Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
1998-05-11
Phys. Rev. E 57, 4238-4249 (1998)
Nonlinear Sciences
Pattern Formation and Solitons
30 pages, 12 figures
Scientific paper
10.1103/PhysRevE.57.4238
Convection in horizontal layers of binary fluids heated from below and in particular the influence of the Soret effect on the bifurcation properties of extended stationary and traveling patterns that occur for negative Soret coupling is investigated theoretically. The fixed points corresponding to these two convection structures are determined for realistic boundary conditions with a many mode Galerkin scheme for temperature and concentration and an accurate one mode truncation of the velocity field. This solution procedure yields the stable and unstable solutions for all stationary and traveling patterns so that complete phase diagrams for the different convection types in typical binary liquid mixtures can easily be computed. Also the transition from weakly to strongly nonlinear states can be analyzed in detail. An investigation of the concentration current and of the relevance of its constituents shows the way for a simplification of the mode representation of temperature and concentration field as well as for an analytically manageable few mode description.
Hollinger St.
Luecke Manfred
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