We describe and implement an approach for determining the eigenfrequencies of solar acoustic oscillations (p modes) in a convective envelope. By using the ray approximation, we transform the problem into one in which we seek the eigenfrequencies of a Hamiltonian system. To find these eigenfrequencies we have written a computer program which implements the method of adiabatic switching. In this technique, we begin with a system with no convective perturbations for which the eigenmodes and eigenfrequencies are known. The code adiabatically increases the strength of the convective structures, allowing the mode eigenfrequency to adjust from its initial value to the eigenfrequency of the perturbed state. The ray approximation restricts our investigations to perturbations which are large compared to the mode wavelength.

For a simple class of structures we test our results against the predictions of semi-classical EBK quantization and find the two methods agree. We then examine more complicated perturbations, concentrating on the dependence of the frequency shifts on the radial and angular mode numbers as well as the perturbation strength. Among our results, we conclude that the fractional frequency shift is given by the weighted average of the perturbation over the resonant cavity. As a result, convective perturbations with horizontally anti-symmetric structures generate downward frequency shifts which are second-order in the perturbation strength. We also examine more complex convective structures which we find tend to produce downshifts whose magnitude scales with the strength of the perturbation. These results may have implications for resolving the differences between eigenfrequencies derived from solar models and those deduced from helioseismic observations.

}, year = {1999}, publisher = {University of Colorado Boulder}, }