EULER-LAGRANGE RELATIONSHIP FOR RANDOM DISPERSIVE WAVES

It is shown that the equations for the motion of a tagged fluid particle in a random wave field define a singular perturbation problem, characterized by a nonuniformity at large times. The uniformly valid asymptotic expansion to this problem, the Euler-Lagrange relationship for random dispersive waves, is obtained. As an application of these general results, an integral representation of the solution is worked out for the case of vertically propagating random acoustic waves in an isothermal atmosphere. It is shown that the nonuniformity of medium leads to a wave generated diffusion process. The time and length scales over which the process is diffusive are determined, and a formula for the diffusion coefficient is presented.