in the numerical simulations and allows for the subduction of fluid to the lower pycnocline. For the frontal configuration and forcing used in the experiments, it was found that subduction was strongest when both wind stress and surface cooling were applied. The volume of water subducted into the interior was larger in the cooling-forced experiment than in the wind-forced experiment, even though winds drive stronger ageostrophic motions. This is not surprising since a portion of the wind-driven ageostrophic flow is time dependent and unbalanced, whereas subduction is primarily accomplished through an eddy-driven circulation associated with balanced eddies and meanders.

The experiments revealed that the efficacy of subduction was also affected by the direction of the wind relative to the frontal jet. While a downfront wind enhances subduction when the wind opposes the frontal jet, Ekman flow transports light water over dense, releasing the available potential energy of the front, deenergizing baroclinic instability, and weakening the eddy-driven circulation and the subduction that it induces.