Symmetric and Geostrophic Instabilities in the Wave-Forced Ocean Mixed Layer

Abstract

Here, the effects of surface waves on submesoscale instabilities are studied through analytical and linear analyses as well as nonlinear large-eddy simulations of the wave-averaged Boussinesq equations. The wave averaging yields a surface-intensified current (Stokes drift) that advects momentum, adds to the total Coriolis force, and induces a Stokes shear force. The Stokes–Coriolis force alters the geostrophically balanced flow by reducing the burden on the Eulerian–Coriolis force to prop up the front, thereby potentially inciting an anti-Stokes Eulerian shear, while maintaining the Lagrangian (Eulerian plus Stokes) shear. Since the Lagrangian shear is maintained, the Charney–Stern–Pedlosky criteria for quasigeostrophic (QG) baroclinic instability are unchanged with the appropriate Lagrangian interpretation of the shear and QG potential vorticity. While the Stokes drift does not directly affect vorticity, the anti-Stokes Eulerian shear contributes to the Ertel potential vorticity (PV). When the Stokes shear and geostrophic shear are aligned (antialigned), the PV is more (less) cyclonic. If the Stokes-modified PV is anticyclonic, the flow is unstable to symmetric instabilities (SI). Stokes drift also weakly impacts SI through the Stokes shear force. When the Stokes and Eulerian shears are the same (opposite) sign, the Stokes shear force does positive (negative) work on the flow associated with SI. Stokes drift also allows SI to extract more potential energy from the front, providing an indirect mechanism for Stokes-induced restratification.

Submesoscales Enhance Storm‐Driven Vertical Mixing of Nutrients: Insights From a Biogeochemical Large Eddy Simulation

“…With regard to waves, real storms are expected to generate strong wind waves, which substantially modify the Lagrangian mean shear in the upper ocean. Hence, as several previous studies have shown, waves can substantially modify the upper‐ocean turbulence (e.g., Li et al, ; McWilliams & Sullivan, ), submesoscale/turbulence interactions (Hamlington et al, ; Haney et al, ; Smith et al, ; Sullivan et al, ), and thereby vertical tracer transport. It is difficult to say how waves might impact the results in this scenario, because no previous study has considered the impacts of waves on submesoscale/turbulence interactions under strong storm winds, as in this scenario.…”

“…During storms, winds can increase the vertical nutrient flux (thereby enhancing net phytoplankton growth in oligotrophic oceans), both by enhancing submesoscale vertical velocities (e.g., Brannigan, ; Capet et al, ; Lévy et al, ; Mahadevan & Tandon, ; Mahadevan et al, ; Thomas et al, ) and via entrainment/mixing in submesoscale fronts (e.g., Lévy et al, ; Whitt, Taylor, et al, ). In addition, winds can enhance or suppress the mixed layer restratification rate depending on the magnitude and orientation of the wind stress relative to the horizontal density gradient in the ocean mixed layer and the frequency content of the wind (Long et al, ; Mahadevan et al, ; Thomas & Ferrari, ; Whitt, Taylor, et al, ; Whitt, Lévy, et al, ) as well as the surface wave field (Haney et al, ; Li et al, ). For reviews of recent work on submesoscale impacts on biogeochemistry, see Klein and Lapeyre (), Lévy et al (), Mahadevan (), and Lévy et al ().…”

Seasonal thermal fronts on the northern South China Sea shelf: Satellite measurements and three repeated field surveys

“…Here the lateral velocity shear arising from the mean flows, as an important contributor to the relative vorticity , is encompassed in the vertical component . No attempt is made to correct for the effects of Stokes drift on PV, which may affect the stability of nearshore currents [ Lentz and Fewings , ; Haney et al ., ]. Only diagnostic PV is examined in this study, and there is no discussion on the change of PV due to data limitations, while the modification of PV by frictional and diabatic processes should be expected because of the presence of an active bottom boundary layer [ Benthuysen and Thomas , ; Gula et al ., ].…”

Effects of submesoscale turbulence on ocean tracers

“…Wave spreading effects on Stokes drift are neglected [ Webb and Fox‐Kemper , ], as are breaking wave effects. Prior studies [ McWilliams et al ., ; Van Roekel et al ., ; Hamlington et al ., ] have shown that this parameterization for the Stokes drift velocity leads to the creation of small‐scale, counterrotating Langmuir cells throughout the domain, with the strongest cells occurring close to the surface (i.e., within the upper 25 m of the ocean), and substantial impacts on submesoscale fronts and instabilities [ McWilliams and Fox‐Kemper , ; Haney et al ., ; (N. Suzuki and B. Fox‐Kemper, Understanding Stokes Forces in the Wave‐Averaged Equations, submitted to J. Geophys. Res., 2015)].…”

“…Additionally, the original uniform mixed‐layer depth of −50 m has been modified throughout the domain by the deepening effects of Langmuir turbulence and the shallowing effects of restratifying submesoscale eddies. At the time of tracer introduction, the mixed‐layer depth based on the buoyancy threshold , where and m s −2 , ranges from roughly −30 to −55 m. The mixed‐layer depth based on the critical Richardson number Ri c = 0.25 ranges from −20 to −40 m, and the depth based on the Ertel potential vorticity threshold q ( x , y , z ) > q c , where q c = 8 × 10 −11 s −3 , ranges from −30 to −60 m. These different depths indicate a variety of mixing processes, including convective, Langmuir, and symmetric instabilities [ Taylor and Ferrari , ; Hamlington et al ., ; Haney et al ., ].…”