Abstract:

The motion of sound ray trajectories in deep ocean environments is considered, assuming that the internal wave-induced sound speed fluctuations can be treated stochastically. The ray equations then constitute a system of stochastic differential (Langevin) equations. Equivalently, the expected ray density---an approximation to the average acoustic intensity---can be shown to satisfy a Fokker--Planck equation. The Fokker--Planck equation can be interpreted in fluid mechanical terms as an advection-diffusion equation. This observation leads to the notion of a diffusion-limited (as opposed to diffraction-limited) estimate of the chaos-induced ``predictability horizon.'' [Work supported by ONR.]