Abstract
The half-century history of the experimental evaluation of the von Karman “constant” in the atmospheric surface layer is reviewed, an evidence indicating that this well-known scaling factor,k, is actually a weak variable that decreases with increasing Reynolds number is discussed. A combined average ofk=0.390 with a standard error of ±0.010 is found from two field studies, a result which indicates that there is only one chance in 40 that the true value of the scaling factor in the population from which the experimental sample was drawn could have been as large as the laboratory value of 0.40. Based on experimental and theoretical results given by others, it is suggested thatk varies from a maximum of 0.41 in light winds over open water and smooth land surfaces, to a minimum near 0.37 in stronger winds over forests and cities. This range is shown to imply that a working value ofk=0.39±1% is appropriate for flows over surfaces characterized by 0.7<z 0<8.7 cm, a roughness subrange which corresponds to a wide variety of terrain types from sparsely vegetated level plains to mixed croplands with occasional hedges and trees.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Busch, N. E. and Kristensen, L.: 1976, ‘Cup Anemometer Overspeeding’,J. Appl. Meteorol. 15, 1328–1332.
Businger, J. A., Wyngaard, J. C., Izumi, Y., and Bradley, E. F.: 1971, ‘Flux-Profile Relationships in the Atmospheric Surface Layer’,J. Atmos. Sci. 28, 181–189.
Charnock, H.: 1955, ‘Wind Stress on a Water Surface’,Quart. J. Roy. Meteorol. Soc. 81, 639.
Chevray, R., and Methieu, J.: 1993,Topics in Fluid Mechanics, Cambridge University Press, 320 pp.
DeLeonibus, P. S., and Simpson, L. S.: 1989, ‘Observations of the von Karman Constant over Open-Ocean Waves’,IEEE J. Oceanic Eng. 14, 248–253.
Dyer, A. J.: 1974, ‘A Review of Flux-Profile Relationships’,Boundary-Layer Meteorol. 7, 363–372.
Dyer, A. J., and Bradley, E. F.: 1982, ‘An Alternative Analysis of Flux-Gradient Relationships at ITCE’,Boundary-Layer Meteorol. 22, 3–19.
Francey, R. J., and Garratt, J. R.: 1981, ‘Interpretation of Flux-Profile Relationships at ITCE-76’,J. Appl Meteorol. 20, 603–618.
Frenzen, P.: 1988, ‘Fast Response Cup Anemometers for Atmospheric Turbulence Research’,Proc. Eighth Symp. on Turbc. and Diffusion, San Diego, CA, 25–29 April 1988, Amer. Meteorol Soc., pp. 112–115.
Frenzen, P., and Vogel, C. A.: 1992a, ‘The Turbulent Kinetic Energy Budget in the Atmospheric Surface Layer: A Review and Experimental Reexamination in the Field’,Boundary-Layer Meteorol. 60, 49–76.
Frenzen, P., and Vogel, C. A.: 1992b, ‘A New Study of the TKE Budget in the Surface Layer, Part I: The von Karman Constant and Rates of TKE Production’,Proc. Tenth Symp. on Turbc. and Diffusion, Portland, OR., 29 Sept–2 Oct 1992, Amer. Meteorol. Soc., pp. 157–160.
Frenzen, P., and Vogel, C. A.: 1994, ‘An Inadvertent Demonstration of the Sensitivity of φ m tok: A Corrected Illustration for “The Turbulent Kinetic Energy Budget”’,Boundary-Layer Meteorol. 68, 439–442.
Frisch, U., and Orszag, S. A.: 1990, ‘Turbulence: Challenges for Theory and Experiment’,Phys. Today, Jan 1990, 24–32.
Garratt, J. R.: 1977, ‘Review of Drag Coefficients over Oceans and Continents’,Mon. Wea. Rev. 105, 915–929.
Garratt, J. R.: 1980, ‘Surface Influence on Vertical Profiles in the Atmosphere’,Quart. J. Roy. Meteorol. Soc. 106, 803–819.
Gryning, S. E.: 1993, ‘Vind, Turbulens, og Graenselagshoejde over Kattegat’,Marine Res. Rep., Natl. Agency Environ. Protection, Copenhagen, Denmark, 45 pp.
Hicks, B. B.: 1976, ‘Reply to J. H. Schreffler’,Boundary-Layer Meteorol. 10, 237–240.
Hinze, J. O.: 1962, ‘Turbulent Pipe Flow’,Mecanique de Turbulence,108, Ed. du Centre National de la Recherche Scientifique, Paris; pp. 129–165.
Hinze, J. O.: 1975,Turbulence (2nd Ed.), McGraw Hill, New York 790 pp.
Högström, U.: 1985, ‘Von Karman's Constant in Atmospheric Boundary Layer Flow: Reevaluated’,J. Atmos. Sci. 42, 263–270.
Högström, U.: 1986, ‘Reply’,J. Atmos. Sci. 43, 2131–2134.
Högström, U.: 1988, ‘Non-Dimensional Wind and Temperature Profiles in the Surface Layer: A Reevaluation’,Boundary-Layer Meteorol. 42, 55–78.
Huffman, G. D., and Bradshaw, P.: 1972, ‘A Note on von Karman's Constant in Low Reynolds Number Flows’,J. Fluid Mech. 53, Part 1, 45–60.
Karman, Th. von.: 1930, ‘Mechanische Ähnlichkeit und Turbulenz’, Nachrichten der Akademie der Wissenschaften, Göttingen, Math-Phys. Klasse,58.
Kondo, J., and Sato, T.: 1982, ‘The Determination of the von Karman Constant’,J. Meteorol. Soc. of Japan 60, 461–470.
Larsen, S. E.: 1993, ‘Observing and Modelling the Planetary Boundary Layer’, inEnergy and Water Cycles in the Climate System. NATO ASI Series,15, Springer-Verlag, Berlin, pp. 365–418.
Lettau, H.: 1961, ‘A Generalized Mathematical Model of the Mean Velocity Distribution in Fully Turbulent Flow’, Tech Rep. No. 3, DA-36-039-SC-80292, Dept. of Meteorol. and Civil Eng., Univ. of Wisconsin, 115–142.
Long, C. E., Wiberg, P. L., and Nowell, A. R.: 1993, ‘Evaluation of von Karman's Constant from Integral Flow Parameters’,J. Hydr. Eng. 119, 1182–1190.
Melville, W. K.: 1977, ‘Wind Stress and Roughness Length over Breaking Waves’,J. Phys. Oceanog. 7, 702–710.
Mortensen, N. G., Larsen, S. E., Troen, L., and Mikkelsen, T.: 1987, ‘Two-Years Worth of Turbulence Data Recorded by a Sonic-Anemometer Data Acquisition System’,Proc. Sixth Symp. on Meteorol. and Instrumentation, 1987, New Orleans, LA.,Amer. Meteorol. Soc., 393–396.
Nikuradse, J.: 1932, ‘Gesetzmässigkeiten der Turbulenten Strömungen in Glatten Rohren’,Forschungsheft Verein Deutscher Ingenieure 356.
Oncley, S. P., Businger, J. A., Friehe., C. A., LaRue, J. C., Itsweire, E. C., and Chang, S. S.: 1990, ‘Surface Layer Profiles and Turbulence Measurements over Univorm Terrain in Near-Neutral Conditions’,Proc. Ninth Symp. on Turbc. and Diffusion, 30 Apr–3 May, Røskilde, Denmark, Amer. Meteorol. Soc., 237–240 (submitted toJ. Atmos. Sci.).
Pasquill, F.: 1950, ‘The Aerodynamic Drag of Grassland’,Proc. Roy. Soc. London, Ser. A 202, 143–153.
Plate, E. J.: 1971,Aerodynamic Characteristics of Atmospheric Boundary Layers, AEC Crit. Rev., U.S. Atomic Energy Comm., Oak Ridgé, TN, 190 pp.
Prandtl, L.: 1925, ‘Uber die Ausgebildete Turbulenz’,Z. Angew. Math Mech. 5, 136–139.
Pruitt, W. O., Morgan, D. L., and Lourence, F. J.: 1973, ‘Momentum and Mass Transfers in the Surface Boundary Layer’,Quart. J. Roy. Meteorol. Soc. 97, 370–386.
Purtell, L. P., Klebanoff, P. S., and Buckley, F. T.: 1981, ‘Turbulent Boundary Layer at Low Reynolds Number’,Phys. Fluids 24, 802–811.
Raupach, M. R., Thom, A. S., and Edwards, I.: 1980, ‘A Wind Tunnel Study of Turbulent Flow Close to Regularly Arrayed Rough Surfaces’,Boundary-Layer Meteorol. 18, 373–397.
Raupach, M. R., Antonia, R. A., and Rajagopalan, S.: 1991, ‘Rough-Wall Boundary Layers’,Appl. Mech. Rev. 44, 1–25.
Sheppard, P. A.: 1946, ‘The Aerodynamic Drag of the Earth's Surface and the Value of von Karman's Constant in the Lower Atmosphere’,Proc. Roy. Soc. London, Ser. A 188, 208–222.
Silva Filho, V. de P.: 1988, A Study of Wind Profiles under Quasi-Neutral and Inversion Atmospheric Conditions over Terra Firma Forest’, M.S. Dissertation, Inst. de Pesquisas Espaciais, Sao Jose dos Campos, S. P., Brazil, 91 pp, NTIS, INPE-4694-RPE/575.
Simpson, R. L.: 1970, ‘Characteristics of Turbulent Boundary Layers at Low Reynolds Numbers’,J. Flu. Mech. 42, 769–802.
Simpson, R. L.: 1976, ‘Comments on “Prediction of Turbulent Boundary Layers at Low Reynolds Numbers”’,AIAA J. 14, 1662.
Stull, R. B.: 1988,An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, 666 pp.
Telford, J. W.: 1982, ‘A Theoretical Value for von Karman's Constant’,PAGEOPH. 120, 648–661.
Telford, J. W., and Businger, J. A.: 1986, ‘Comments on “Von Karman's Constant in Atmospheric Boundary Layer Flow Reevaluated”’,J. Atmos. Sci. 43, 2127–2130.
Tennekes, H.: 1968, ‘Outline of a Second-Order Theory of Turbulent Pipe Flow’,AIAA J. 6, 1735–1740.
Tennekes, H.: 1973, ‘The Logarithmic Wind Profile,’J. Atmos. Sci. 30, 234–238.
Vogel, C. A., and Frenzen, P.: 1992, ‘A New Study of the TKE Budget in the Surface Layer, Part II: The Dissipation Function and the Divergent Transport Terms’,Proc. Tenth Symp. on Turbc. and Diffusion, Portland, OR, 29 Sept-2 Oct. Amer. Meteorol. Soc., pp. 161–164.
Wieringa, J.: 1980, ‘A Reevaluation of Kansas Mast Influence on Measurements of Stress and Cup Anemometer Overspeeding’,Boundary-Layer Meteorol. 18, 411–430.
Wyngaard, J. C., Businger, J. A., Kaimal, J. C., and Larsen, S. E.: 1982, ‘Comments on “A Reevaluation of Kansas Mast Influence on Measurements of Stress and Cup Anemometer Overspeeding”’,Boundary-Layer Meteorol. 22, 245–250.
Yakhot, V., and Orszag, S. A.: 1986, ‘Renormalization Group Analysis of Turbulence’,Phys. Rev. Letters 57, 1722–1724.
Zhang, S. F., Oncley, S. P., and Businger, J. A.: 1988, ‘Evaluation of the von Karman Constant from a New Surface Layer Experiment’,Proc. Eighth Symp. on Turbc. and Diffusion, San Diego, CA, 25–29 April, Amer. Meteorol Soc., 148–150.
Author information
Authors and Affiliations
Additional information
sponsored in part by the Global Change Post Doctoral Program, Office of Health and Environmental Research, U. S. Department of Energy.
Work sponsored by the National Science Foundation under Grant No. ATM-9019682.
Rights and permissions
About this article
Cite this article
Frenzen, P., Vogel, C.A. On the magnitude and apparent range of variation of the von Karman constant in the atmospheric surface layer. Boundary-Layer Meteorol 72, 371–392 (1995). https://doi.org/10.1007/BF00709000
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00709000