Ekman Suction Enhances Entrainment at Fronts

A mathematical model with a closed-form solution is derived for the time-evolution of the boundary layer depth and entrainment velocity across an isolated submesoscale front subject to a destabilizing a down-front wind stress and/or buoyancy loss to the atmosphere. This model is a generalization of the model proposed by Taylor and Ferrari (J. Phys. Oceanogr., 40, 1222-1242) in that it is derived by integrating the flux form of the potential vorticity (PV) equation across a surface layer of zero depth-integrated PV. This model adds the effects of cross-front variations in absolute vertical vorticity, which modify the entrainment velocity directly via the PV at the base of the mixed layer and indirectly via Ekman suction. The upshot is that the resulting cross-front variations in PV and Ekman suction significantly enhance both the maximum deepening of the surface mixing layer and the maximum time-integrated entrainment flux in response to an atmospheric forcing event. The potential physical and biogeochemical implications will be addressed by referring to observations and an idealized numerical simulation, where these vertical vorticity effects result in a doubling of the maximum time-integrated entrainment flux at an isolated submesoscale front forced by a modest down-front wind event characteristic of synoptic atmospheric variabilty.