Baroclinic instability and loss of balance

Under the influences of stable density stratification and the earth's rotation, large-scale flows in the ocean and atmosphere have a mainly balanced dynamics-sometimes called the slow manifold-in the sense that there are diagnostic hydrostatic and gradient-wind momentum balances that constrain the fluid acceleration. The nonlinear balance equations are a widely successful, approximate model for this regime, and mathematically explicit limits of their time integrability. have been identified. It is hypothesized that these limits are indicative, at least approximately, of the transition from the larger-scale regime of inverse energy cascades by anisotropic flows to the smaller-scale regime of forward energy cascade to dissipation by more nearly isotropic flows and intermittently breaking inertia-gravity waves. This paper analyzes the particular example of an unbalanced instability of a balanced, horizontally uniform, vertically sheared current, as it occurs within the Boussinesq equations. This ageostrophic, anticyclonic, baroclinic instability is investigated with an emphasis on how it relates to the breakdown of balance in the neighborhood of loss of balanced integrability and on how its properties compare with other examples of ageostrophic anticyclonic instability of rotating, stratified, horizontally sheared currents. It is also compared with the more familiar types of instability for a vertically sheared current: balanced (geostrophic) baroclinic instability, centrifugal instability, and Kelvin-Helmholtz instability.