Submesoscale baroclinic instability in the balance equations

Abstract

AbstractOcean submesoscale baroclinic instability is studied in the framework of the balance equations. These equations are an intermediate model that includes balanced ageostrophic effects with higher accuracy than the quasigeostrophic approximation, but rules out unbalanced wave motions. As such, the balance equations are particularly suited to the study of baroclinic instability in submesoscale ocean dynamics. The linear baroclinic instability problem is developed in generality and then specialized to the case of constant vertical shear. It is found that non-quasigeostrophic effects appear only for perturbations with cross-front variation, and that perturbation energy can be generated through both baroclinic production and shear production. The Eady problem is solved analytically in the balance equation framework. Ageostrophic effects are shown to increase the range of unstable modes and the growth rate of the instability for perturbations with cross-front variation. The increased level of instability is attributed to both ageostrophic baroclinic production and shear production of perturbation energy; these results are verified in the primitive equations. Finally, submesoscale baroclinic instability is examined in a case where the buoyancy frequency increases rapidly near the bottom boundary, mimicking the increase of stratification at the base of the oceanic mixed layer. The qualitative results of the Eady problem are repeated in this case, with increased growth rates attributed to the production of perturbation energy by the ageostrophic velocity. The results show that submesoscale baroclinic instability acts to reduce lateral buoyancy gradients and their associated geostrophic shear simultaneously through lateral buoyancy fluxes and vertical momentum fluxes.