论文标题
无应力边界之间的二维雷利 - 贝纳德对流的高波稳定解决方案
High-wavenumber steady solutions of two-dimensional Rayleigh--Bénard convection between stress-free boundaries
论文作者
论文摘要
最近的调查表明，稳定的解决方案与动荡的雷利 - 贝纳德对流（RBC）具有许多特征，并形成了湍流动力学的状态空间骨架。在无滑动边界之间二维（2D）RBC中稳定滚动解决方案的先前计算表明，对于固定的雷利数字$ ra $和prandtl Number $ pr $，热量最大化的解决方案始终处于高波动型状态。在这项研究中，我们探索了高波动的稳定对流胶卷解决方案，这些解决方案是从一动不动的导电状态上超级判断的2D rbc之间的2D RBC。我们的计算证实了在高波式制度中存在局部热量最大化解决方案。为了阐明该解决方案的渐近特性，我们在瑞利号的八个数量级上执行计算，$ 10^{8} \ le ra \ le ra \ le 10^{16.5} $，在prandtl数字中的两个数量级，$ 10^{ - 1} { - 1} \ leq pr \ leq pr \ leq pr \ leq 10^3/3/2} $。数值结果表明，作为$ ra \ to \ infty $，本地热量升级倍数倍数$γ^*_ {loc} \ simeq ra^{ - 1/4} $，nusselt nusselt nusselt $ nu $ nu（γ^_ {loc}）*_ {loc}） $ re（γ^*_ {loc}）\ simeq pr^{ - 1} ra^{2/5} $，所有预取子取决于$ pr $。此外，分析热 - 交换器解决方案可以很好地描述局部$ NU $ MAXIMAKINE的内部流动，并讨论了Blennerhassett＆Bassom给出的高波渐近溶液的连接。固定的纵横比$ 0.06 \leγ\leπ/5 $ at $ pr = 1 $，但是，我们的计算表明，随着$ ra $的增加，稳定的滚动汇聚到Chini＆cox构建的半分析渐近解决方案，带有scaleings $ nu \ sim ra^{1/3} $和$ re re pr \ sim pr^ra^ra^ra^ra^ra^ra最后，对相图进行了描绘，以获得高射线数 - 噪声平面中稳定溶液的全景。
Recent investigations show that steady solutions share many features with turbulent Rayleigh--Bénard convection (RBC) and form the state space skeleton of turbulent dynamics. Previous computations of steady roll solutions in two-dimensional (2D) RBC between no-slip boundaries reveal that for fixed Rayleigh number $Ra$ and Prandtl number $Pr$, the heat-flux-maximizing solution is always in the high-wavenumber regime. In this study, we explore the high-wavenumber steady convection roll solutions that bifurcate supercritically from the motionless conductive state for 2D RBC between stress-free boundaries. Our computations confirm the existence of a local heat-flux-maximizing solution in the high-wavenumber regime. To elucidate the asymptotic properties of this solution, we perform computations over eight orders of magnitude in the Rayleigh number, $10^{8} \le Ra \le 10^{16.5}$, and two orders of magnitude in the Prandtl number, $10^{-1} \leq Pr \leq 10^{3/2}$. The numerical results indicate that as $Ra\to\infty$, the local heat-flux-maximizing aspect ratio $Γ^*_{loc}\simeq Ra^{-1/4}$, the Nusselt number $Nu(Γ^*_{loc})\simeq Ra^{0.29}$, and the Reynolds number $Re(Γ^*_{loc})\simeq Pr^{-1}Ra^{2/5}$, with all prefactors depending on $Pr$. Moreover, the interior flow of the local $Nu$-maximizing solution can be well described by an analytical heat-exchanger solution, and the connection to the high-wavenumber asymptotic solution given by Blennerhassett & Bassom is discussed. With a fixed aspect ratio $0.06\leΓ\leπ/5$ at $Pr=1$, however, our computations show that as $Ra$ increases, the steady rolls converge to the semi-analytical asymptotic solutions constructed by Chini & Cox, with scalings $Nu\sim Ra^{1/3}$ and $Re\sim Pr^{-1}Ra^{2/3}$. Finally, a phase diagram is delineated to gain a panorama of steady solutions in the high-Rayleigh-number-wavenumber plane.
