Abstract
We perform direct numerical simulations of wall sheared Rayleigh–Bénard convection for Rayleigh numbers up to [Image: see text], Prandtl number unity and wall shear Reynolds numbers up to [Image: see text]. Using the Monin–Obukhov length [Image: see text] we observe the presence of three different flow states, a buoyancy dominated regime ([Image: see text]; with [Image: see text] the thermal boundary layer thickness), a transitional regime ([Image: see text]; with [Image: see text] the height of the domain) and a shear dominated regime ([Image: see text]). 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 [Image: see text] 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 [Image: see text] effectively scales as [Image: see text] with [Image: see text], while we find [Image: see text] in the buoyancy dominated regime. In the transitional regime, the effective scaling exponent is [Image: see text], 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.