Two types of patterns of localized travelingwave convection in binary fluid mixtures with different structures

The researches on nonlinear science currently cause extensive concern all over the world. The natural phenomena which we usually see, such as the convection in atmosphere, the reservoir, the ocean and so on, are all in nonequilibrium open system away from heat equilibrium. The deep research for these phenomena is indispensable both in harmonious coexistence between human and nature, and in controlling, using nature. Rayleigh-Benard convection is one of the typical models for the research of these phenomena. Its experiment is easy to control and the governing equations for convection are well known. Therefore, the research on the convection stability, spatiotemporal structure and the nonlinear dynamics in Rayleigh-Benard convection model has certain representative, theory value and very important practical significance. So far, investigators have got various traveling waves in Rayleigh-Benard convection in binary fluid mixture by experiments and simulations, and found the dynamics of these states. By using a two-dimensional numerical simulation of the fully hydrodynamic equations in this paper, the formation of the localized traveling wave (LTW) without defects and the dynamics of the LTW with defects in convection in binary fluid mixtures with strong Soret effect in a rectangular at the aspect ratio Γ =20 are studied. The SIMPLE algorithm was used to numerically solve the governing equations consisting of the coupled heat and concentration transfer and fluid flows. The governing equations were solved in primitive variables in a two-dimensional staggered grids with an uniform spatial resolution based on the control (finite) volume method. The power law scheme was used to treat the convective-diffusive terms in the discrete formulation. The discrete equations were solved by an iterative tri-diagonal matrix algorithm (TDMA). For the separation ratio ψ = - 0.60, system appears the LTW without the defects near saddle node of the bifurcation curve for the reduced Rayleigh number r =1.926 - 2.074. Then, system becomes the LTW with the defects from the LTW without the defects with increasing r and forms the stable LTW with the defects in the range of r =2.075 - 2.224. The width of the LTW convection increases with increasing r and enlarges rapidly as the transition of the convection pattern at r =2.075. The LTW with the defects loses its stability, convection dominates the rectangular and evolves into the traveling wave (TW) with the defects with further increasing r . The LTW with the defects is a new type of convection structure which is found for the first time. The formation of the LTW with the defects depends on the width of the LTW. In the range of existence of the LTW with the defects, the period appearing the defects increases with r .