ENERGY, ENERGY FLUX AND LAGRANGIAN OF ROSSBY WAVE

The energy flux derived from the barotropic vorticity equation differs from that obtained directly from the momentum equation. We re-study this problem raised in early 60's. The results show that if the momentum equation is rewritten in such a form that it contains the same conditions as that for barotropic vorticity equation, then the same energy flux form can be obtained for the waves with the constant amplitude. With this new momentum equation, the potential energy of Rossby wave is derived and the Lagrangian of the non-linear barotropic vorticity equation can be found approximately with this potential energy. This privides the physical basis for studying the dynariics of non-linear Rossby wave with the approach of variation.