Numerical simulations of frequency shift and amplitude alteration of sound waves in random mass density and velocity fields

Abstract

We investigate the effect of space-and time-dependent random mass density and velocity fields on frequencies and amplitudes of small sinusoidal acoustic waves. The dispersion relations and their approximate solutions, which are valid in the limit of weak random fields and long sound waves, are presented. These approximate solutions are verified by numerical simulations for the full set of hydrodynamic equations. The main findings are: (a) both the analytical and numerical results reveal that random fields affect the frequencies and amplitudes of sound waves. A space-dependent (time-dependent) random field leads to wave attenuation (amplification). Random mass density and time-dependent random velocity fields lift up frequencies of sound waves. A space-dependent random velocity field produces redshifts in frequencies; (b) in the limit of validity of analytical solutions the numerical results are close to the analytical data; (c) for a stronger random field and for shorter sound waves, numerical and analytical data depart from each other.