Nonlinear saturation of thermal instabilities

TL;DR

This paper demonstrates that a convex pseudoenergy-momentum integral of motion causes nonlinear saturation of thermal instabilities in a one-layer model, explaining observed circulatory motions without indefinite growth.

Contribution

It introduces a new mechanism based on pseudoenergy-momentum conservation for the nonlinear saturation of thermal instabilities in a simplified ocean model.

Findings

Circulatory motions resemble submesoscale observations.

Thermal instabilities do not grow indefinitely due to nonlinear saturation.

The mechanism is based on convex pseudoenergy-momentum invariants.

Abstract

Low-frequency simulations of a one-layer model with lateral buoyancy variations (i.e., thermodynamically active) have revealed circulatory motions resembling quite closely submesoscale observations in the surface ocean rather than indefinitely growing in the absence of a high-wavenumber instability cutoff. In this note it is shown that the existence of a convex pseudoenergy--momentum integral of motion for the inviscid, unforced dynamics provides a mechanism for the nonlinear saturation of such thermal instabilities in the zonally symmetric case. The result is an application of \citet{Arnold-66} and \citet{Shepherd-88a} methods.