Abstract
Period-doubling transitions to chaos, periodic windows, strange attractors, and intermittencies are observed in direct numerical simulations of convection in a closed cavity with differentially heated vertical walls. The cavity contains a Newtonian-Boussinesq fluid and is subject to horizontal oscillatory displacements with a frequency \ensuremath{\Omega}. The transitions occur through a sequence of bifurcations that exhibit the features of a Feigenbaum-type scenario. The first transition from a single-frequency response to a two-frequency response occurs through a parametric excitation of the subharmonic mode $\ensuremath{\Omega}/2$ by the driving frequency \ensuremath{\Omega}. Bifurcation diagrams also exhibit periodic windows and reveal the self-similar structure of the ``period-doubling tree.'' Intermittent flows show characteristics corresponding to a Pomeau-Manneville type-I intermittency.
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