Solar Oscillations and Convection. I. Formalism for Radial Oscillations

We present a formalism for investigating the interaction between pmodeoscillations and convection by analyzing realistic, three-dimensionalsimulations of the near-surface layers of the solar convection zone. Bychoosing suitable definitions for fluctuations and averages, we obtain aseparation that retains exact equations. The equations for the horizontalaverages contain one part that corresponds directly to the wave equations for a1-D medium, plus additional terms that arise from the averaging and correspondto the turbulent pressure gradient in the momentum equation and the divergenceof the convective and kinetic energy fluxes in the internal energy equation.These terms cannot be evaluated in closed form, but they may be measured innumerical simulations. The additional terms may cause the mode frequencies toshift, relative to what would be obtained if only the terms corresponding to a1-D medium were retained---most straightforwardly by changing the meanstratification, and more subtly by changing the effective compressibility ofthe medium. In the presence of time dependent convection, the additional termsalso have a stochastic time dependence, that acts as a source of randomexcitation of the coherent modes. In the present paper, we derive an expressionfor the excitation power and test it by applying it to a numerical experimentof sufficient duration for the excited modes to be spectrally resolved.Comment: 13 pages, 3 figure