The first entirely self-consistent 2D model of rotational mixing in a stellar radiative zone is presented. This nonlinear problem is solved numerically assuming axisymmetry of the system. The dynamical behaviour of a rotating star is found to be controlled by one parameter only, the ratio of the Eddington-Sweet timescale to the viscous timescale. In the quasi-steady state, the limit of slow rotation recovers Eddington-Sweet theory, whereas in the limit of rapid rotation, the system settles into a centrifugal equilibrium. The evolution of the dynamical structure of the star undergoing spin-down is then studied, and the relevance of these findings to observations of rotational mixing is discussed.