Flow over Topography and Instability on a Sphere

Abstract

The linear instability properties of exact steady-state solutions is examined for barotropic flow over topography on a sphere, in both severely truncated and high-resolution formulations. In particular, we consider the instability of flows consisting of a solid-body rotation plus a single nonzonal spherical harmonic. We compare our results with previous beta-plane studies and find that, while the results are generally qualitatively similar, there are some differences. In particular, there are some disturbances in the beta-plane study, which show no form drag mechanism, although the analogous disturbances in the spherical case show that form drag instability plays some role, even if only a very subordinate one. Results are presented that show that topography can promote the growth of perturbations either through a form drag mechanism, which modifies the globally averaged angular momentum of the basic state, or through its action as a catalyst that can initiate wave-wave interactions between the basic state wave and the disturbance, while leaving the globally average angular momentum unchanged. Both types of topographic instability are illustrated using simple triad calculations. It is shown that analogous beta-plane results hold for sufficiently large channel width. Further, we show that the effects of the inclusion of topography on the instability of basic states, which are normally barotropically unstable, are to (i) promote stationary flow patterns, (ii) stabilize the flow in the super-resonant region, (iii) destabilize subresonant flows, and (iv) excite smaller-scale disturbances as the solid-body rotation term of the basic state approaches zero from above.