Ray chaos in underwater acoustics

Abstract

Generically, in range-dependent environments, the acoustic wave equation cannot be solved by techniques which require that variables be separated. Under such conditions, the acoustic ray equations, which have Hamiltonian form, are nonintegrable. At least some ray trajectories are expected to exhibit chaotic motion, i.e., extreme sensitivity to initial and environmental conditions. These ideas are illustrated numerically using simple models of the ocean sound channel with weak periodic range dependence. The use of Poincaré sections, power spectra, and Lyapunov exponents to investigate and characterize ray chaos are discussed. The practical importance of chaotic ray trajectories—a limitation on one’s ability to make deterministic predictions using ray theory—is emphasized.