Resonant Topographic Waves in Barotropic and Baroclinic Flows

Abstract

The problem of resonant, topographic quasi-geostrophic waves is examined analytically by exploiting simplifications that arise when the flow is nearly resonant. The barotropic and (two-layer) baroclinic problems are studied. In each case the topographic linear stability problem is solved explicitly and analytic expressions are given for the growth rate. The bifurcation problem in finite amplitude also is described. Some differences with earlier treatment are noted. In particular, in the barotropic problem subresonant instability may occur if the zonal wavelength is long enough. In both the barotropic and baroclinic problems the critical point at which multiple equilibria occur does not correspond to the stability thresholds of the linear problem. In the baroclinic problem Reynolds stresses are found to be of equal importance with eddy heat fluxes in altering the zonal flow although only the latter can transfer energy to the wave field for the zonal velocity profile considered. Analysis of the marginally stable wave at the minimum critical shear of the ordinary baroclinic stability problem shows that topography is stabilizing.