Heat transport in a cell heated at the bottom and the side

Turbulent thermal convection of water (Prandtl number 5.4) in a cubic cell heated from the bottom and the side and cooled from the top and the opposite side is studied numerically by means of direct numerical simulations and large-eddy simulations. The temperature difference between the bottom and top horizontal walls, Δ, is fixed, whereas the temperature difference between the two vertical walls, θ, is varied in the range $0 \leq \theta/\Delta \leq 1.5$ . The other vertical walls are adiabatic. The Rayleigh number determined by Δ equals $\text{Ra}_{\Delta} = 5.2 \times 10^8$ . General laws on the momentum and heat transport in turbulent convection under a joint action of the vertical and horizontal temperature gradients are not yet known, and our study sheds light on the effect of additional horizontal thermal driving (as in vertical convection) on turbulent Rayleigh-Bénard convection. We show that the effective heat transfer and the structure of the flow are strongly affected by the additional heating from the side. Even weak side heating $(\theta/\Delta = 0.05)$ turns the large-scale circulation (LSC), directing it along the walls rather than diagonally. The total kinetic energy and heat flux through the heated walls increase, while the mean flow and vertical heat flux even decrease slightly. Further increase of the side heating accelerates the mean flow, the LSC continues to accelerate up to $\theta/\Delta = 0.4$ , but the turbulent energy starts to decrease at $\theta/\Delta > 0.25$ indicating a change in the flow structure. For $\theta/\Delta > 0.4$ , the effect of the increasing heat flux is complimented by a strong suppression of the LSC and small-scale turbulence. At highest considered side heating $(\theta/\Delta = 1.5)$ , the vertical heat flux is increased by 43% compared to RBC, while the Reynolds number is lower than in RBC. Thus, the rearranged global flow structure allows a stronger heat transport with a weaker flow. For the studied $\text{Ra}_{\Delta}$ , the contribution to the total kinetic energy of the system (characterized by the Reynolds number) from the large-scale flow is higher than the contribution from the turbulent fluctuations for all values of $\theta/\Delta$