Random damping and frequency reduction of the solar f-mode

We present observations showing that the frequency of the high-degree f-mod e is significantly lower than the frequency given by the simple dispersion relation, omega(2) = gk, and that the line width grows with the wavenumber k. We attempt to explain that this behavior is the result of the interactio n with granulation, which we model as a random flow. Because the f-mode spe nds more time propagating against the how than with the flow, its effective speed and, consequently, frequency are reduced. Additionally, an eddy visc osity introduces the negative imaginary part of frequency. This negative im aginary part represents the damping of the coherent field due to scattering . The line width is proportional to the magnitude of the imaginary part of the frequency. We apply an analytical perturbation technique and numerical methods to estimate the line width and the frequency shift, and we show tha t the results are consistent with the properties of the f-mode obtained fro m the high-resolution Michelson Doppler Imager data from the Solar and Heli ospheric Observatory.