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

Abstract

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 + ∇.( ε c g ) = 0, (1) where ε = ∂ L /∂ω, L being the average Lagrangian, ω the frequency and c g the group velocity. The energy density E is given by ω (∂ L / ∂ ω )– L , but as L = 0 We have ε = E / ω .