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, L_parallel and L_perp, that describe the growth of order parallel and perpendicular to the mean domain orientation. In space dimension d=3 we find, up to constants, L_parallel = gamma t3/2, L_perp = t1/2, where gamma is the shear rate, while for d = 2 we find L_parallel = gamma1/2 t (ln t)1/4, L_perp = gamma-1/2(ln t)-1/4 . Our predictions for d=2 can be tested by experiments on twisted nematic liquid crystals.