On the Self-Similar Behavior of the Intense Acoustics Noise
A.Noullez (Observatoire de Nice, Nice, France); S.N.Gurbatov (Department of Radiophysics, University of Nizhny Novgorod, Nizhny Novgorod, Russia )
The Burgers equation can be used to describe the propagation of high ampli-tude acoustic noise. Even though it can be integrated explicitly, it was recently realized [S.N. Gurbatov, S.I. Simdyankin, E. Aurell, U.Frisch and G. Toth, J. Fluid. Mech. 1997, v. 344, p. 339] that the asymptotic form of the spectrum is self-similar and depends only on two integral parameters of the initial spectrum: the variance of the velocity and its spatial scale. Moreover, widely different initial conditions having the same value of these parameters could converge to the same asymptotic state, without any rescaling of this state. This prediction is checked numerically and found to be valid for sufficiently steep initial spectra. In this quasi-monochromatic case, the spectrum is found to evolve by the simultaneous generation of low-frequency compo-nents and high-frequency harmonics with different growth and decay rates. This leads to various successive regimes of energy decay before going to the asymptotic state. These different regimes can be predicted analytically and have been checked by direct numerical simulations of the equation. Work supported by RFBR grants 02-02-17374.
Section : 8