Exponential growth of multipaths under chaotic conditions in a simple deterministic range-dependent waveguide

Abstract

Propagation is considered in a simple range-dependent waveguide consisting of a constant sound-speed gradient, g, overlying a reflecting sinusoidal bottom. Let a and R denote the amplitude and wavelength of the bottom sinusoid. Previously it has been shown [F. D. Tappert and M. G. Brown, J. Acoust. Soc. Am. 83, 537 (1988)] that when γ = 4π2ac0/Rg exceeds 0.97 ray trajectories exhit global chaos. Under such conditions, ray trajectories have an extreme sensitivity to initial conditions and environmental parameters; they are free to wander without bound in angle-depth space. Under such conditions it is shown that the number of eigenrays connecting a source and receiver on the bottom grows exponentially as the separation between them increases. Meanwhile, the average intensity of the eigenrays decays exponentially. The exponential growth and decay rates are compared to the average Lyapunov exponent for the ray trajectories. These results vividly demonstrate that under chaotic conditions predictability using ray theory is unattainable.