Jiang, Zhong-Yue

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.

Acoustic radiation pressure exerted by an arbitrary acoustic wave in a three-dimensional lossy medium is calculated by extending an indirect approach developed by Chu and Apfel [B-T. Chu and R. E. Apfel, ‘‘Acoustic radiation pressure produced by a beam of sound,’’ J. Acoust. Soc. Am. 72, 1673–1687 (1982)]. Without appealing to the detailed solutions of equations governing fluid motion, a general analytic expression for the radiation pressure in lossy media with arbitrary waves is obtained. When an infinite lossy medium is considered, the expression states that the radiation pressure, to the lowest order of approximation (i.e., second order), is equal to corresponding total energy density. For a special class of confined spaces, the expression leads to a rather general formula for the radiation pressure, in which the radiation pressure is given in terms of various energy densities in the field. Furthermore, a relationship among these energy densities is generalized to the case of lossy media, which enables one to compute the radiation pressure in the class of spaces with the knowledge of the first-order perturbation solution only.

It has 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. Analytical derivation of sufficient conditions for chaos in acoustic systems has been restricted to inherently discrete problems. This article reports a theoretical study of the existence of ray chaos in a class of continuous parabolic ray systems. This class of ray systems is indexed by a family of analytically prescribed double-channel sound-speed profiles perturbed by periodic range-dependent disturbances. The perturbed Hamiltonian ray systems are studied analytically via the Melnikov method. It is shown that, under certain conditions, ray trajectories of the systems are equivalent to trajectories of a classic chaotic system known as the horseshoe map when the perturbation is periodic and small. These conditions are sufficient for ray chaos and easily satisfied, thus explaining why double-channel propagation is very likely to exhibit chaotic behavior.