Abstract

This study concerns the combined effects of Earth’s rotation and stabilizing surface buoyancy flux upon the wind-induced turbulent mixing in the surface layer. Two different length scales, the Garwood scale and Zilitinkevich scale, have been proposed for the stabilized mixing layer depth under Earth’s rotation. Here, this study analyzes observed mixed layer depth plus surface momentum and buoyancy fluxes obtained from Argo floats and satellites, finding that the Zilitinkevich scale is more suited for observed mixed layer depths than the Garwood scale. Large-eddy simulations (LESs) reproduce this observed feature, except under a weak stabilizing flux where the mixed layer depth could not be identified with the buoyancy threshold method (because of insufficient buoyancy difference across the mixed layer base). LESs, however, show that the mixed layer depth if defined with buoyancy ratio relative to its surface value follows the Zilitinkevich scale even under such a weak stabilizing flux. LESs also show that the mixing layer depth is in good agreement with the Zilitinkevich scale. These findings will contribute to better understanding of the response of stabilized mixing/mixed layer depth to surface forcings and hence better estimation/prediction of several processes related to stabilized mixing/mixed layer depth such as air–sea interaction, subduction of surface mixed layer water, and spring blooming of phytoplankton biomass.

Abstract

Turbulent mixing induced by tidal currents near the sea bottom plays a key role in coastal and shallow sea environments. Many attempts have been made to quantify turbulent mixing near the seabed, such as velocity microstructure measurements with microstructure profilers and turbulent Reynolds stress measurements using acoustic Doppler current profilers (ADCPs). This study proposes an alternative method in which the Ekman balance equations are solved with measured velocity spirals to estimate the eddy viscosity profile. Three schemes (schemes 1, 2, and 3) are described in this paper; schemes 1 and 2 were used in previous studies, while scheme 3 is newly proposed in the present study. The performance of the three schemes was tested using velocity spirals simulated with an idealized eddy viscosity profile, showing that scheme 2 is useful if the random measurement errors are small, while scheme 3 is useful when the errors in the Ekman balance are small. The performance was also evaluated using measured velocity spirals. This method utilizes velocity measured with standard ADCPs operated in normal modes, allowing for easier and more frequent quantifications of the mixing averaged over longer periods.

Abstract

Wave-resolving simulations of monochromatic surface waves and Langmuir circulations (LCs) under an idealized condition are performed to investigate the dynamics of wave–current mutual interaction. When the Froude number (the ratio of the friction velocity of wind stress imposed at the surface and wave phase speed) is large, waves become refracted by the downwind jet associated with LCs and become amplitude modulated in the crosswind direction. In such cases, the simulations using the Craik–Leibovich (CL) equation with a prescribed horizontally uniform Stokes drift profile are found to underestimate the intensity of LCs. Vorticity budget analysis reveals that horizontal shear of Stokes drift induced by the wave modulation tilts the wind-driven vorticity to the downwind direction, intensifying the LCs that caused the waves to be modulated. Such an effect is not reproduced in the CL equation unless the Stokes drift of the waves modulated by LCs is prescribed. This intensification mechanism is similar to the CL1 mechanism in that the horizontal shear of the Stokes drift plays a key role, but it is more likely to occur because the shear in this interaction is automatically generated by the LCs whereas the shear in the CL1 mechanism is retained only when a particular phase relation between two crossing waves is kept locked for many periods.

Abstract

In the present study, large-eddy simulations (LESs) were performed to investigate mixed layer depth (MLD) and sea surface warming (SSW) under diurnally cycling surface heat flux in the heating season, in which a mixed layer (ML) is shoaling on intraseasonal time scales. The LES results showed that the diurnal cycle makes the MLD greater (smaller) at lower (higher) latitudes than the MLD without the cycle. Time scales of the wind-induced shear and the surface heat are a key to understand this latitudinal dependence of the diurnal cycle effects. The wind-induced shear-driven turbulence developed from early morning and became strongest at half the inertial period (T _i/2), while nighttime cooling weakened the ML stratification until the end of the nighttime (T ₂₄ = 24 h). At lower latitudes where T _i/2 > T ₂₄ (lower than 15°), the shear-driven turbulence continued to grow after T ₂₄ and determined the time of the greatest MLD. Thus, the shear-driven turbulence shaped the latitudinal dependence of the MLD, though convective turbulence helped further deepening of the ML. At higher latitudes (T _i/2 < T ₂₄), on the other hand, the shear-driven turbulence ceased growing before the nighttime cooling ended. However, reduced stratification due to the nighttime cooling supported the shear-driven turbulence to continue deepening the ML. Thus, the nighttime cooling shaped the latitudinal dependence of the MLD at higher latitudes. The MLD change induced by the diurnal cycle altered the SSW rate. At higher latitudes, the diurnal cycle is expected to reduce the MLD and increase the SSW by 10% in the heating season.

Abstract

The formation and circulation processes of intermediate water in the Japan Sea have been investigated by study of the subduction of mixed layer water. To simulate realistic seasonal variations in the velocity and hydrographic structures, a numerical model with a nudging method for potential temperature and salinity, which reproduced the general features in the Japan Sea, is used. Close investigation of the subduction process reveals two major formation areas (A and B) of intermediate water. Area A (41°∼43°N, west of 135°E) corresponds to the region reported by recent observations, whereas Area B (40°∼43°N, east of 136°E) has not been reported so far. The mixed layer water subducted in Area A is advected southwestward and eventually its upper portion (above 200 m) reaches the eastern part of the Japan Basin, whereas the lower branch (below 200 m) reaches the Tsushima Basin. This indicates that the East Sea Intermediate Water originates from the mixed layer in Area A, and suggests that the East Sea Intermediate Water and the upper portion of the Japan Sea Proper Water represent the same type of intermediate water. In contrast, the water subducted in Area B is advected northward and some of it flows out through the Soya Strait, while another portion is reentrained into the mixed layer off the Primorye coast. Tracking of the subducted water particles clearly shows that the southward transport of the intermediate water takes a seasonally varying path: for example, a path along the continental coast in winter and one along the Japanese coast in summer. The total formation rate of the intermediate water is estimated to range between 0.48 and 0.69 (×10⁶ m³ s⁻¹) according to the strength of nudging terms, and the corresponding range in ventilation time is 20.3∼25.6 years.

Abstract

Fujiwara et al. explicitly simulated Langmuir circulations using a wave-resolving simulation (WRS) technique and found that the residual wave effect on vorticity was well represented by the vortex force of the Craik–Leibovich (CL) equation, at least in the simulated situation. In response to the simulation results, Mellor has proposed a view that ubiquitous applicability of the CL formulation is still questionable and that the three-dimensional radiation stress (3DRS) formulation that he has derived encompasses both of the vortex force effect and an effect that is lower order in terms of wave steepness. Here, these opinions are discussed in terms of the approximations used in the wave-averaged formulations. The asymptotic expansion of the Eulerian-averaged momentum equation allows the separate discussion of two different wave effects: pressure correction and torque. It is argued that the approximation adopted in Mellor’s 3DRS formulation is presumably not accurate enough to properly parameterize the wave torque effect, and possible approaches to examine its performance are proposed. We agree with the view that the applicability of the CL formulation needs further investigation. WRS will be a helpful tool for this purpose.

Abstract

The present study performs a wave-resolving simulation of wind-driven currents under monochromatic surface gravity waves using the latest nonhydrostatic free-surface numerical model. Here, phase speed of the waves is set much greater than the current speed. Roll structures very similar to observed Langmuir circulations (LCs) appear in the simulation only when both waves and down-wave surface currents are present, demonstrating that the rolls are driven by the wave–current interaction. A vorticity analysis of simulated mean flow reveals that the rolls are driven by the torque associated with wave motion, which arises from a correlation between wave-induced vorticity fluctuation and the wave motion itself. Furthermore, it is confirmed that the wave-induced torque is very well represented by the curl of the vortex force (VF), that is, the vector product of mean vorticity and Stokes drift velocity. Therefore, it is concluded that the simulated rolls are LCs and that the wave effects are well represented by the VF expression in the present simulation. The present study further revisits the scaling assumptions made by previous studies that derived VF formulation and shows that there is disagreement among the previous studies regarding the applicability of VF formulation when the wave orbital velocity (proportional to the amplitude times the frequency) is much smaller than the mean flow velocity. The result from the present simulation shows that the VF expression is still valid even with such small wave amplitudes, as long as phase speed of the waves is much greater than the current speed.

ABSTRACT

The effects of wind stress and surface cooling on ageostrophic vertical circulation and subduction at the subpolar front of the Japan/East Sea are investigated using a nonhydrostatic numerical model. In experiments forced by wind and/or cooling, ageostrophic vertical circulation is enhanced relative to the unforced case. Both surface cooling and wind stress intensify the circulation by enhancing frontogenesis associated with frontal meandering. Winds further strengthen vertical motions by generating internal gravity waves. Downfront winds (i.e., oriented along the frontal jet) transport surface water from the denser to lighter side of the front, causing it to migrate toward the region of higher stratification and enhancing the vertical mixing at the front. This induces outcropping of isopycnals from the middle of the pycnocline along which surface water is subducted. Hence downfront winds enhance subduction down to the middle of the pycnocline, but not beneath. On the other hand, cooling uplifts isopycnals from greater depths to the surface so that it allows for the subduction of fluid to greater depths. In contrast to the vertical circulation, frontal subduction is more intensified by surface cooling than wind stress, because part of wind-forced circulation (e.g., internal gravity wave) does not contribute to subduction. Ageostrophic vertical circulation and frontal subduction are most intense when both wind stress and surface cooling are at play.

Abstract

An inverse method for inferring vertical velocities from high-resolution hydrographic/velocity surveys is formulated and applied to observations collected at the subpolar front of the Japan/East Sea (JES) taken during several cold-air outbreaks. The method is distinct from vertical velocity inferences based on the omega equation in that the driving mechanism for the ageostrophic flow is inferred rather than assumed and hence is particularly appropriate for application to wind- or buoyancy-forced upper-ocean currents where friction, mixing, inertial/superinertial motions, or higher-order effects can contribute along with shear/strain of the geostrophic flow to force vertical motions.

The inferred vertical circulation at the subpolar front of the JES has amplitudes O(100 m day⁻¹) compared to the ∼20 m day⁻¹ vertical velocities predicted by the omega equation. Time-dependent, near-inertial motions driven by the winds and modified by the vertical vorticity of the frontal jet appear to be the primary cause of the strong vertical motions. The strongest vertical motions are associated with submesoscale, O(5 km), frontal downdrafts that tend to align with the slanted isopycnal surfaces of the front and advect water with low salinity and high chlorophyll fluorescence down the dense side of the front.

Abstract

Several features of Langmuir turbulence remain unquantified despite its potentially large impacts on ocean surface mixing. For example, its vertical velocity variance, expected to be proportional to based on numerical simulations, was proportional to in recent field observations, where is the friction velocity and is surface Stokes velocity. To investigate unquantified features of Langmuir turbulence, we conducted a field experiment around a marine observation tower in a shallow sea off the southern coast of Japan in early winter when winds and waves (often swells) were often misaligned. Coherent structures similar to Langmuir cells were successfully identified in the horizontal and vertical structures of turbulent flows measured with upward- and horizontally looking acoustic Doppler current profilers (ADCPs). ADCPs and several anemometers attached at the tower showed that turbulent vertical velocity variance was large when the Langmuir number and Hoenikker number (; where B is surface buoyancy flux and H is the water depth) were both small and that the orientation of the cells was generally aligned in the direction of Lagrangian current shear. These results agree well with the previous numerical results. As in the previous observations, however, the vertical velocity variance appeared to be proportional to . In our experiment, this curious feature was explained by compensatory effects between waves and convection. Misaligned wind with waves also seems to characterize the observed Langmuir turbulence, though further quantitative analysis is required to confirm this result.