Description of Nonlinear Internal Wave Interactions Using Langevin Methods

A comparison is made between several different methods for calculating energy transport within a wave field. Two Langevin techniques are developed. The first is based on the fluctuation dissipation theorem and provides relaxation rates nu(F)and a transport equation. The second method is an application of the Krylov-Bogoliubov-Mitropolsky perturbation theory and provides a Langevin rate constant nu(P) at lowest order. The two formulations are shown to be closely related to the radiative transfer (Boltzmann) equation whose rate is the difference between nu(F) and nu(P). Specific application of the Langevin methods is to internal waves in the ocean. Computations show that the GM-76 spectrum is approximately an equilibrium spectrum except for frequencies near the inertial frequency and at the lowest vertical mode numbers. The sensitivity of nu(F) and nu(P) to spectral form is also discussed. Simple analytic expressions for the rates are derived for the induced diffusion, elastic scattering, and parametric subharmonic instability mechanisms. Only the first of these mechanisms is ever of much numerical significance. Finally, net energy flow in the non-equilibrium portion of the GM-76 spectrum is discussed.