 Energy partition of rotating internal waves

For a plane inertia-gravity wave independent of one horizontal coordinate, period-mean kinetic and available potential energy obey $⟨K⟩-⟨A⟩=2⟨K_y⟩$. The transverse rotating velocity is in quadrature with the in-plane velocity. The modified oscillator balance is $⟨K_{xz}⟩=⟨A⟩+⟨K_y⟩$; ordinary kinetic/potential equipartition occurs only when the transverse amplitude vanishes.