Long-wave oscillatory convection in a binary liquid: Hexagonal patternsS. Shklyaev1, A. A. Nepomnyashchy2, 3 and A. Oron4
1 Department of Theoretical Physics, Perm State University - Bukirev 15, 614990 Perm, Russia
2 Department of Mathematics, Technion - Israel Institute of Technology - Haifa 32000, Israel
3 Minerva Center for Nonlinear Physics of Complex Systems, Technion - Israel Institute of Technology Haifa 32000, Israel
4 Department of Mechanical Engineering, Technion - Israel Institute of Technology - Haifa 32000, Israel
received 27 August 2008; accepted in final form 12 March 2009; published April 2009
published online 17 April 2009
We consider long-wave oscillatory convection in a layer of a binary liquid. Weakly nonlinear analysis is carried out on a hexagonal lattice. It is shown that the set of amplitude equations with cubic nonlinearity is degenerate. In order to investigate the pattern formation it is necessary to proceed to the fifth order in terms of the amplitude of convective motion. The resulting set of equations demonstrates the emergence of a heteroclinic cycle: The system wanders between three unstable limit cycles, being alternately attracted to and then repelled from each of them. The heteroclinic cycle is found to be stable.
47.20.Ky - Nonlinearity, bifurcation, and symmetry breaking.
47.54.-r - Pattern selection; pattern formation.
47.20.Dr - Surface-tension-driven instability.
© EPLA 2009