论文标题
热驱动的高射线数垂直对流中的政权过渡
Regime transitions in thermally driven high-Rayleigh number vertical convection
论文作者
论文摘要
使用在二维Prandtl数字$ pr = 10 $的二维对流单元中，使用固定的prandtl数字$ pr = 10 $，使用广泛的雷利数字上的直接数值模拟进行了垂直对流研究。发现平均垂直中心温度梯度$ s $对$ ra $的依赖性显示了三种不同的政权：在制度I（$ ra \ lyseSim 5 \ times10^{10} $）中，$ s $几乎独立于$ ra $;在新确定的制度II（$ 5 \ times10^{10} \ Lessim ra \ Lessim 10^{13} $）中，$ S $首先随着$ ra $的增加而增加（Legime $ {\ rm {ii}} _ a $），并再次达到最大值，然后再次降低（commime $ $ $ {bmmmmmm {bmmmm {在政权III（$ ra \ gtrsim10^{13} $）中，$ s $再次变得微弱地依赖于$ ra $，比政权I略小。讨论了不同政权之间的过渡。在三个不同的制度中，确定了显着不同的流组织：在制度I和制度中，$ {\ rm {ii}} _ a $，最大水平速度的位置靠近顶部和底壁；但是，在制度$ {\ rm {ii}} _ b $和制度III中，带状的Zonal流量结构发展，最大水平速度现在位于散装区域。 在有效的功率法尺度中，这三个制度中的不同流动组织也反映在缩放指数中$ nu \ sim ra^β$和$ re \ sim ra^γ$。 In regime I, the fitted scaling exponents ($β\approx0.26$ and $γ\approx0.51$) are in excellent agreement with the theoretical predication of $β=1/4$ and $γ=1/2$ for laminar VC (Shishkina, {\it{Phys. Rev. E.}} 2016, 93, 051102).但是，在II和III中，$β$增加到接近1/3的值，$γ$降低到接近4/9的值。 $ nu $的$ ra $依赖性与羽毛的弹射和墙壁上较大的局部热量有关。
Vertical convection is investigated using direct numerical simulations over a wide range of Rayleigh numbers $10^7\le Ra\le10^{14}$ with fixed Prandtl number $Pr=10$, in a two-dimensional convection cell with unit aspect ratio. It is found that the dependence of the mean vertical centre temperature gradient $S$ on $Ra$ shows three different regimes: In regime I ($Ra \lesssim 5\times10^{10}$), $S$ is almost independent of $Ra$; In the newly identified regime II ($5\times10^{10} \lesssim Ra \lesssim 10^{13}$), $S$ first increases with increasing $Ra$ (regime ${\rm{II}}_a$), reaches its maximum and then decreases again (regime ${\rm{II}}_b$); In regime III ($Ra\gtrsim10^{13}$), $S$ again becomes only weakly dependent on $Ra$, being slightly smaller than in regime I. The transitions between diffeereent regimes are discussd. In the three different regimes, significantly different flow organizations are identified: In regime I and regime ${\rm{II}}_a$, the location of the maximal horizontal velocity is close to the top and bottom walls; However, in regime ${\rm{II}}_b$ and regime III, banded zonal flow structures develop and the maximal horizontal velocity now is in the bulk region. The different flow organizations in the three regimes are also reflected in the scaling exponents in the effective power law scalings $Nu\sim Ra^β$ and $Re\sim Ra^γ$. In regime I, the fitted scaling exponents ($β\approx0.26$ and $γ\approx0.51$) are in excellent agreement with the theoretical predication of $β=1/4$ and $γ=1/2$ for laminar VC (Shishkina, {\it{Phys. Rev. E.}} 2016, 93, 051102). However, in regimes II and III, $β$ increases to a value close to 1/3 and $γ$ decreases to a value close to 4/9. The stronger $Ra$ dependence of $Nu$ is related to the ejection of plumes and larger local heat flux at the walls.
