Influence of turbulent energy spectra on damping and frequency reduction of the solar f-mode

This paper generalizes the random wave theory that was developed to explain the recently observed line width spreading and frequency reduction of the f-mode. The generalization is based on a replacement of the Gaussian energy spectrum by a more realistic spectrum such as von Karman, Reynolds, or exponential as well as on an averaging of the results over various granules. The f-mode reduces its frequency as it spends more time propagating against the flow than with the flow. As a result, its effective speed and consequent frequency omega are reduced. This reduction is revealed by the real part of omega. The negative imaginary part of the frequency represents the damping of the coherent f-mode held due to scattering by turbulent flow. The f-mode damping is a result of the generation of the turbulent field at the expense of the coherent held. Theoretical estimation of the line width and frequency shift leads to the conclusion that for high spherical degree the results are consistent with the properties of the f-mode obtained from the high-resolution Michelson Doppler Imager (MDI) data from the Solar and Heliospheric Observatory recently reported by Duvall et al. As a result of averaging, we have obtained a significant improvement of our theoretical results.