ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

4pPAa5. Analytical method for describing the paraxial region of finite amplitude sound beams.

Mark F. Hamilton

Dept. of Mech. Eng., Univ. of Texas at Austin, Austin, TX 78712-1063

Vera A. Khokhlova

Oleg V. Rudenko

Moscow State Univ., Moscow 119899, Russia

The paraxial region of finite amplitude sound beams in lossless fluids is studied theoretically. Both focused and unfocused beams are considered. A special analytical method which combines the parabolic approximation (KZ equation) with nonlinear geometrical acoustics (NGA) is developed to model nonlinear and diffraction effects near the axis of the beam. The corresponding system of nonlinear equations describing waveform evolution is derived. For the case of an initially sinusoidal wave radiated by a Gaussian source, an analytical solution of the coupled equations is obtained along the axis of the beam. The solution is expressed in both the time and frequency domains. In the high-frequency limit, classical simple wave solutions are recovered (plane-wave solution for unfocused beams and spherical wave solution for focused beams). In the limit of weak nonlinearity, the quasilinear axial solutions of the KZ equation for the fundamental and second-harmonic components are recovered. The analytical solution is in good agreement with numerical solutions of the KZ equation for a wide range of ratios between the focal length, Rayleigh distance, and shock formation distance. Harmonic propagation curves, waveform distortion, focusing amplification factors, and other characteristics are calculated. [Work supported in part by NATO and ISF.]