Jiang, Zhong-Yue

It has previously been shown that acoustic ray paths in range-dependent ocean models exhibit chaotic behavior. Most of the investigations into the ray chaos phenomenon have been primarily numerical in nature. The objective of this report is to study theoretically the existence of ray chaos in a parabolic ray system with an analytically prescribed sound-speed model consisting of a double-channel profile perturbed by a typical periodic range-dependent disturbance. The perturbed Hamiltonian ray system is studied analytically via Melnikov’s method. It is shown that, under certain conditions, ray trajectories in some regions of the Poincaré section are equivalent to trajectories of the horseshoe map no matter how small the corresponding perturbation is. These conditions are sufficient for ray chaos and easily satisfied, thus explaining why double-channel propagation is very likely to exhibit chaotic behavior. [Work supported by CA43920 NIH.]

Earlier studies [P. J. Westervelt, J. Acoust. Soc. Am. 29, 199–203, 934–935 (1957)] of the mutual nonlinear interaction of two plane waves of sound with each other are extended to include the viscous effect. The viscous effect is considered both from the equations of motion and the equation of state of the medium. An analytical solution to the lowest order scattering process is obtained if the viscous effect of second order and higher can be neglected. In fact, it is shown that the scattered density ρs of two interacting plane waves having the frequencies ω1 and ω2, respectively, satisfies the following equation: ⧠2vρs=⧠2v{c0−2E12+[(2cosθ +B/A)/2ω1ω2 (1−cosθ)]∇2W12 +[DB(c20ω1ω2)−1 / 4A ×(1−cosθ)2]∇2(∂W12/∂t)+[DB(3+cosθ)/2Ac40 (1−cosθ)](∂V12/∂t)}, where E12, V12, and W12 are, respectively, the total, potential, and special defined energy densities, D is the sound diffusivity, B and A are nonlinearity parameters, θ is the intersecting angle, and ⧠2v is a modified d’Alembertian operator. [Work supported by CA43920 NIH.]

Theories on acoustic radiation pressure associated with plane acoustic waves and lossless media have been examined extensively. The radiation pressure produced by a non-plane wave in a lossy unbounded medium was analyzed. The distinction between Lagrangian and Eulerian pressure was used to clarify the understanding of radiation pressure. The radiation pressure exerted on a perfectly absorbing pointwise target by an arbitrary acoustic wave in an unbounded lossy medium was then considered. By using an indirect approach developed in Chu and Apfel [B.-T. Chu and R. E. Apfel, 1673–1687 (1982)], the radiation pressure was analyzed without appealing to the detailed solutions of the governing fluid dynamic equations. It was shown that even in lossy media with arbitrary waves, the radiation pressure experienced by a pointwise target is equal to the Langevin pressure which is the time average energy density at that point. The radiation pressure exerted on a specific target by an arbitrary acoustic wave in an infinite lossy medium was studied and a concise theoretical result was obtained. [The work was supported by grants CA 43920 and HL 41046 from the National Institutes of Health.]