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

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.