Orographically Induced Rossby Wave Instabilities

Abstract

Recently, the effects of nonlinearity on waves forced by sinusoidal orography in severely truncated barotropic and baroclinic models have been explored. Multiple equilibria were found for fixed forcing and these have been associated with zonal and blocked states of the global circulation, although the contrast between states was less marked in the baroclinic model. The presence of multiple equilibria is dependent on instability of the basic forced solution. This instability in barotropic and baroclinic models is the subject of this study. In the barotropic case, the instability seems to be new but the baroclinic counterpart is shown to be a variation of the dynamics exhibited by Simmons in his study of planetary-scale waves in the polar winter stratosphere. These two instabilities are shown to play important, but different, roles in determining the behavior of simple models in the presence of forcing and dissipation. An extension is made to a five-layer, σcoordinate, primitive equation model on the sphere, using more degrees of freedom. Taking as the basic state the Northern Hemisphere winter zonal mean flow, orographically unstable modes are found. In all but one case, the associated growth rates are much smaller than those corresponding baroclinic instability, even for rather large mountains. This is in contrast with the results from simple, highly truncated β-plane models and suggests that in more realistic situations, orographically induced instabilities may not be so important. However, the work has deepened our understanding of some of the possible interactions of Rossby waves with mountains.