Statistical Dynamics of Weakly Nonlinear Internal Waves.

The Hamiltonian for triad interactions among internal waves in an incompressible, inviscid, rotating, stratified fluid is obtained by expanson of the Lagrangian. The amplitudes of the eigenfunctions of the linear system are used as canonical coordinates. Numerical evidence is presented which indicates that the test wave model, a truncation of the full Hamiltonian, is integrable. The explicit integrals of motion are presented for the case when all triads are resonant and coupling coefficients equals. Application of two Langevin methods yields relaxation rates for the test wave when the ambient wave amplitudes are random and their number is continuously infinite. The relationship between these methods and the radiative transport equation is discussed.