Buoyancy and Wind-Driven Convection at Mixed Layer Density Fronts

In this study, the influence of a geostrophically balanced horizontal density gradient on turbulent convection in the ocean is examined using numerical simulations and a theoretical scaling analysis. Starting with uniform horizontal and vertical buoyancy gradients, convection is driven by imposing a heat loss or a destabilizing wind stress at the upper boundary, and a turbulent layer soon develops. For weak lateral fronts, turbulent convection results in a nearly homogeneous mixed layer (ML) whose depth grows in time. For strong fronts, a turbulent layer develops, but this layer is not an ML in the traditional sense because it is characterized by persistent horizontal and vertical gradients in density. The turbulent layer is, however, nearly homogeneous in potential vorticity (PV), with a value near zero. Using the PV budget, a scaling for the depth of the turbulent low PV layer and its time dependence is derived that compares well with numerical simulations. Two dynamical regimes are identified. In a convective layer near the surface, turbulence is generated by the buoyancy loss at the surface; below this layer, turbulence is generated by a symmetric instability of the lateral density gradient. This work extends classical scalings for the depth of turbulent boundary layers to account for the ubiquitous presence of lateral density gradients in the ocean. The new results indicate that a lateral density gradient, in addition to the surface forcing, can affect the stratification and the rate of growth of the surface boundary layer.