Propagation and localization of Rossby waves over random topography (two-layer model)

We study propagation of Rossby waves over randomly stratified bottom topography in a two-layer system. The problem is reduced to coupled stochastic wave equations in latitudinal variable with suitable boundary conditions. When the two-dimensional system is broken into its basic barotropic and baroclinic modes, each one is scattered by the medium, and generates the like-wise and the cross-wise components. We study statistics of the reflection and transmission coefficients for both types of generated modes, and show localization for the like-wise components, and propagation for the cross-wise components. The localization lengths and the transmission rates are estimated in terms of the basic parameters of the system and the correlation-function of topographic fluctuations.