Flow organization and heat transfer in turbulent wall sheared thermal convection

Abstract

We perform direct numerical simulations of wall sheared Rayleigh-Bénard convection for Rayleigh numbers up to Ra = 108, Prandtl number unity and wall shear Reynolds numbers up to Rew = 10 000. Using the Monin-Obukhov length LMO we observe the presence of three different flow states, a buoyancy dominated regime (LMO. λθ; with λθ the thermal boundary layer thickness), a transitional regime (0.5H & LMO & λθ; with H the height of the domain) and a shear dominated regime (LMO & 0.5H). In the buoyancy dominated regime, the flow dynamics is similar to that of turbulent thermal convection. The transitional regime is characterized by rolls that are increasingly elongated with increasing shear. The flow in the shear dominated regime consists of very large-scale meandering rolls, similar to the ones found in conventional Couette flow. As a consequence of these different flow regimes, for fixed Ra and with increasing shear, the heat transfer first decreases, due to the breakup of the thermal rolls, and then increases at the beginning of the shear dominated regime. In the shear dominated regime the Nusselt number Nu effectively scales as Nu ∼ Raα with α ≪ 1/3, while we find α ' 0.30 in the buoyancy dominated regime. In the transitional regime, the effective scaling exponent is α > 1/3, but the temperature and velocity profiles in this regime are not logarithmic yet, thus indicating transient dynamics and not the ultimate regime of thermal convection.