论文标题
在辐射驱动的对流实验中过渡到最终状态
Transition to the ultimate regime in a radiatively driven convection experiment
论文作者
论文摘要
我们在辐射驱动的对流实验中报告了两个热传输机制之间的过渡，在该实验中，在储罐底部附近的可调加热长度$ \ ell $中，液体在可调加热长度内加热。第一个制度类似于标准雷利 - 纳德实验中观察到的一个制度，努塞尔特数字$ nu $与雷利数字$ ra $通过powerlaw $ nu $ nu \ sim ra^{1/3} $相关。第二个制度对应于热对流的“最终”或混合长度缩放制度，其中$ nu $变化为$ ra $的平方根。 Lepot等人已经报道了这两个缩放制度的证据。 （Proc。Nat。Acad。Sci。Us a，{\ bf 115}，36，2018），我们现在详细研究系统如何从一个转变为另一个。我们提出了一个简单的模型，该模型描述了混合长度方案中辐射驱动的对流。 \ corr {它导致缩放关系$ nu \ sim \ frac {\ ell} {h} pr^{1/2} ra^{1/2} $，}，其中$ h $是单元的高度，从而使我们允许我们推迟$ ra $ ra $ and $ ra $ and $ ra $ and $ ra $和$ nu $的过渡。这些预测通过收集的各种$ ra $和$ \ ell $的实验数据证实。 \ corr {我们通过表明边界层校正可以持续修改$ nu $在大$ ra $时的prandtl数字依赖性，对于$ pr \ gtrsim 1 $。
We report on the transition between two regimes of heat transport in a radiatively driven convection experiment, where a fluid gets heated up within a tunable heating length $\ell$ in the vicinity of the bottom of the tank. The first regime is similar to the one observed in standard Rayleigh-Bénard experiments, the Nusselt number $Nu$ being related to the Rayleigh number $Ra$ through the power-law $Nu \sim Ra^{1/3}$. The second regime corresponds to the "ultimate" or mixing-length scaling regime of thermal convection, where $Nu$ varies as the square-root of $Ra$. Evidence for these two scaling regimes have been reported in Lepot et al. (Proc. Nat. Acad. Sci. U S A, {\bf 115}, 36, 2018), and we now study in detail how the system transitions from one to the other. We propose a simple model describing radiatively driven convection in the mixing-length regime. \corr{It leads to the scaling relation $Nu \sim \frac{\ell}{H} Pr^{1/2} Ra^{1/2}$,} where $H$ is the height of the cell, thereby allowing us to deduce the values of $Ra$ and $Nu$ at which the system transitions from one regime to the other. These predictions are confirmed by the experimental data gathered at various $Ra$ and $\ell$. \corr{We conclude by showing that boundary layer corrections can persistently modify the Prandtl number dependence of $Nu$ at large $Ra$, for $Pr \gtrsim 1$.
