Frontogenesis in Mixed Layers

Abstract

A unified theory of frontogenesis in mixed layers is proposed. Analytical solutions of the nonlinear mass and density balances in a mixed layer are found in the Lagrangian frame for a wide class of entrainment parameterizations. These solutions show mixed-layer depth and density to be functions of particle position and separation, where mixing is represented by an integral over time following a particle. Thus, given a knowledge of only the crossfront velocity field, the likelihood of frontal formation can be predicted. Both surface convergence, and divergence in conjunction with vertical mixing can be frontogenetic. Three different types of fronts, distinguished by their associated crossfront velocity fields, are discussed. Large-scale fronts, such as the subtropical front, are described by a convergent surface flow acting upon an initial horizontal density gradient. The powerful divergence caused by an offshore Ekman flow forced to zero at a coast causes upwelling fronts. The divergence associated with a shoaling barotropic flow forms tidal mixing fronts, which may be sharpened by convergence during an outgoing tide.