Angular momentum transport by gravity waves and its effect on the rotation of the solar interior

We calculate the excitation of low frequency gravity waves by turbulent convection in the sun and the effect of the angular momentum carried by these waves on the rotation profile of the sun's radiative interior. We find that the gravity waves generated by convection in the sun provide a very efficient means of coupling the rotation in the radiative interior to that of the convection zone. In a differentially rotating star, waves of different azimuthal number have their frequencies in the local rest frame of the star Doppler shifted by different amounts. This leads to a difference in their local dissipation rate and hence a redistribution of angular momentum in the star. We find that the time scale for establishing uniform rotation throughout much of the radiative interior of the sun is $\sim 10^7$ years, which provides a possible explanation for the helioseismic observations that the solar interior is rotating as a solid body.