Dynamics of plumes in turbulent Rayleigh–Bénard convection

De, A K and Eswaran, Vinayak and Mishra, P K (2018) Dynamics of plumes in turbulent Rayleigh–Bénard convection. European Journal of Mechanics, B/Fluids, 72. pp. 164-178. ISSN 0997-7546

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Abstract

Direct Numerical Simulation of turbulent Rayleigh–Bénard convection of air (Pr=0.7Pr=0.7) in an infinite horizontal layer is performed in the range 7×104≤Ra≤2×1067×104≤Ra≤2×106. The incompressible Navier–Stokes equations with Boussinesq approximation are solved in a 6:6:1 horizontally periodic box using finite-difference method with a high resolution convective scheme and 2nd-order Adams–Bashforth Crank–Nicolson (ABCN) time-stepping. Instantaneous turbulent flow structures suggest the formation of thin two-dimensional thermal plumes with filament-like cross sections that form disorganized networks of randomly oriented cells near the solid walls, and which gradually expand to form broader plumes in the bulk region. The second invariant technique and the second largest negative eigenvalue method yield identical flake-like vortical structures in the flow. The primary source of plume formation is observed to be boundary layer instabilities. Strong evidence of background large-scale convection cells with horizontal movement is found. Horizontal velocity components near the opposite walls are in opposite phase. The sustained opposite phase motion is disturbed by boundary layer instabilities causing bursts of vertical motion which act as the source of plume formation. The large scale motion yields a quasi-periodic state whose periodicity is of the order of the diffusion time-scale of the flow.

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