Stochastic interpretations of the oceanic primitive equations with relaxed hydrostatic assumptions

TL;DR

This paper explores stochastic models of oceanic primitive equations with relaxed hydrostatic assumptions, establishing well-posedness and analyzing intermediate models bridging hydrostatic and non-hydrostatic regimes.

Contribution

It introduces a stochastic interpretation of primitive equations with relaxed hydrostatic assumptions and proves their well-posedness in a specific flow regime.

Findings

Well-posedness of stochastic primitive equations with relaxed hydrostatic assumptions

Development of intermediate models between hydrostatic and non-hydrostatic regimes

Analysis of eddy-viscosity models for oceanic flows

Abstract

In this paper, we investigate how weakening the classical hydrostatic balance hypothesis impacts the well-posedness of the stochastic LU primitive equations. The models we consider are intermediate between the incompressible 3D LU Navier-Stokes equations and the LU primitive equations with standard hydrostatic balance. As such, they are expected to be numerically tractable, while accounting well for phenomena within the grey zone between hydrostatic balance and non-hydrostatic processes. Our main result is the well-posedness of a low-pass filtering-based stochastic interpretation of the LU primitive equations, with rigid-lid type boundary conditions, in the limit of ``quasi-barotropic'' flow. This assumption is linked to the structure assumption proposed in the work of Agresti et al., which can be related to the dynamical regime where the primitive equations remain valid. Furthermore, we present and study two eddy-(hyper)viscosity-based models.