Transport equations for waves in randomly perturbed Hamiltonian systems, with application to Rossby waves

Transport equations for linear waves in randomly perturbed media are derived for a general class of Hamiltonian systems. These equations govern the evolution in position-wavevector space of the energy density of the waves; they describe the modulations caused by large-scale inhomogeneities of the medium, and the scattering due to weak random perturbations with spatial scales comparable to the wavelengths. Particular attention is paid to the conservative properties of the transport equations inherited from the Hamiltonian structure of the systems considered. The general results are used to derive transport equations for Rossby waves propagating in a two-layer model with random topography.