Old-age stage evolution of intense cylindrical and spherical acoustic noise

Abstract

The investigation of the old-age behavior of an intense periodic spreading wave was one of the significant contributions of Crighton in nonlinear acoustics. By him and his co-workers a classification of different regimes of evolution was done and it was shown at which condition the saturation of the amplitude takes place. Here the evolution of intense spreading acoustic noise is considered on the base of generalized Burgers’ equations. It is shown that at the old-age (linear) stage the energy spectrum of the noise has a universal structure: it is proportional to the second power of the frequency at small frequencies and decreases exponentially at high frequencies. The proportionality coefficient does not depend on the distance and is determined by the nonlinear effects on the initial stage of the propagation. It is shown that even for a small acoustical Reynolds number the energy of the noise at the old-age stage is proportional to the third power of the initial energy for cylindrical waves and to the power 5/2 with some logarithmic correction for spherical waves. The analytical estimations are supported by numerical simulation. [Work supported by RFBR and INTAS grants.]