Local structure of turbulence in an incompressible viscous fluid at very high Reynolds numbers

1967 ◽  
Vol 93 (11) ◽  
pp. 476-481
Author(s):  
A.N. Kolmogorov
2007 ◽  
Vol 29 (3) ◽  
pp. 385-396
Author(s):  
Khanh Le Chau

A variational principle for channel and pipe flows of incompressible viscous fluid is proposed. For low Reynolds numbers this variational principle reduces to the principle of minimum dissipation. For high Reynolds numbers it enables one to calculate the velocity profiles and the corresponding friction factors with reasonably good accuracy.


2015 ◽  
Vol 779 ◽  
pp. 371-389 ◽  
Author(s):  
M. Vallikivi ◽  
M. Hultmark ◽  
A. J. Smits

Measurements are presented in zero-pressure-gradient, flat-plate, turbulent boundary layers for Reynolds numbers ranging from $\mathit{Re}_{{\it\tau}}=2600$ to $\mathit{Re}_{{\it\tau}}=72\,500$ ($\mathit{Re}_{{\it\theta}}=8400{-}235\,000$). The wind tunnel facility uses pressurized air as the working fluid, and in combination with MEMS-based sensors to resolve the small scales of motion allows for a unique investigation of boundary layer flow at very high Reynolds numbers. The data include mean velocities, streamwise turbulence variances, and moments up to 10th order. The results are compared to previously reported high Reynolds number pipe flow data. For $\mathit{Re}_{{\it\tau}}\geqslant 20\,000$, both flows display a logarithmic region in the profiles of the mean velocity and all even moments, suggesting the emergence of a universal behaviour in the statistics at these high Reynolds numbers.


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