We discuss the effects of internal gravity waves on the mean radial differential rotation profile in the solar tachocline. Vertical transport of horizontal momentum arises from the radiative damping of inwardly traveling waves that are generated by low-frequency, convective fluid motions. For a viscosity typical of the radiative layers below the convection zone, the equilibrium profile of radial differential rotation is demonstrated to be unstable, possibly leading to turbulent mixing in the tachocline. The effect of a uniform, toroidal magnetic field is discussed. ©2000 American Institute of Physics.