### 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
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*Dept. of Mech. Eng., Univ. of Texas at Austin, Austin, TX 78712-1063
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**Vera A. Khokhlova
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Oleg V. Rudenko
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*Moscow State Univ., Moscow 119899, Russia
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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.]