Diapycnal mixing in a frontal system forced by an oscillating deformation field

A frontogenesis model with shear-induced diapycnal mixing has been developed to investigate the importance of mixing in the evolution of a frontal system. The model estimates the intensity of mixing induced by geostrophic shear through the mean density tendency, which represents the material derivative of the mean density due to the divergence of the vertical density flux. This flux is determined by the vertical gradient of the mean density and the turbulent diffusivity, the latter being related to the gradient Richardson number. The process of frontogenesis is based on an oscillating horizontal deformation field characterised by a compression phase and an expansion phase. During the compression phase both the vertical density gradient and the diapycnal velocity gradient increase their values. Therefore the gradient Richardson number decreases and the density tendency increases, characterising zones with high diapycnal mass convergence/divergence. These high values cause significant mixing and a redistribution of the isopycnal surfaces that persist in the phase of expansion. In this last phase, the gradient Richardson number increases leading to a decay of the diapycnal mixing, except in zones where mixing maintains its intensity.