Double-diffusive convection of a binary mixed fluid in a rectangular enclosure with horizontal temperature and concentration gradients is numerically investigated. The problem with thermal Rayleigh numbers of 10(4) and 10(5), the Prandtl number being range of [0.015,12], the Lewis number being range of [0.05, 100], the buoyancy ratio of 0.8, and the height-to-width aspect ratio of 2 are considered. A compact difference method with fully fourth-order accuracy and high resolution in space, involving a, at least, fourth-order upwind compact scheme suggested for approximation of the nonlinear convective terms, a fourth-order symmetrical compact scheme to discretize the viscous terms and the third-order TVD Runge-Kutta method employed for time discretization, is proposed for solving this unsteady double-diffusive convection problem. The effects of Prandtl and Lewis numbers on flow structure, the temperature and concentration distribution are investigated and discussed for Ra = 10(4) and 10(5) respectively in a rectangular enclosure with the aspect ratio A = 2. A bifurcation for the double-diffusive convection is captured with the variation of Prandtl number, and two different types of periodic flow motion with Lewis number in different ranges are observed. (C) 2013 Elsevier Ltd. All rights reserved.