J. Vanneste et F. Vial, INTERACTION EQUATIONS FOR ROSSBY WAVES DERIVED FROM HAMILTONS PRINCIPLE IN THE EULERIAN DESCRIPTION, Proceedings - Royal Society. Mathematical and physical sciences, 450(1940), 1995, pp. 667-676
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.