Abstract

Continuous and Discontinuous Asymptotically Universal Waveforms for Sound Beams: Exact Solutions of KZ Equation

Yu.N.Makov (Department of Acoustics, Faculty of Physics, Moscow State University, Moscow, Russia)

e-mail: makov@acs364.phys.msu.su

Continuing the investigation started previously [see: Makov Yu. N., Acoust. Phys. 43(6), 722 (1997);Makov Yu. N., Proc. of 16th Int. congress on Acoustics and 135th Meeting Acoust. Soc. of America, Seattle 1998, v.4, pp 2887-2888], two different types of exact analytical and physically realistic solutions of the Khokhlov-Zabolotskaya (KZ) equation were found. These solutions correspond to asymptotically universal wave profiles of sound beam after passage of sufficiently large distance then profile acquires the specific invariable form. The ratio of nonlinearity, initial curvature of the phase front and diffraction leads to forming either discontinuous asymptotically universal wave profile (type of N-wave) or continuous asymptotically universal wave profile (type of U-wave). The self-similar traveling wave profiles (indifferent to starting conditions) are used for the procedure of analytical funding of these solutions of KZ equation. The obtained analytical wave profiles consist of the periodically repeating parts of corresponding hyperbolas. These profiles play the same role among all variations of solutions of KZ equation, such as the well-known sawtooth-shaped wave among all possible solutions of the equation of the simple waves (Riemann.s equations). The analytically derived two different types of asymptotically universal waveform for sound beams are in excellent agreement with the currently available experimental data and numerical results. [Work supported by RFBR, # 01-02-16655]

Section : 1