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

TL;DR

This paper extends geophysical flow models under location uncertainty to include strong turbulence effects, leading to modified geostrophic balance and a simplified SQG model that aids in understanding frontal dynamics.

Contribution

It develops a mesoscale flow model incorporating strong submesoscale activity within the location uncertainty framework, revealing new insights into geostrophic balance and frontogenesis.

Findings

Modified geostrophic balance under strong turbulence.

Zero Potential Vorticity in the SQG model.

Simplified diagnosis of frontolysis and frontogenesis.

Abstract

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.