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 a 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)M² in the long-wavelength limit, and the shift at short wavelengths is -2/3 M², where M is the average Mach number of the flow. In our model of solar convection, the low-degree f-mode shift is positive and unobservably small, whereas the fractional frequency shift at high degrees (l ≫ 500) is -M², where M is the Mach number of convection near the solar surface.