Friction, Frontogenesis, and the Stratification of the Surface Mixed Layer

The generation and destruction of stratification in the surface mixed layer of the ocean is understood to result from vertical turbulent transport of buoyancy and momentum driven by air-sea fluxes and stresses. In this paper, it is shown that the magnitude and penetration of vertical fluxes are strongly modified by horizontal gradients in buoyancy and momentum. A classic example is the strong restratification resulting from frontogenesis in regions of confluent flow. Frictional forces acting on a baroclinic current either imposed externally by a wind stress or caused by the spindown of the current itself also modify the stratification by driving Ekman flows that differentially advect density. Ekman flow induced during spindown always tends to restratify the fluid, while wind-driven Ekman currents will restratify or destratify the mixed layer if the wind stress has a component up or down front (i.e., directed against or with the geostrophic shear), respectively. Scalings are constructed for the relative importance of friction versus frontogenesis in the restratification of the mixed layer and are tested using numerical experiments of mixed layer fronts forced by both winds and a strain field. The scalings suggest and the numerical experiments confirm that for wind stress magnitudes, mixed layer depths, and cross-front density gradients typical of the ocean, wind-induced friction often dominates frontogenesis in the modification of the stratification of the upper ocean. The experiments reveal that wind-induced destratification is weaker in magnitude than restratification because the stratification generated by up-front winds confines the turbulent stress to a depth shallower than the Ekman layer, which enhances the frictional force, Ekman flow, and differential advection of density. Frictional destratification is further reduced over restratification because the stress associated with the geostrophic shear at the surface tends to compensate a down-front wind stress.