Editorial Type:
Article
Article Type:
Research Article

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

Search for other papers by Juan C. Bergmann in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Nov 1998
DOI:
https://doi.org/10.1175/1520-0469(1998)055<3403:APIOVK>2.0.CO;2
Page(s):
3403–3407
Restricted access

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.

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.

Save
Cover Journal of the Atmospheric Sciences
Journal of the Atmospheric Sciences

  • Cai, X.-M., and D. G. Steyn, 1996: The von Kármán constant determined by large eddy simulation. Bound.-Layer Meteor.,78, 143–164.

  • Eyink, G. L., 1994: The renormalization group method in statistical hydrodynamics. Phys. Fluids,6, 3063–3078.

  • Hinze, J. O., 1975: Turbulence. 2d ed. McGraw-Hill, 790 pp.

  • Högström, U., 1985: Von Kármán’s constant in atmospheric boundary layer flow: Reevaluated. J. Atmos. Sci.,42, 263–270.

  • ——, 1996: Review of some basic characteristics of the atmospheric surface layer. Bound.-Layer Meteor.,78, 215–246.

  • Monin, A. S., and A. M. Obukhov, 1954: Fundamental laws of turbulent exchange in the near-surface layer of the atmosphere. Trudy Geophys. Inst. Acad. Nauk SSSR,24 (151), 163–187. [In Sammelband zur Statistichen Theorie der Turbulenze, Akademie-Verlag, Berlin, 1958, 199–225.].

  • ——, and A. M. Yaglom, 1971: Statistical Fluid Mechanics: Mechanics of Turbulence. Vol. 1. The MIT Press, 769 pp. [Originally published as Statisticheskaya Gidromekhanika, Chast I, in 1965 by Nauka Press, Moscow.].

  • Oncley, S. P., J. A. Businger, E. C. Itsweire, C. A. Friehe, J. C. La Rue, and S. S. Chang, 1990: Surface layer profiles and turbulence measurements over uniform land under near-neutral conditions. Preprints, Ninth Symp. on Turbulence and Diffusion, Roskilde, Denmark, Amer. Meteor. Soc., 237–240.

  • Prandtl, L., 1904: Proc. III Internationaler Mathematischer Kongress, Heidelberg, Germany, 484.

  • Telford, J. W., 1982: A theoretical value for von Kármán’s constant. Pure Appl. Geophys.,120, 648–661.

  • ——, and J. A. Businger, 1986: Comments on “Von Kármán’s constant in atmospheric boundary layer flow: Reevaluated.” J. Atmos. Sci.,43, 2127–2134.

  • Tennekes, H., 1973: The logarithmic wind profile. J. Atmos. Sci.,30, 234–238.

  • Tseng, R.-S., Y.-H. Hsu, and J. Wu, 1992: Methods of measuring wind stress over a water surface—Discussions of displacement height and von Kármán constant. Bound.-Layer Meteor.,58, 51–68.

  • Wyngaard, J. C., and L. J. Peltier, 1996: Experimental micrometeorology in an era of turbulence simulation. Bound.-Layer Meteor.,78, 71–86.

  • Yajnik, K. S., 1970: Asymptotic theory of turbulent shear flows. J. Fluid Mech.,42, 411–427.

  • Yakhot, V., and S. A. Orszag, 1986: Renormalization-group analysis of turbulence. Phys. Rev. Lett.,57, 1722–1724.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 822 392 25
PDF Downloads 314 85 7