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arXiv physics/0601130physics.flu-dynmath-phmath.MPnlin.CD
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湍流中的热平衡分布

Heat equilibrium distribution in a turbulent flow

Z. Haba

摘要:

本文考虑尺度不变的均匀高斯随机速度场的剪切流,它不依赖于流动方向上的坐标。本文研究了来自高斯随机均匀热源的热平流。我们讨论了由强迫对流扩散方程确定的温度分布在大时间的松弛。温度关联函数由Feynman-Kac公式表示。Jensen不等式被应用于关联函数的上下界。我们表明,在有限的时间有没有速度依赖的远程温度相关性(低动量渐近)在流动的方向,但平衡热分布有大的距离相关性(低动量行为)的指数取决于随机流的标度指数和指数的随机强迫。如果速度具有随距离增长的相关性(湍流),则大距离相关性以关键方式取决于湍流的标度指数。在这种情况下,相关性在流动方向上增加,在垂直于流动的方向上减少,使得热流更连贯。

英文摘要:

We consider a shear flow of a scale invariant homogeneous Gaussian random velocity field which does not depend on coordinates in the direction of the flow. We investigate a heat advection coming from a Gaussian random homogeneous source. We discuss a relaxation at large time of a temperature distribution determined by the forced advection-diffusion equation. We represent the temperature correlation functions by means of the Feynman-Kac formula. Jensen inequalities are applied for lower and upper bounds on the correlation functions. We show that at finite time there is no velocity dependence of long range temperature correlations (low momentum asymptotics) in the direction of the flow but the equilibrium heat distribution has large distance correlations (low momentum behaviour) with an index depending on the scaling index of the random flow and of the index of the random forcing. If the velocity has correlations growing with the distance (a turbulent flow) then the large distance correlations depend in a crucial way on the scaling index of the turbulent flow. In such a case the correlations increase in the direction of the flow and decrease in the direction perpendicular to the flow making the stream of heat more coherent.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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