Convection in the cores of intermediate-mass and massive stars becomes anisotropic when these stars rotate. Both this anisotropy and the centrifugal force lead to a misalignment of the thermal gradient and the thermal flux, which in turn results in baroclinicity in the upper radiative zone. I argue that this induces a much stronger meridional flow in the radiative zone than previously thought. This leads to significantly enhanced mixing and substantially alters the evolution of these stars by enhancing core-envelope mixing. Unusually, this mixing mechanism does not yield surface abundance enhancement directly, though it may via interactions with other mixing processes.