INTERACTION EQUATIONS FOR ROSSBY WAVES DERIVED FROM HAMILTONS PRINCIPLE IN THE EULERIAN DESCRIPTION

Variational principles provide a useful tool for deriving the evolutio n equations of a resonant triad of hydrodynamic waves, but they are of ten considered in the Lagrangian description, as Eulerian variational principles require the introduction of extra variables, related to the particle displacements. To show that a variational approach remains p ossible with these extra variables, the derivation of interaction equa tions is presented in detail for Rossby waves on a beta-plane, using a variational principle based on the Clebsch representation of the velo city field.