On the universality of inertial energy in the log layer of turbulent boundary layer and pipe flows

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• 作者：D. Chung ; I. Marusic ; J. P. Monty ; M. Vallikivi ; A. J. Smits
• 刊名：Experiments in Fluids
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：56
• 期：7
• 全文大小：1,170 KB
• 参考文献：Bailey SCC, Hultmark M, Smits AJ, Schultz MP (2008) Azimuthal structure of turbulence in high Reynolds number pipe flow. J Fluid Mech 615:121-38View Article
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• 作者单位：D. Chung (1)
  I. Marusic (1)
  J. P. Monty (1)
  M. Vallikivi (2)
  A. J. Smits (2) (3)
  
  1. Department of Mechanical Engineering, University of Melbourne, Parkville, VIC, 3010, Australia
  2. Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ, 08544, USA
  3. Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC, 3800, Australia
  
• 刊物类别：Engineering
• 刊物主题：Engineering Fluid Dynamics
  Fluids
  Industrial Chemistry and Chemical Engineering
  Measurement Science and Instrumentation
  Thermodynamics
  Theoretical and Applied Mechanics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1114

文摘

Recent experiments in high Reynolds number pipe flow have shown the apparent obfuscation of the \(k_x^{-1}\) behaviour in spectra of streamwise velocity fluctuations (Rosenberg et al. in J Fluid Mech 731:46-3, 2013). These data are further analysed here from the perspective of the \(\log r\) behaviour in second-order structure functions, which have been suggested as a more robust diagnostic to assess scaling behaviour. A detailed comparison between pipe flows and boundary layers at friction Reynolds numbers of \({{Re}}_\tau \approx\)?5000-0,000 reveals subtle differences. In particular, the \(\log r\) slope of the pipe flow structure function decreases with increasing wall distance, departing from the expected \(2A_1\) slope in a manner that is different to boundary layers. Here, \(A_1 \approx 1.25\), the slope of the log law in the streamwise turbulence intensity profile at high Reynolds numbers. Nevertheless, the structure functions for both flows recover the \(2A_1\) slope in the log layer sufficiently close to the wall, provided the Reynolds number is also high enough to remain in the log layer. This universality is further confirmed in very high Reynolds number data from measurements in the neutrally stratified atmospheric surface layer. A simple model that accounts for the ‘crowding-effect near the pipe axis is proposed in order to interpret the aforementioned differences.