Numerical simulations of stochastically excited sound waves in a random medium

In turbulent acoustic media such as the solar envelope, both wave sources and the propagation characteristics (background density, refractive index, dissipation, etc.) are stochastic quantities. By means of numerical simulation of the Euler equations, we study two cases in a homogeneous stochastic medium in which the background density fluctuations and wave sources are 1) correlated and 2) uncorrelated. We find that in the uncorrelated case, the coherent (or mean) acoustic field is zero, leaving only an incoherent field. In the correlated case, the coherent field is nonzero, yielding both coherent and incoherent fields. We question the use of mean-field dispersion relations to determine frequency shifts in p-mode and f-mode spectra, since the coherent field can be non-existent or weak relative to the incoherent field. We demonstrate the importance of accounting for a stochastic wave source by showing that the two cases give very different frequency shifts