title: Pattern dynamics near inverse homoclinic bifurcation in fluids.
abstract: We report the pattern dynamics in the vicinity of an inverse homoclinic bifurcation in an extended dissipative system. We observe, in direct numerical simulations of three dimensional Rayleigh-Bénard convection with stress-free top and bottom plates, a spontaneous breaking of a competition of two mutually perpendicular sets of oscillating cross rolls to one of two possible sets of oscillating cross rolls as the Rayleigh number is raised above a critical value. The time period of the oscillating cross-roll patterns diverges and shows scaling behavior near the bifurcation point. This is an example of a transition from nonlocal to local pattern dynamics near an inverse homoclinic bifurcation. We also present a simple four-mode model that captures the pattern dynamics quite well.
authors.affiliation: Department of Mathematics, National Institute of Technology, Durgapur-713 209, India.
authors.forename: Pinaki
authors.initials: P
authors.lastname: Pal
authors.forename: Krishna
authors.initials: K
authors.lastname: Kumar
authors.forename: Priyanka
authors.initials: P
authors.lastname: Maity
authors.forename: Syamal Kumar
authors.initials: SK
authors.lastname: Dana
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical; D012212:Rheology / Q000379:methods*; D012996:Solutions / Q000737:chemistry*
chemical_list: D012996:Solutions