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DY: Dynamik und Statistische Physik
DY 16: Nichtlineare Dynamik und Turbulenz
DY 16.8: Talk
Wednesday, March 19, 1997, 16:30–16:45, R4
Bifurcation Analysis of 2D Rayleigh-Bénard Convection — •E. Zienicke1 and N. Seehafer2 — 1Observatoire de la Côte d’Azur, BP 4229, F-06304 Nice Cedex 04, France — 2Institut für Theoretische Physik und Astrophysik, Universität Potsdam, PF 601553, D-14415 Potsdam, Germany
The dynamics of two-dimensional Rayleigh-Bénard convection with free-free boundary conditions at top and bottom and periodicity in the horizontal direction is numerically re-investigated. For a fixed Prandtl number of 6.8 (corresponding to water) the Rayleigh number is varied up to a value of 300 Rc, where Rc = 665.5 is the critical Rayleigh number for the onset of convection. We find a symmetry breaking bifurcation to a periodic state at R1 = 45 Rc and another symmetry breaking bifurcation at R2 = 68 Rc to a torus solution involving two frequencies. The frequency originating in the first bifurcation corresponds to a mirror symmetric periodic deformation of the convection rolls. Symmetry axes are the vertical lines separating neighbouring convection rolls. The second frequency originating in the second bifurcation corresponds to a periodically changing inclination of the convection rolls caused by a horizontal shear flow. With increasing Rayleigh number these two frequecies undergoe several phase lockings. Near 300 Rc the power spectra of individual modes as well as phase space plots show a qualitative change to an apparently turbulent state.