Baroclinic instability of a symmetric, rotating, stratified flow: a study of the nonlinear stabilisation mechanisms in the presence of viscosity

Abstract

Abstract. This paper presents the analysis of symmetric circulations of a rotating baroclinic flow, forced by a steady thermal wind and dissipated by Laplacian friction. The analysis is performed with numerical time-integration. Symmetric flows, vertically bound by horizontal walls and subject to either periodic or vertical wall lateral boundary conditions, are investigated in the region of parameter-space where unstable small amplitude modes evolve into stable stationary nonlinear solutions. The distribution of solutions in parameter-space is analysed up to the threshold of chaotic behaviour and the physical nature of the nonlinear interaction operating on the finite amplitude unstable modes is investigated. In particular, analysis of time-dependent energyconversions allows understanding of the physical mechanisms operating from the initial phase of linear instability to the finite amplitude stable state. Vertical shear of the basic flow is shown to play a direct role in injecting energy into symmetric flow since the stage of linear growth. Dissipation proves essential not only in limiting the energy of linearly unstable modes, but also in selecting their dominant spacescales in the finite amplitude stage.

Parametric smoothness and self-scaling of the statistical properties of a minimal climate model: What beyond the mean field theories?

“…in the ultralong planetary waves associated with the so called low frequency variability [5,6,15,68]) and at smaller scales (e.g. in the banded sub-frontal structures [55]). The definition of the basic ingredients in the physical mechanism of baroclinic conversion is to be considered one the main successes of the dynamical meteorology of the past century.…”