Turbulent f-mode in a stratified solar atmosphere

The solar f-mode is a surface gravity wave which high horizontal wavenumber k and the frequency ω satisfy 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. We derive a general dispersion equation which is valid for arbitrary vertical profiles of the stratified solar atmosphere. As an illustrative example the case of isothermal atmosphere is considered. Solving this equation numerically for various parameters of the equilibrium and the turbulent flow we find that the frequencies and line-widths of the turbulent f-mode are close to those observed recently by the SOHO/MDI.