Turbulence and surface gravity waves on the Sun

The interior of the Sun cannot be observed directly. Deductions about the structure of the interior are made by observing wave motions at the surface of the Sun ("helioseismology"). Thus, it is desirable to have as full an understanding as possible of these waves, and of how they are influenced by different physical factors. Here we consider only the solar f-mode: an incompressible, buoyancy-driven oscillation confined to the near-surface region. In the classical theory f-modes are described by the standard water wave theory for incompressible, infinitely deep water. Observations of the f-mode show small, but significant, deviations from the classical dispersion relation. In particular, at large wavenumber the observed frequency is smaller by a few percent. One of the physical effects which is neglected in the classical theory is that of turbulent flows in the Sun's photosphere. We examine the impact of such random flows, revisiting the approach of Murawski and Roberts [12]. We assume that the random flow is quasi-steady, and that the turbulent velocity scale is small compared with the phase velocity of f-modes with wavelength comparable to the turbulence length scale - both reasonable assumptions for the parameter regime of interest. For simplicity we also take the flow to be irrotational, which means we cannot capture the scattering of the wave by the turbulence. We then find that, to leading order, the effect of the random flow is to reduce the frequency, by a little more than that observed, and to damp the wave. At large wavenumber we obtain damping identical to that obtained by Sazontov and Shagalov [14]. In contrast to ours, their result was derived purely from the scattering of the wave.