Nonlinear Critical Layers in Barotropic Stability

Abstract

Abstract Applying the method of matched asymptotic expansions (MAE) to the shallow water equations on a rotating sphere, the structure of critical layers that occur in the linear and inviscid analysis of neutral disturbances of barotropic zonal flows is investigated, assuming that the critical layers are controlled by nonlinearity rather than viscosity or nonparallel flow effects. It turns out that nonlinearity is insufficient to resolve the critical layer singularity completely. It suffices however to connect linear and nondissipative solutions across critical latitudes.