A Physical Interpretation of von Kármán’s Constant Based on Asymptotic Considerations—A New Value

Juan C. Bergmann Risø National Laboratory, Wind Energy and Atmospheric Physics Department, Roskilde, Denmark

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Abstract

The asymptotic profiles of a viscous flow and an inviscid turbulent flow are matched by the appropriate choice of the only free parameter, the von Kármán constant κ. The matching result is κ = exp(−1) = 0.3678 · · · . This value is supported by recent experimental evidence from measurements at the very large Reynolds numbers required for the determination of the (asymptotic) value of von Kármán’s constant.

Corresponding author address: Dr. Juan C. Bergmann, Risø National Laboratory, Wind Energy and Atmospheric Physics Department, P.O. Box 49, DK-4000 Roskilde, Denmark.

Email: juan.bergmann@risoe.dk

Abstract

The asymptotic profiles of a viscous flow and an inviscid turbulent flow are matched by the appropriate choice of the only free parameter, the von Kármán constant κ. The matching result is κ = exp(−1) = 0.3678 · · · . This value is supported by recent experimental evidence from measurements at the very large Reynolds numbers required for the determination of the (asymptotic) value of von Kármán’s constant.

Corresponding author address: Dr. Juan C. Bergmann, Risø National Laboratory, Wind Energy and Atmospheric Physics Department, P.O. Box 49, DK-4000 Roskilde, Denmark.

Email: juan.bergmann@risoe.dk

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