Non-Oberbeck-Boussinesq effects on flow structure in Rayleigh-B\'{e}nard convection in water

Non-Oberbeck-Boussinesq (NOB) effects on the flow organization in two-dimensional Rayleigh-B\'{e}nard convection are numerically analyzed for water. The Rayleigh number $Ra$ and the temperature difference $\Delta(=T_{b}-T_{t})$ between top and bottom plates are varied up to $10^{8}$ and $60$K, respectively. The simulation captures broken symmetry features, i.e., the center temperature $T_{c}$ shift and the Nusselt number deviation, which are observed in the experiment of Ahlers et al. (2006, J. Fluid Mech., {\bf 569}). Beyond $Ra\approx 10^{6}$ the flow consists of a large diagonal center convection roll and two smaller rolls in the upper and lower corner, respectively. In the NOB case the center convection roll is still characterized by only one velocity scale, while the top and bottom corner flows are of different strength. We find the total energy based Reynolds number $Re^{E}=\langle{\bf u}^{2}/2\rangle^{1/2}L/\nu$ scales as $Re_{NOB}^{E}/Re_{OB}^{E}\sim (\beta(T_{c})/\beta(T_ {m}))^{1/2}$, with $\beta$ the thermal expansion coefficient and $T_{m}(=(T_{b}+T_{t})/2)$ the arithmetic mean temperature, corresponding to the ratio of the free fall velocities.