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Logarithmic boundary layers in strong Taylor-Couette turbulence
Sander G Huisman1, Sven Scharnowski, Christian Cierpka
1Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.
Physical Review Letters
|July 16, 2013
Summary
This study measures turbulent Taylor-Couette flow properties, finding the von Kármán constant approaches 0.40 at high Taylor numbers (Ta). Velocity variance profiles show universal behavior, independent of friction velocity.
Area of Science:
- Fluid dynamics
- Turbulence research
- Experimental fluid mechanics
Background:
- Turbulent boundary layers are crucial in many engineering applications.
- Taylor-Couette flow provides a well-defined system to study turbulence.
- Understanding flow behavior near boundaries is essential for predicting drag and heat transfer.
Purpose of the Study:
- To experimentally investigate boundary layer properties in highly turbulent Taylor-Couette flow.
- To determine the von Kármán constant in this flow regime.
- To analyze the scaling and universality of velocity variance profiles.
Main Methods:
- Utilizing high-resolution particle image velocimetry (PIV).
- Employing particle tracking velocimetry (PTV) for detailed flow measurements.
- Conducting experiments in a turbulent Taylor-Couette flow setup up to Re=2×10^6 (Ta=6.2×10^12).
Main Results:
- The mean azimuthal velocity profile fits the von Kármán log law (u+=1/κ lny+ +B).
- The von Kármán constant (κ) approaches approximately 0.40 for large Taylor numbers (Ta).
- Velocity variance profiles exhibit universal peaks and collapse when rescaled by driving velocity, not friction velocity.
Conclusions:
- The von Kármán constant in turbulent Taylor-Couette flow is dependent on the driving strength (Ta).
- Logarithmic scaling of velocity variance is observed, similar to channel and pipe flows.
- Boundary layer behavior in this flow regime shows universal characteristics.
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