Investigation of coherent structures in rotating Rayleigh-Benard convection

Abstract

The current work involves identification of coherent structures in rotating turbulent Rayleigh-Benard convection (RBC) in a moderately large aspect-ratio (8:8:1) rectangular enclosure. The enclosure is rotating about a vertical axis passing through its center of gravity. The incompressible Navier-Stokes and energy equations are solved in a rotating frame of reference and the resulting velocity and thermal fields are analyzed to educe coherent structures. The flow structures have been investigated at different nondimensional rotation rates ranging from ω=0 to 104 for a fixed Rayleigh number Ra=107 and Prandtl number Pr=0.01, keeping the Raw∕Ta ratio constant at 10−3 in order to stringently maintain Boussinesq approximation as well as to attain experimentally realizable rotational Rayleigh numbers. Coherent structures in the flow domain have been sought using different identification techniques, namely large eddy simulation (LES) decomposition using top-hat filter, proper orthogonal decomposition (POD) considering larger energy modes, second invariant (Q) of the velocity gradient tensor, and regions of negative λ2, the second largest eigenvalue of the tensor SikSkj+ΩikΩkj. It has been found that the coherent structures educed using POD or LES decomposition at low to moderate rotation (ω=10 to 103) show the formation of two to three large-scale rolls aligned along both horizontal directions. At higher-rotation rates corresponding to ω=104, there is a breakup of large-scale structures into multiple small-scale rolls having random spatial orientation. The thermal structures educed using both POD and large-scale LES decomposition at zero rotation show randomly rising and descending plumes that at Ω=10 coalesce to form a large cylindrical thermal plume in the core of the cavity. Further increase of rotation leads again to breakup of the cylindrical plume into multiple random plumes. Isosurfaces of Q and λ2 reveal elongated tubular roll-like structures mainly concentrated near the side-wall regions, though at higher rotation-rate (ω=104) the density of tubular structures increases significantly. There is a strong similarity of results obtained by large-scale LES decomposition and results obtained using mean plus first mode of POD decomposition. The structures educed using Q and λ2 are different in shape compared to LES or POD educed structures.