Instability of a periodic flow in geostrophic and hydrostatic balance

Instability of a flow in geostrophic and hydrostatic balance is investigated using numerical simulations of the fully nonlinear, rotating, stratified Boussinesq equations. Burger numbers less than one and small aspect ratio are considered. Although the model we consider has continuous stratification in the vertical, in terms of phenomenology, the large scale baroclinic instability we find is most closely related to that found in the classical setting of Eady 1949 [8]. Indeed, the growth rate and scale of the most unstable mode scale similarly. The advantage of the model we consider lies in being able to use it in studies of unbalanced processes. Preliminary experimentation suggests that there is a small scale instability at small values of Burger number. This instability is initiated in anticyclonic regions, is likely imbalanced, and likely leads to small scale dissipation. By considering two measures of balance-one based on a wave-vortex decomposition and another based on the quasi-geostrophic omega equation-we study the dependence of imbalance on Rossby number. We, however, find that kinetic energy spectra display slopes consistent with quasi-geostrophic turbulence, with no break in slope at high wavenumbers.