Long-wave oscillatory convection in a binary liquid: Hexagonal patterns

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

Corresponding authors: shklyaev@psu.ru nepom@math.technion.ac.il meroron@techunix.technion.ac.il

Received: 27 August 2008
Accepted: 12 March 2009

Abstract

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.