Traveling-Wave Convection with Periodic Source Defects in Binary Fluid Mixtures with Strong Soret Effect

Abstract

This paper studied the Rayleigh–Bénard convection in binary fluid mixtures with a strong Soret effect (separation ratio ψ = − 0.6 ) in a rectangular container heated uniformly from below. We used a high-accuracy compact finite difference method to solve the hydrodynamic equations used to describe the Rayleigh–Bénard convection. A stable traveling-wave convective state with periodic source defects (PSD-TW) is obtained and its properties are discussed in detail. Our numerical results show that the novel PSD-TW state is maintained by the Eckhaus instability and the difference between the creation and annihilation frequencies of convective rolls at the left and right boundaries of the container. In the range of Rayleigh number in which the PSD-TW state is stable, the period of defect occurrence increases first and then decreases with increasing Rayleigh number. At the upper bound of this range, the system transitions from PSD-TW state to another type of traveling-wave state with aperiodic and more dislocated defects. Moreover, we consider the problem with the Prandtl number P r ranging from 0.1 to 20 and the Lewis number L e from 0.001 to 1, and discuss the stabilities of the PSD-TW states and present the results as phase diagrams.