On Stable and Unstable Rossby Waves in Non-Zonal Oceanic Shear Flow

Abstract

We derive linear equations for the study of baroclinic instability of a non-zonal oceanic shear flow whose direction is allowed to change with depth. These equations can be used to study unstable disturbances as well as stable Rossby waves in such a flow. We find an approximate analytic solution of the equations by using a two-level model. According to this solution a non-zonal shear flow is always unstable, and the length scales of the unstable disturbances are larger than the internal Rossby radius of deformation (corresponding wavelengths are larger than 2π times the internal Rossby radius of deformation). In all our examples of non-zonal shear flow, and strongly unstable zonal shear flow, the wavelength of the fastest growing disturbance is ∼10 times the internal Rossby radius of deformation. Only for weak westward unstable zonal shear flow do we find the fastest growing unstable disturbance to have a wavelength close to 2π times the internal Rossby radius of deformation. We also compute numerical solutions for a stable baroclinic Rossby shear mode in the California Current by using a continuous model.