Statistics of normal mode amplitudes in a random ocean

Abstract

Acoustic waves in a random ocean have been studied by means of coupled mode equations, a system of stochastic ordinary differential equations for the acoustic normal mode amplitudes as a function of range. The random coupling coefficients represent scattering from internal wave normal modes. Deterministic master equations, which predict the average power in each mode as a function of range, can be derived from the coupled mode equations by using certain approximations. Monte Carlo simulations, numerically solving many realizations of the coupled mode equations, have been carried out in order to establish the validity of the master equations as a function of range and acoustic frequency. In addition, fluctuations of the power about the average value are predicted by yet another system of equations, but whose coefficients are linear combinations of those appearing in the master equations. The Monte Carlo results also establish the region of validity of these fluctuation predictions. [Work supported by ONR.]