Rapidly rotating turbulent Rayleigh-Bénard convection

Abstract

Turbulent Boussinesq convection under the influence of rapid rotation (i.e. with comparable characteristic rotation and convection timescales) is studied. The transition to turbulence proceeds through a relatively simple bifurcation sequence, starting with unstable convection rolls at moderate Rayleigh ( Ra ) and Taylor numbers ( Ta ) and culminating in a state dominated by coherent plume structures at high Ra and Ta . Like non-rotating turbulent convection, the rapidly rotating state exhibits a simple power-law dependence on Ra for all statistical properties of the flow. When the fluid layer is bounded by no-slip surfaces, the convective heat transport ( Nu − 1, where Nu is the Nusselt number) exhibits scaling with Ra 2/7 similar to non-rotating laboratory experiments. When the boundaries are stress free, the heat transport obeys ‘classical’ scaling ( Ra 1/3 ) for a limited range in Ra , then appears to undergo a transition to a different law at Ra ≈ 4 × 10 7 . Important dynamical differences between rotating and non-rotating convection are observed: aside from the (expected) differences in the boundary layers due to Ekman pumping effects, angular momentum conservation forces all plume structures created at flow-convergent sites of the heated and cooled boundaries to spin-up cyclonically; the resulting plume/cyclones undergo strong vortex-vortex interactions which dramatically alter the mean state of the flow and result in a finite background temperature gradient as Ra → ∞, holding Ra / Ta fixed.