Non-Oberbeck-Boussinesq effects due to large temperature differences in a differentially heated square cavity filled with air

Regime transitions in thermally driven high-Rayleigh number vertical convection

“…It is also seen that a slightly faster growth of Nu with Ra is obtained for Ra ≤ 10 9 . A similar increase of the scaling exponent for small Ra has also been found previously in both confined (Shishkina 2016;Wang, Zhang & Guo 2017;Wang et al 2019) and double periodic VC (Ng et al 2015 theory for RBC (Grossmann & Lohse 2000). Such observation of scaling transitions further demonstrates that there are no pure scaling laws in thermal convection.…”

“…The power law exponents β = 1/4 and γ = 1/2 were also confirmed by the DNS of Ng et al (2020) in a 3-D cell with span-wise periodic boundary conditions for 10 8 ≤ Ra ≤ 1.3 × 10 9 . For 2-D VC, past studies with Ra ≤ 10 10 have also shown that β is closer to 1/4 than 1/3 (Xin & Le Quéré 1995;Trias et al 2007Trias et al , 2010Wang et al 2019). Wang et al (2019) simulated 2-D VC over 10 5 ≤ Ra ≤ 10 9 for fixed Pr = 0.71, and found β ≈ 0.27 and γ ≈ 0.50.…”

“…Nu ∼ Ra β and Re ∼ Ra γ , at least in a certain Ra range. The reported scaling exponent β was found to vary from 1/4 to 1/3 (Xin & Le Quéré 1995;Le Quéré & Behnia 1998;Trias et al 2007Trias et al , 2010Ng et al 2015;Shishkina 2016;Wang et al 2019;Ng et al 2020), depending on the Ra range and Pr. Ng et al (2015) simulated three-dimensional (3-D) VC with periodic conditions in the range 10 5 ≤ Ra ≤ 10 9 with Pr = 0.709, and obtained β = 0.31 as the considered range.…”

Café latte: spontaneous layer formation in laterally cooled double diffusive convection

“…As a result, there is a region formed in the bulk with nearly uniform concentration, whereas the concentration only changes sharply near the top and bottom boundary layers. This flow structure is similar to that in vertical convection VC (Ng et al 2015; Shishkina & Horn 2016; Wang et al 2019). We thus classify this and corresponding cases into the so-called quasi-VC regime.…”

From zonal flow to convection rolls in Rayleigh–Bénard convection with free-slip plates

“…Note that the 2-D flow structures mentioned here are very similar to those observed in 2-D RB convection, however, quite different from the 2-D Taylor column structures occurring for RB convection rotating about the vertical axis with large angular velocity (Grooms et al 2010;Chong et al 2020a). Two-dimensional simulations, which are computationally more accessible than 3-D simulations, have also been widely used to study thermal convection with no-slip plates in recent years (Johnston & Doering 2009;Sugiyama et al 2010;Huang & Zhou 2013;van der Poel et al 2015b;Zhu et al 2018a;Wang et al 2019b;Zhu et al 2019;Chong et al 2020b;Wan et al 2020;Wang, Zhou & Sun 2020a;Yang et al 2020). In van der Poel, Stevens & Lohse (2013), 2-D and 3-D simulations are compared in detail, and many similarities are found for Pr 1.…”