Non-acceleration theorem for quasi-geostrophic waves

Steady conservative small-amplitude waves have divergence-free Eliassen–Palm flux by wave activity conservation. In a balanced mean state with homogeneous impermeable boundaries and no independently forced residual mean circulation, this gives zero residual circulation and zero mean acceleration. The Eulerian mean circulation can nevertheless be nonzero because the residual circulation includes an eddy-induced correction. Wave dissipation, time-dependent wave activity or boundary forcing can invalidate the conclusion.