title: Oscillatory long-wave Marangoni convection in a layer of a binary liquid: hexagonal patterns.
abstract: We consider a long-wave oscillatory Marangoni convection in a layer of a binary liquid in the presence of the Soret effect. A weakly nonlinear analysis is carried out on a hexagonal lattice. It is shown that the derived set of cubic amplitude equations is degenerate. A three-parameter family of asynchronous hexagons (AH), representing a superposition of three standing waves with the amplitudes depending on their phase shifts, is found to be stable in the framework of this set of equations. To determine a dominant stable pattern within this family of patterns, we proceed to the inclusion of the fifth-order terms. It is shown that depending on the Soret number, either wavy rolls 2 (WR2), which represents a pattern descendant of wavy rolls (WR) family, are selected or no stable limit cycles exist. A heteroclinic cycle emerges in the latter case: the system is alternately attracted to and repelled from each of three unstable solutions.
authors.affiliation: Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: S
authors.initials: S
authors.lastname: Shklyaev
authors.forename: A A
authors.initials: AA
authors.lastname: Nepomnyashchy
authors.forename: A
authors.initials: A
authors.lastname: Oron
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D015233:Models, Statistical; D008962:Models, Theoretical; D009991:Oscillometry / Q000379:methods*; D010825:Physics / Q000379:methods*; D013696:Temperature