HAMILTONIAN DESCRIPTION OF BAROTROPIC ROSSBY WAVES ON A SPHERE AND INA PARABOLOID

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 deri ve an expression for the matrix of a three-wave interaction. Canonical variables describing barotropic Rossby waves in a fluid with a free s urface on a sphere are also found. In addition, canonical variables de scribing Rossby waves in a thin fluid layer inside a rotating parabolo id are obtained both in the rigid lid approximation and in the presenc e of a free surface. The problem with such a geometry is of interest i n connection with the use of rotating parabolic setups in laboratory e xperiments on modeling nonlinear waves and vortices in geophysics (Ros sby waves) and in a plasma (drift waves).