Submesoscale surface fronts and filaments: secondary circulation, buoyancy flux, and frontogenesis

Problems are posed and solved for upper-ocean submesoscale density fronts and filaments in the presence of surface wind stress and the associated boundary-layer turbulent mixing, their associated geostrophic and secondary circulations and their instantaneous buoyancy fluxes and frontogenetic evolutionary tendencies in both velocity and buoyancy gradients. The analysis is diagnostic rather than prognostic, and it is based on a momentum-balanced approximation that assumes the ageostrophic acceleration is negligible, although the Rossby number is finite and ageostrophic advection is included, justified by the quasi-steady, coherent-structure flow configurations of fronts and filaments. Across a wide range of wind and buoyancy-gradient parameters, the ageostrophic secondary circulation for a front is a single overturning cell with downwelling on the dense side, hence with a positive (rest:ratifying) vertical buoyancy flux. For a dense filament the circulation is a double cell with central downwelling and again positive vertical buoyancy flux. The primary explanation for these secondary-circulation cells is a 'turbulent thermal wind' linear momentum balance. These circulation patterns, and their associated frontogenetic tendencies in both the velocity and buoyancy gradients, arc qualitatively similar to those due to the 'classical' mechanism of strain-induced frontogenesis. For linear solutions, the secondary circulation and frontogenesis are essentially independent of wind direction, but in nonlinear solutions ageostrophic advection provides a strong intensification of the peak vertical velocity, while generally preserving the ageostrophic circulation pattern, when the Rossby number is order one and the wind orientation relative to the frontal axis is favourable. At large Rossby number the solution procedure fails to converge, with an implication of a failure of existence of wholly balanced circulations.