Inertial instabilities of stratified jets: Linear stability theory

Abstract

This paper uses a linear stability analysis to investigate instabilities of barotropic and baroclinic jets that satisfy the necessary condition for inerital instabilities within the context of a rotating, stratified Boussinesq model. First, we review the different types of instabilities that can occur in these jets and the conditions that make the jet subject to inertial instability but stable to Rayleigh–Taylor instability. Second, we numerically solve one-dimensional and two-dimensional eigenvalue problems for the linear stability problems and examine the dependence of the growth rates on the Rossby number, Burger number, the aspect ratio, and the Reynolds number. We find that there are two critical Reynolds numbers where there is a transition between what type of instability has the largest growth rate. Finally, we examine the characteristics of inertial instabilities in more detail for three selected parameter sets: a low Reynolds number regime, a high Reynolds number regime, and a regime with low Reynolds number and larger aspect ratio. The most unstable mode in the low Reynolds number regime is a barotropic–baroclinic instability and has a barotropic spatial structure. In contrast, the most unstable mode in the high Reynolds number regime is an inertial instability and its spatial structure is independent of the along-flow direction. Modes with this property are commonly referred to as symmetric instabilities. In the intermediate regime, the flow can be unstable to both barotropic–baroclinic and inertial instabilities, possibly with comparable growth rates.