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 (Ohta T, Jasnow D and Kawasaki K 1982 Phys. Rev. Lett. 49 1223), modified to allow for shear-induced anisotropy, we calculate the asymptotic time dependence of the characteristic length scales, L∥ and L⊥, that describe the growth of order parallel and perpendicular to the mean domain orientation. In space dimension d = 3 we find L∥~γt3/2, L⊥~t1/2, where γ is the shear rate, while for d = 2 we find L∥~γ1/2t(ln t)1/4, L⊥~γ-1/2(ln t)-1/4. Our predictions for d = 2 can be tested by experiments on twisted nematic liquid crystals.