A Lagrangian fluctuation–dissipation relation for scalar turbulence. Part III. Turbulent Rayleigh–Bénard convection
A Lagrangian fluctuation–dissipation relation for scalar turbulence. Part III. Turbulent Rayleigh–Bénard convection
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标量湍流的拉格朗日涨落-耗散关系第三部分。
DOI：
10.1017/jfm.2017.788
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发表时间：
2016
影响因子：
3.7
通讯作者：
Theodore D. Drivas
中科院分区：
文献类型：
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作者：
G. Eyink;Theodore D. Drivas
在以前的工作中，已经导出了一个拉格朗日涨落-耗散关系来描述有壁流动中平流标量的被动和主动耗散率。我们在此应用这一关系式，在任意横截面的右圆柱形单元中，在上下壁上施加温差或施加热流的情况下，建立了紊流瑞利-巴姆纳德对流热耗散的拉格朗日描述。我们得到了稳态热耗散率与在顶壁或底壁释放的被动示踪粒子混合到最终均匀值的时间$\unicode[STIX]{x1D70F}_{mix}$之间的精确关系。我们证明了Spiegel （Annu）预测的具有努塞尔数缩放的“终极状态”。启阿斯特朗。，第9卷，1971年，第323页)或由Kraichnan (Phys。流体，vol. 5 (11), 1962, pp. 1374-1389)将发生在高瑞利数，除非这个近壁混合时间渐近地远远长于自由落体时间$\unicode[STIX]{x1D70F}_{free}$。确切地说，我们证明$\unicode[STIX]{x1D70F}_{mix}/\unicode[STIX]{x1D70F}_{free}=(RaPr)^{1/2}/Nu,$ Ra$是瑞利数，$ Pr$是普朗特数，$ Nu$是努塞尔数。我们提出了一个关于热“混合区”向湍流过渡的最终状态的新准则，它比标准热边界层宽得多。然而，如果热羽流的强度和体积随瑞利数的增加而迅速下降，则Kraichnan-Spiegel标度可能不成立。为了解决这个问题，我们提出了一个测量近壁混合时间$\unicode[STIX]{x1D70F}_{mix}$的程序，该程序在论文中有精确的定义，我们认为它可以通过实验室实验和数值模拟来实现。
A Lagrangian fluctuation–dissipation relation has been derived in a previous work to describe the dissipation rate of advected scalars, both passive and active, in wall-bounded flows. We apply this relation here to develop a Lagrangian description of thermal dissipation in turbulent Rayleigh–Bénard convection in a right-cylindrical cell of arbitrary cross-section, with either imposed temperature difference or imposed heat flux at the top and bottom walls. We obtain an exact relation between the steady-state thermal dissipation rate and the time $\unicode[STIX]{x1D70F}_{mix}$ for passive tracer particles released at the top or bottom wall to mix to their final uniform value near those walls. We show that an ‘ultimate regime’ with the Nusselt number scaling predicted by Spiegel (Annu. Rev. Astron., vol. 9, 1971, p. 323) or, with a log correction, by Kraichnan (Phys. Fluids, vol. 5 (11), 1962, pp. 1374–1389) will occur at high Rayleigh numbers, unless this near-wall mixing time is asymptotically much longer than the free-fall time $\unicode[STIX]{x1D70F}_{free}$ . Precisely, we show that $\unicode[STIX]{x1D70F}_{mix}/\unicode[STIX]{x1D70F}_{free}=(RaPr)^{1/2}/Nu,$ with $Ra$ the Rayleigh number, $Pr$ the Prandtl number, and $Nu$ the Nusselt number. We suggest a new criterion for an ultimate regime in terms of transition to turbulence of a thermal ‘mixing zone’, which is much wider than the standard thermal boundary layer. Kraichnan–Spiegel scaling may, however, not hold if the intensity and volume of thermal plumes decrease sufficiently rapidly with increasing Rayleigh number. To help resolve this issue, we suggest a program to measure the near-wall mixing time $\unicode[STIX]{x1D70F}_{mix}$ , which is precisely defined in the paper and which we argue is accessible both by laboratory experiment and by numerical simulation.
DOI：
10.1140/epje/i2012-12108-8
发表时间：
2012-10
期刊：
The European Physical Journal E
影响因子：
--
作者：
M. Emran;J. Schumacher
通讯作者：
M. Emran;J. Schumacher