The largest scales of turbulent wall flows
The largest scales of turbulent wall flows
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最大尺度的湍流壁流
DOI：
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发表时间：
1999
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通讯作者：
J. Jiménez
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文献类型：
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作者：
J. Jiménez
近几年来，壁面湍流的小尺度流动受到了广泛的关注，特别是在近壁区，部分原因是由于直接数值模拟的可用性，使得详细的研究成为可能（Kim，Moin & Moser 1987）。由于这些模拟必须具有中等的雷诺数，并且它们的最大和最小尺度之间几乎没有分离，因此很难独立于后者对前者进行研究。本文的目的是研究与通道宽度或边界层厚度相当或更大的流动尺度。我们将看到，它们对积分流量的贡献是不可忽略的.实验和模拟的分辨率通常被调整，使得离散变量是平滑的，而数值盒或实验记录的大小被选择，使得在与盒大小相当的距离处的相关函数衰减到可以忽略的水平。后者旨在保证在比盒子尺寸大的尺度上几乎没有能量，但必须小心解释。在λ阶尺度下被低通滤波的流中的能量与相关函数在大于λ的分离上的积分成比例，并且衰减得比函数本身慢。由于奇异谱，如湍流中的奇异谱，会产生代数衰减的相关尾，因此可能存在看起来已经衰减但在其尾中仍有相当大一部分能量的相关。此外，一维谱的峰值通常在k = 0处。如果滤波后的信号是感兴趣的信号，例如在声学中，声音衰减随波长而减小，并且只有长波才能在长距离处存活，则这一点变得很重要。大型结构在物理上也很有趣，因为长波长意味着长寿命和大体积，即使它们的每单位体积功率不相等，它们的集成相干效应也可以与较小的结构相媲美。因此，如果信号的一维功率谱随着k → 0而趋于常数E0，则功率包含在比λ长的波长中为O（E0/λ），但是由于每个结构的寿命与λ成比例，因此每个结构的总能量与波长无关。例如，即使很小的横向速度作用很长时间，也会导致速度分布的实质性修改。在这个意义上，要很好地表示流动，意味着它的分辨谱应该在最低波数和最高波数处衰减，这在湍流中可能永远不会成立。
The small scales of wall-bounded turbulent flows have received a lot of attention in recent years, especially in the near-wall region, in part because of the availability of direct numerical simulations that made their detailed study possible (Kim, Moin & Moser 1987). Since those simulations had necessarily moderate Reynolds numbers and little or no separation between their largest and smallest scales, the study of the former independently of the latter in them was difficult. The purpose of this paper is to study the flow scales which are of the order of or larger than the channel width or the boundary layer thickness. We will see that their contribution to the integral flow quantities is not negligible. The resolution of experiments and simulations is usually adjusted so that the discretized variables are smooth while the size of the numerical box, or of the experimental record, is chosen so that the correlation functions at distances comparable to the box size decay to a negligible level. The latter is intended to guarantee that there is little energy at scales larger than the box size, but it has to be interpreted with care. The energy in a flow that has been low-passed filtered at scales of order λ is proportional to the integral of the correlation function over separations longer than λ and decays slower than the function itself. Since singular spectra such as those in turbulent flows give rise to algebraically decaying correlation tails, it is possible to have correlations which appear to have decayed but which still have a substantial fraction of the energy in their tails. The peak of the one-dimensional spectrum is moreover typically at k = 0. This becomes important if the filtered signals are the interesting ones such as in acoustics, where sound attenuation decreases with wavelength and only long waves survive at long distances. Large structures are also physically interesting because long wavelengths imply long lifetimes and large volumes, and their integrated coherent effect can be comparable to those of the smaller ones even when their power per unit volume is not. Thus if the one-dimensional power spectrum of a signal tends to a constant E0 as k → 0, the power is contained in wavelengths longer than λ is O(E0/λ), but since the lifetime of each structure is proportional to λ, the total energy per structure is independent of the wavelength. As an example, even a small transverse velocity acting for a long time would lead to substantial modifications of the velocity profile. For a flow to be well represented in this sense implies that its resolved spectrum should decay at the lowest wavenumbers as well as at the highest ones, which may never be true in turbulent flows.