Large-scale flows and resonances in 2-D thermal convection

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Abstract
Recent experiments of thermal convection in finite containers of intermediate and large aspect ratios have shown the presence of flows spanning the largest dimension of the container [R. Krishnamurti and L. N. Howard, Proc. Natl. Acad. Sci. 78, 1985 (1981); J. Fluid Mech. 170, 385 (1986)]. Large‐scale flows of this kind computed from two‐dimensional (2‐D) numerical simulations are presented. The marginal stability curves for the bifurcations are computed in the range of aspect ratios L=1,...,6 and for Prandtl number σ =10. The nonlinear dynamics of the bifurcated solution is explored for containers with aspect ratios L=1,2,4. By increasing the Rayleigh number from criticality the system produces different sequences of symmetry breaking, Hopf‐type bifurcations, which finally result in large scale flows, oscillatory net mass flux and chaos. The bifurcation involves different mode resonances with vertical and horizontal couplings, which are modeled using formal group theoretical techniques.

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