Group velocity and energy transport by Rossby waves

A variational method gives a proof that, for normal modes of Rossby waves in the ocean on a-plane with depth variable in the meridional direction, the time average of the energy flux defined as the product of the pressure and the fluid-particle velocity agrees with the time average of the energy density multiplied by the group velocity. This conclusion holds in considerably general situations and sheds light on the controversial problem of the energy transport by Rossby waves. Moreover, the variational method gives a remarkable relation between the group velocity and the phase velocity. In particular this relation shows that the absolute value of the group velocity never exceeds that of the phase velocity.