The effects of gravity waves on the mean radial differential rotation profile in the solar tachocline are studied, including the effect of a uniform, toroidal magnetic field. Vertical transport of horizontal momentum arises from the radiative damping of inwardly traveling waves that are generated by low-frequency, convective fluid motions. By considering two-wave and one-wave interactions, the radiatively damped gravity waves are shown to accentuate the shear in the mean radial differential rotation. In the presence of a strong horizontal magnetic field, internal gravity waves become nearly Alfvénic and cannot propagate downward through the tachocline. For a magnetic field that is weak enough to permit wave propagation, the mean shear profile is shown to be smoother than that obtained in the case of purely hydrodynamic waves. The implications of our results for gravity-wave forcing of the internal solar rotation are discussed.
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