Transition to two-dimensional turbulent convection in a rapidly-rotating annulus

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Abstract
We study a semi-analytical model of convection in a rapidly-rotating, differentially-heated annulus with sloping top and bottom lids. Rapid rotation leads to a preservation of relatively simple, two-dimensional (2-D) structure in the experimentally-observed flow, while temporal complexity increases with the Rayleigh number. The model is, therefore, two-dimensional; it exhibits a sequence of bifurcations from steadily-drifting, azimuthally-periodic convection columns, also called thermal Rossby waves, through vacillation and a period-doubling cascade, to aperiodic, weakly-turbulent solutions. Our semi-analytical results match to within a few percent previous numerical results with a limited-resolution 2-D model, and extend these results, due to the greater flexibility of the model presented here. Two types of vacillation are obtained, which we call, by analogy with classical nomenclature of the baroclinic annulus with moderate rotation rates, amplitude vacillation and tilted-trough vacillation. Their properties and dependence on the problem's nondimensional parameters are investigated. The period-doubling cascade for each type of vacillation is studied in some detail.

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