ON THE GENERATION OF SOUND BY TURBULENT CONVECTION .1. A NUMERICAL EXPERIMENT

Motivated by the problem of the origin of the solar p-modes, we study the generation of acoustic waves by turbulent convection. Our approach uses the results of high-resolution, three-dimensional simulations as the experimental basis for our investigation. The numerical experiment describes the evolution of a horizontally periodic layer of vigorously convecting fluid. The sound is measured by a procedure, based on a suitable linearization of the equations of compressible convection that allows the amplitude of the acoustic field to be determined. Through this procedure we identify unambiguously some 400 acoustic modes. The total energy of the acoustic field is found to be a fraction of a percent of the kinetic energy of the convection. The amplitudes of the observed modes depend weakly on (horizontal) wavenumber but strongly on frequency. The line widths of the observed modes typically exceed the natural linewidths of the modes as inferred from linear theory. This broadening appears to be related to the (stochastic) interaction between the modes and the underlying turbulence which causes abrupt, episodic events during which the phase coherence of the modes is lost.