Baroclinic Instability of Nonzonal Flows and Bottom Slope Effects on the Propagation of the Most Unstable Wave

Abstract

AbstractA linear, two-layer potential vorticity (PV) equation model on the β plane is employed to study the baroclinic instability of nonzonal basic currents flowing over a uniform bottom slope. Criteria for the instability, phase speed, and growth rate of unstable waves are all given as functions of the basic shear velocity, β, and bottom slope. The study suggests two kinds of long wave cutoff, one induced by the slope and the other by β; the first one exists in all directions, while the second requires at least a slight deviation of the wave vector from the meridians. Subtle differences between configurations of the PV gradient lead to completely different characteristics of unstable perturbations, such as propagation and scale. In the case of a positive slope (the bottom slope in the same direction as the isopycnal tilt), the fastest-growing wave is capable of propagating across the basic flow streamlines. By contrast, in the case of a negative slope (the bottom slope opposed to the isopycnal tilt), the most unstable wave always propagates along the streamlines. In addition, the spatial scale of the most unstable mode can be heavily reduced by a negative slope.