Coarsening dynamics of a nonconserved field advected by a uniform shear flow

We consider the ordering kinetics of a nonconserved scalar field advected by a uniform shear flow. Using the Ohta-Jasnow-Kawasaki approximation, modified to allow for shear-induced anisotropy, we calculate the asymptotic time dependence of the characteristic length scales, Lₚarallel and Lₚerp, that describe the growth of order parallel and perpendicular to the mean domain orientation. In space dimension d=3 we find, up to constants, Lₚarallel = gamma t^3/2, Lₚerp = t^1/2, where gamma is the shear rate, while for d = 2 we find Lₚarallel = gamma^1/2 t (ln t) ^1/4, Lₚerp = gamma^-1/2 (ln t) ^-1/4. Our predictions for d=2 can be tested by experiments on twisted nematic liquid crystals.