2000. The American Astronomical Society. All rights reserved. Printed in U.S.A.( INFLUENCE OF COHERENT AND RANDOM FLOWS ON THE SOLAR f-MODE

The solar f-mode is referred to as a surface gravity wave that exists right below the solar corona. For a high horizontal wavenumber k, the frequency u of this mode is given by the dispersion relation u2 \ gk, where g is the surface gravity of the Sun. However, the observations of this mode revealed deviations from this simple dispersion relation. According to these observations, for high values of k, the f-mode frequency is signiÐcantly lower than the frequency given by the simple dispersion relation and the line width grows with k. The purpose of this paper is to display some of the features that go into a theoretical description of the Ñow that occurs in the convection zone and its eect on the spectrum of the f-mode oscillations. In particular, we aim to consider coherent and random Ñows that may be associ-ated with supergranules and granules. In the case of the coherent horizontal Ñow we derive a generalV0,dispersion equation that is valid for arbitrary equilibrium proÐles. The space-dependent Ñow V0(z)exhibits a singularity at the vertical position for which As a special example, thez \ z c, u/k \ V0(zc).case of an isothermal atmosphere and a uniform Ñow is discussed in detail to show the Doppler eect. In the case of the random Ñow, we generalize the dispersion relation derived by Murawski & Roberts for a space- and time-dependent velocity Ðeld. While the eect of a space-dependent random Ðeld is to reduce frequencies and attenuate the f-mode, a time-dependent random Ñow can increase frequencies and amplify the f-mode. Solving the random dispersion equation numerically for various parameters of the equilibrium and random Ðeld, we Ðnd that the frequencies and line widths of the random f-mode are close to those observed recently by the Solar and Heliospheric Observatory (SOHO) MDI instrument