Abstract |

**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 )*

*e-mail:
anz@obs-nice.fr*

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