Abstract
A submesoscale filament of dense water in the oceanic surface layer can undergo frontogenesis with a secondary circulation that has a surface horizontal convergence and downwelling in its center. This occurs either because of the mesoscale straining deformation or because of the surface boundary layer turbulence that causes vertical eddy momentum flux divergence or, more briefly, vertical momentum mixing. In the latter case the circulation approximately has a linear horizontal momentum balance among the baroclinic pressure gradient, Coriolis force, and vertical momentum mixing, that is, a turbulent thermal wind. The frontogenetic evolution induced by the turbulent mixing sharpens the transverse gradient of the longitudinal velocity (i.e., it increases the vertical vorticity) through convergent advection by the secondary circulation. In an approximate model based on the turbulent thermal wind, the central vorticity approaches a finite-time singularity, and in a more general hydrostatic model, the central vorticity and horizontal convergence are amplified by shrinking the transverse scale to near the model’s resolution limit within a short advective period on the order of a day.
