Discussion: the adiabatic invariant for wave propagation in a nonuniform moving medium

Whitham (1965) has developed a general approach to dispersive waves in a stationary medium using a Lagrangian. In considering the implications of his theory for the linear case, he obtains the equation (equation (41) of the preceding paper) ∂ε/∂t + ∇.(εcg) = 0, (1) where ε = ∂L/∂ω, L being the average Lagrangian, ω the frequency and cg the group velocity. The energy density E is given by ω(∂L / ∂ω)–L, but as L = 0 We have ε = E/ω.