Influence of Coherent and Random Flows on the Solarf‐Mode

Abstract

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 ω of this mode is given by the dispersion relation ω2 = 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 significantly 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 flow that occurs in the convection zone and its effect on the spectrum of the f-mode oscillations. In particular, we aim to consider coherent and random flows that may be associated with supergranules and granules. In the case of the coherent horizontal flow V0, we derive a general dispersion equation that is valid for arbitrary equilibrium profiles. The space-dependent flow V0(z) exhibits a singularity at the vertical position z = zc, for which ω/k = V0(zc). As a special example, the case of an isothermal atmosphere and a uniform flow is discussed in detail to show the Doppler effect. In the case of the random flow, we generalize the dispersion relation derived by Murawski & Roberts for a space- and time-dependent velocity field. While the effect of a space-dependent random field is to reduce frequencies and attenuate the f-mode, a time-dependent random flow can increase frequencies and amplify the f-mode. Solving the random dispersion equation numerically for various parameters of the equilibrium and random field, we find 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.