title: Asymmetric squares as standing waves in rayleigh-Benard convection
abstract: Possibility of thermal convection in the form of asymmetric squares in a thin layer of Boussinesq fluids of large lateral extension confined between stress-free and conducting flat boundaries is investigated numerically using a seven mode Lorenz-like model. For fluids with moderate and high Prandtl numbers (4<sigma<20) and in a narrow window of high Rayleigh numbers (12<R/R(c)<15), which depend on Prandtl number, the stationary rolls become unstable and asymmetric squares appear as standing waves at the onset of secondary instability. Asymmetric squares, two-dimensional rolls, and again asymmetric squares with their corners shifted by half a wavelength form a stable limit cycle. The oscillatory bifurcation is supercritical.
authors.affiliation: Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Calcutta 700 035, India.
authors.initials: A
authors.lastname: Das
authors.initials: U
authors.lastname: Ghosal
authors.initials: K
authors.lastname: Kumar