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Pomphrey et al. 1980
Pomphrey, N., Meiss, J.D. and Watson, K.M. (1980). Description of nonlinear internal wave interactions using Langevin methods. Journal of Geophysical Research 85: doi: 10.1029/JC085iC02p01085. issn: 0148-0227.

A comparison is made between several methods for calculating energy transport among the linear normal modes of the internal wave field. Two Langevin techniques are presented. The first is based on the Fluctuation-dissipation theorem and provides a relaxation rate vF and a transport equation. The second method is an application of the Krylov-Bogoliubov-Mitropolsky perturbation theory and provides a Langevin rate constant vp calculated here only to lowest order. The two formulations are closely related to the radiative transfer (Boltzmann) equation, whose rate is the difference between VF and Vp. Computations confirm the conclusion of McComas and Bretherton that the GM-76 spectrum is approximately a steady state spectrum for three-wave interactions except for frequencies near the inertial frequency and at the lowest vertical modenumbers. The sensitivity of VF and Vp to spectra form is also discussed. Simple analytic expressions for the rates are derived for the induced diffusion, elastic scattering, and parametric subharmonic instability mechanisms. The first of these expressions provides a useful fit to the full computation over much of the spectrum. Finally, net energy flow in the nonequilibrium portion of the GM-76 spectrum is discussed.

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Journal of Geophysical Research
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