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

We consider the ordering kinetics of a nonconserved scalar field advected b y a uniform shear flow. Using the Ohta-Jasnow-Kawasaki approximation (Ohta T, Jasnow D and Kawasaki K 1982 Phys. Rev. Lett. 49 1223), modified to allo w for shear-induced anisotropy, we calculate the asymptotic time dependence of the characteristic length scales, L-parallel to and L-perpendicular to, that describe the growth of order parallel and perpendicular to the mean d omain orientation. In space dimension d = 3 we find L-parallel to similar t o gamma t(3/2), L-perpendicular to similar to t(1/2), where gamma is the sh ear rate, while for d = 2 we find L-parallel to similar to gamma (1/2)t (ln t)(1/4) L-perpendicular to similar to gamma(-1/2)(ln t)(-1/4). Our predict ions for d = 2 can be tested by experiments on twisted nematic liquid cryst als.