论文标题
稳定的瑞利 - 无压力边界之间的对流
Steady Rayleigh--Bénard convection between stress-free boundaries
论文作者
论文摘要
通过数值计算研究了无应力等温边界之间稳定的二维雷利 - 贝纳德对流。我们探索稳定的对流卷和宽高比$π/5 \ le4π$的属性，其中$γ$是一对反旋转卷的宽度比率，超过八个数量级的雷利数，$ 10^3 \ le ra \ le ra \ le ra \ le ra \ le ra \ le ra \ le ra \ le ra \ le ra \ le ra \ le ra \ le ra \ le ra \ le ra \ le ra \ le ra \ le ra \ le ra \ le10^{11} $ 10} pr \ le10^2 $。在稳定的卷动不稳定的情况下，计算的卷显示$ ra \ rightarrow \ infty $渐近缩放。在此制度中，将热传输量表的努塞尔数$ NU $在$ pr $中均匀地均匀。此缩放的预先成品取决于$γ$，最大的$γ\约1.9 $。 reynolds number $ re $ re $ y-$ ra $ rolls量表为$ pr^{ - 1} ra^{2/3} $，带有最大的$γ\约4.5 $的预取子。所有这些大的$ ra $特征与Chini \＆Cox（2009）构建的半分析渐近解决方案定量一致。当$ pr $更大并且$γ$较小时，$ nu $和$ re $ to y渐近级的收敛性会更慢。
Steady two-dimensional Rayleigh--Bénard convection between stress-free isothermal boundaries is studied via numerical computations. We explore properties of steady convective rolls with aspect ratios $π/5\leΓ\le4π$, where $Γ$ is the width-to-height ratio for a pair of counter-rotating rolls, over eight orders of magnitude in the Rayleigh number, $10^3\le Ra\le10^{11}$, and four orders of magnitude in the Prandtl number, $10^{-2}\le Pr\le10^2$. At large $Ra$ where steady rolls are dynamically unstable, the computed rolls display $Ra \rightarrow \infty$ asymptotic scaling. In this regime, the Nusselt number $Nu$ that measures heat transport scales as $Ra^{1/3}$ uniformly in $Pr$. The prefactor of this scaling depends on $Γ$ and is largest at $Γ\approx 1.9$. The Reynolds number $Re$ for large-$Ra$ rolls scales as $Pr^{-1} Ra^{2/3}$ with a prefactor that is largest at $Γ\approx 4.5$. All of these large-$Ra$ features agree quantitatively with the semi-analytical asymptotic solutions constructed by Chini \& Cox (2009). Convergence of $Nu$ and $Re$ to their asymptotic scalings occurs more slowly when $Pr$ is larger and when $Γ$ is smaller.
