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.
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