A generalized statistical Burgers equation to predict the evolution of the power spectral density of high-intensity noise in atmosphere

Abstract

The present work is a theoretical/numerical investigation of the combined effect of nonlinearity, geometrical spreading, and atmospheric absorption on the evolution of the power spectral density of a noise field, when only the power spectral density is known at source, not the signal itself. This is often the case in aircraft noise measurements. The method presented here is based on and extends previous work [P. Menounou and D. T. Blackstock, J. Acoust. Soc. Am. 115, 567-580 (2004)], where a recursion equation [statistical Burgers equation (SBE)] describing the evolution of the joint moments of the noise source was derived. The SBE is restricted to plane waves, thermoviscous fluids, and short propagation distances (preshock region). In the present work, the SBE is extended to include the effects of geometrical spreading and arbitrary absorption, in order to be applicable to propagation of high-intensity noise through atmosphere. A new equation is derived and termed generalized SBE, and a method for its numerical implementation is presented. Results are in good agreement with time domain calculations for propagation in atmosphere of (i) sinusoidal signals (benchmark case) and (ii) Gaussian processes with known power spectral densities at source.