Scaling of Reynolds number based on maximum velocity and characteristic Reynolds number in two-dimensional thermal turbulence convection

Rayleigh number (<i>Ra</i>) dependence in Rayleigh-Bénard (RB) convection has been studied by many investigators, but the reported power-law scaling expressions are different these researches. Previous studies have found that when <i>Ra</i> reaches a critical value, flow patterns change and transition appears of <i>Nu</i>(<i>Ra</i>) (where <i>Nu</i> represents Nusselt number) <i>Re</i>(<i>Ra</i>) <i>Re</i> denotes Reynold number). The Grossmann-Lohse(GL) model divides <i>Ra-Pr(</i>where <i>Pr</i> refers to Prandtl phase into several regions predict <i>Nu</i>(<i>Ra,Pr</i>) <i>Re</i>(<i>Ra,Pr</i>), indicating thermal dissipation behavior kinetic behaviors diverse regions. Moreover, some physical quantities also show structures fields, such as large scale circulation boundary layer, increases. In this work, we conduct series numerical simulations two-dimensional RB with ranging from 10<sup>7</sup> 10<sup>12</sup> Pr 0.25 100, which is unprecedentedly wide. relationship between maximum velocity investigated, an unexpected drop happens value <i>Ra</i><sub>c</sub>, <i>Ra</i><sub>c</sub> increases increasing. number, defined velocity, shows plateau at <i>Ra</i><sub>c</sub>. Before after exponent remains 0.55, gets smaller very high <i>Ra</i>. Specially, under values, <i>Re</i><sub>c</sub> ≈ 1.4 × 10<sup>4</sup>. addition, <i>Ra</i><sub>c</sub>~<i>Pr</i><sup>1.5</sup> compensated for <i>Pr</i><sup>–1.5</sup> disscuss <i>RaPr</i><sup>–1.5</sup>. It interesting <i>Re</i>(<i>RaPr</i><sup>–1.5</sup>) expressons values well coincide, self-similarity <i>Re</i>(<i>RaPr</i><sup>–1.5</sup>). <i>RaPr</i><sup>–1.5</sup> = 1 10<sup>9</sup>, meaning would reach 10<sup>4</sup> any 10<sup>9</sup>. To further investigate <i>Re</i>, compared time-averaged fields find (LSC) changes ellipse circle other words, pattern will circular LSC constant mentioned above. This finding can help us distinguish two given <i>Pr</i>, appropriate range values.