Hamiltonian description of barotropic Rossby waves on a sphere and in a paraboloid

Abstract

The transformation to normal canonical variables is found in the rigid top approximation for barotropic Rossby waves of arbitrary amplitude in a thin fluid layer on a sphere. This transformation is used to derive an experssion for the matrix of a three-wave interaction. Canonical variables describing barotropic Rossby waves in a fluid with a free surface on a sphere are also found. In addition, canonical variables describing Rossby waves in a thin fluid layer inside a rotating paraboloid are obtained both in the rigid lid approximation and in the presence of a free surface. The problem with such a geometry is of interest in connection with the use of rotating parabolic setups in laboratory experiments on modeling nonlinear waves and vortices in geophysics (Rossby waves) and in a plasma (drift waves).