Direct numerical simulations of the effects of shear on turbulent Rayleigh-Bénard convection

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Abstract
The interaction between shear and buoyancy effects for Bénard convection in plane Couette flow is studied by performing direct numerical simulations. At moderate Rayleigh number (≈10000−50000), shear tends to organize the flow into quasi-two-dimensional rolls parallel to the mean flow and can enhance heat transfer, while at higher Rayleigh number (>150000), shear tends to disrupt the formation of convective plumes and can reduce heat transfer. A significant temporal oscillation in the local Nusselt number was consistently observed at high Rayleigh numbers, a factor that may contribute to the scatter seen in experimental data. This effect, plus the time-varying reversal of the mean temperature gradient in the middle of the channel, is consistent with a flow model in which the dynamics of large-scale, quasi-two-dimensional, counter-rotating vortical cells are alternately driven by buoyancy and inertial effects. An analysis of the energy balance in the flow shows that the conservative pressure diffusion term, which has been frequently neglected in turbulence models, plays a very important dynamical role in the flow evolution and should be more carefully modelled. Most of the turbulent energy production due to mean shear is generated in the boundary layers, while the buoyant production occurs mainly in the relatively uniform convective core. The simulations and the laboratory experiments of Deardorff & Willis (1967) are in very reasonable qualitative agreement, suggesting that the basic dynamics of the flow are being accurately simulated.