Statistics of normal mode amplitudes in a random ocean. I. Theory

A statistical theory of acoustic propagation in a model random ocean, valid in the limit of low acoustic frequency, is presented. A random internal-wave model gives sound-speed fluctuations δc (r,z,t) about a deterministic profile ? (z). Using normal modes of ? (z) as a basis, the theory gives quantitative estimates of statistical moments of the mode amplitudes ψn(r,t), which are randomly coupled via δc. Invoking a quasistatic approximation, the theory treats time as a parameter. From any initial (r=0) distribution of modal powers ‖ψn‖2, the evolution of their averages to an equilibrium is predicted by ’’coupled power’’ equations. The theory makes similar predictions for average fluctuations of the modal powers about their means. In the equilibrium limit, the theory gives the full probability distribution of the ψn.