在非常高的瑞利数下边界层不稳定性的证据
Evidence of a boundary layer instability at very high Rayleigh number
摘要：
1997年，瑞利-贝纳德实验证明，当瑞利数大于$Ra \sim 10^{12}$时，热传输效率显著增加，并将这一观察结果解释为Kraichnan对流的“Ultime制度”。根据Kraichnan在1962年的预测，冷板和热板上方的流动边界层-其中大部分流体温度下降是局部的-对于足够大的$Ra$变得不稳定，并且与其他湍流状态相比，这种不稳定性增强了热传输。使用相同的对流细胞在1997年的实验中，我们表明，所报告的热传输的增加是伴随着增强的温度波动的底板，这是在恒定的功率水平加热。实际上，对于$Ra < 10^{12}$，底板波动可以简单地从大部分流动中的波动来解释。特别地，它们在低频下共享相同的谱密度，就好像底板遵循块体的缓慢温度波动，模跨底部边界层的恒定温度下降。相反，为了解释在较高$Ra$下板的温度波动，我们不再能够忽略穿过边界层的温降的波动。在高$Ra$时波动的负偏度支持边界层不稳定性的图象。这些观测结果提供了新的证据，证明1997年报告的转变对应于对流的终极体制的触发。
英文摘要：
In 1997, a Rayleigh-Bénard experiment evidenced a significant increase of the heat transport efficiency for Rayleigh numbers larger than $Ra \sim 10^{12}$ and interpreted this observation as the signature of the Kraichnan's ``Ultime Regime'' of convection. According to Kraichnan's 1962 prediction, the flow boundary layers above the cold and hot plates -in which most of the fluid temperature drop is localized- become unstable for large enough $Ra$ and this instability boosts the heat transport compared to the other turbulent regimes. Using the same convection cell as in the 1997 experiment, we show that the reported heat transport increase is accompanied with enhanced temperature fluctuations of the bottom plate, which was heated at constant power levels. Indeed, for $Ra < 10^{12}$, the bottom plate fluctuations can simply be accounted from those in the bulk of the flow. In particular, they share the same spectral density at low frequencies, as if the bottom plate was following the slow temperature fluctuations of the bulk, modulo a constant temperature drop across the bottom boundary layer. Conversely, to account for the plate's temperature fluctuations at higher $Ra$, we no-longuer can ignore the fluctuations of the temperature drop across the boundary layer. The negative skewness of fluctuations at high $Ra$ supports the picture of a boundary layer instability. These observations provide new evidence that the transition reported in 1997 corresponds to the triggering of the Ultimate Regime of convection.
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