A critical-layer framework for turbulent pipe flow
A critical-layer framework for turbulent pipe flow
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DOI：
10.1017/s002211201000176x
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发表时间：
2010-09-01
影响因子：
3.7
通讯作者：
Sharma, A. S.
中科院分区：
文献类型：
--
作者：
McKeon, B. J.;Sharma, A. S.
给出了湍流管流中湍流脉动的标度和径向位置的模型描述，并用来说明超大尺度运动的标度行为。该模型是通过将摄动方程中的非线性(包括雷诺应力)视为未知力而得到的，速度场响应与这种非线性之间存在线性关系。我们不假定有小的扰动。我们研究了传播的螺旋速度响应模式，这些模式在与壁面平行的方向上和在时间上是调和的，允许将我们的结果与实验数据进行比较。速度场中只沿壁面法线方向变化的定常分量称为湍流平均剖面。预解式的奇异值分解确定了在给定波数-频率组合下将导致最大速度响应的强迫形状。这些强迫形状将导致在湍流管流中占主导地位的响应模式的假设，通过使用物理参数来限制波数和频率的范围来验证，这些波数和频率的范围与实验中实际观察到的波数和频率范围相一致。对给定波数-频率组合的最大放大速度响应的研究表明，临界层状行为使人想起线性不稳定流动中Orr-Sommerfeld方程的中性稳定解。在流动中粘度的影响变得重要的两个不同区域可以被识别，即与R+1/2成比例的壁层和传播速度与局部平均速度相等的临界层，其中一个与管流中的R+2/3成比例。这一框架似乎与壁面湍流中的几个标度结果一致，并揭示了一种粘性效应可以延伸到壁面附近以外的机制。该模型再现了壁面附近小尺度的内部尺度和流动内部的外部尺度。利用我们的分析首次预测了超大规模运动的合适标度速度是中心线速度，这与实验结果是一致的。最后，我们将壁模解释为满足壁面边界条件所需的运动，确定了临界模和壁模之间的相互作用是大尺度和小尺度相互作用的潜在来源，在最近的文献中观察到的大尺度和小尺度相互作用是由非常大的尺度对近壁湍流的幅度调制。
A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale motions. The model is derived by treating the nonlinearity in the perturbation equation (involving the Reynolds stress) as an unknown forcing, yielding a linear relationship between the velocity field response and this nonlinearity. We do not assume small perturbations. We examine propagating helical velocity response modes that are harmonic in the wall-parallel directions and in time, permitting comparison of our results to experimental data. The steady component of the velocity field that varies only in the wall-normal direction is identified as the turbulent mean profile. A singular value decomposition of the resolvent identifies the forcing shape that will lead to the largest velocity response at a given wavenumber-frequency combination. The hypothesis that these forcing shapes lead to response modes that will be dominant in turbulent pipe flow is tested by using physical arguments to constrain the range of wavenumbers and frequencies to those actually observed in experiments. An investigation of the most amplified velocity response at a given wavenumber-frequency combination reveals critical-layer-like behaviour reminiscent of the neutrally stable solutions of the Orr-Sommerfeld equation in linearly unstable flow. Two distinct regions in the flow where the influence of viscosity becomes important can be identified, namely wall layers that scale with R+1/2 and critical layers where the propagation velocity is equal to the local mean velocity, one of which scales with R+2/3 in pipe flow. This framework appears to be consistent with several scaling results in wall turbulence and reveals a mechanism by which the effects of viscosity can extend well beyond the immediate vicinity of the wall. The model reproduces inner scaling of the small scales near the wall and an approach to outer scaling in the flow interior. We use our analysis to make a first prediction that the appropriate scaling velocity for the very large scale motions is the centreline velocity, and show that this is in agreement with experimental results. Lastly, we interpret the wall modes as the motion required to meet the wall boundary condition, identifying the interaction between the critical and wall modes as a potential origin for an interaction between the large and small scales that has been observed in recent literature as an amplitude modulation of the near-wall turbulence by the very large scales.