Statistical field theory and the internal wave problem

Abstract

The methods of quantum and classical statistical field theory are discussed in relation to the internal wave problem. The merit of these methods in this context is that they provide a deeper understanding of the approximations currently in use from a viewpoint which has been used systematically and successfully in many areas of physics. These methods can be applied directly to the nonlinear primitive field equations in Eulerian variables, thus avoiding the simplifying assumptions inherent in the resonant interaction formalism. Propagator renormalization techniques provide formulas for the nonlinear internal wave frequency and spectral width in terms of the energy spectrum. The commonly used multiple time and space scale analysis is replaced by an analysis of the two‐point correlation function in terms of sum and difference variables. This permits the systematic development of a Landau equation. This generalization of the Boltzmann equation incorporates spatial variation of the group velocity and scatterin...