Geophysical flows under location uncertainty, Part III: SQG and frontal dynamics under strong turbulence conditions

Models under location uncertainty are derived assuming that a component of the velocity is uncorrelated in time. The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion terms and a multiplicative noise contribution. This change can be consitently applied to all fluid dynamics evolution laws. This paper continues to explore benefits of this framework and consequences of specific scaling assumptions. Starting from a Boussinesq model under location uncertainty, a model is developed to describe a mesoscale flow subject to a strong underlying submesoscale activity. As obtained, the geostrophic balance is modified and the Quasi-Geostrophic (QG) assumptions remarkably lead to a zero Potential Vorticity (PV). The ensuing Surface Quasi-Geostrophic (SQG) model provides a simple diagnosis of warm frontolysis and cold frontogenesis.