Sound Speed in a Random Flow and Turbulent Shifts of the Solar Eigenfrequencies

Perturbation theory is used to calculate the frequency shift of acoustic modes of an homogeneous turbulent fluid and the frequency shifts of solar modes due to turbulent convection. For sound waves in a random flow, the fractional frequency shift is +(11/30)M^2 in the long-wavelength limit, and the shift at short wavelengths is -(2/3)M^2, where M is the average Mach number of the flow. In our model of the solar convection, the low-degree f-mode shift is positive and unobservably small, whereas the fractional frequency shift at high degrees (l\gg 500) is -M^2, where M is the Mach number of convection near the solar surface.