4.7 Article

A critical-layer framework for turbulent pipe flow

期刊

JOURNAL OF FLUID MECHANICS
卷 658, 期 -, 页码 336-382

出版社

CAMBRIDGE UNIV PRESS
DOI: 10.1017/S002211201000176X

关键词

boundary layer receptivity; boundary layer structure; critical layers; pipe flow boundary layer; turbulence theory; turbulent boundary layers

资金

  1. NSF [0747672]
  2. Air Force Office of Scientific Research [FA9550-09-1-0701]
  3. Imperial College
  4. EPSRC
  5. Engineering and Physical Sciences Research Council [EP/E017304/1, EP/H026509/1] Funding Source: researchfish
  6. EPSRC [EP/E017304/1, EP/H026509/1] Funding Source: UKRI
  7. Directorate For Engineering
  8. Div Of Chem, Bioeng, Env, & Transp Sys [0747672] Funding Source: National Science Foundation

向作者/读者索取更多资源

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.

作者

我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。

评论

主要评分

4.7
评分不足

次要评分

新颖性
-
重要性
-
科学严谨性
-
评价这篇论文

推荐

暂无数据
暂无数据