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Hans A. Panofsky’s Integral Similarity Function—At Fifty

¹ Geophysical Institute, University of Alaska Fairbanks, Fairbanks, USA
² Department of Atmospheric Sciences, College of Geosciences, Texas A&M University, College Station, USA
³ Department of Micrometeorology, University of Bayreuth, Bayreuth, Germany
⁴ Geophysical Institute, University of Alaska Fairbanks, Fairbanks, USA

Atmospheric and Climate Sciences·Volume 03 (2013)·Pages 581–594·Published 26 August 2013·DOI10.4236/acs.2013.34061

Abstract

Fifty years ago, Hans A. Panofsky published a paper entitled Determination of stress from wind and temperature measurements . In his famous paper , he presented a new profile function for the mean horizontal wind speed under the condition of diabatic stratification that includes his integral similarity function. With his integral similarity function , he opened the door for Monin-Obukhov scaling in a wide range of micrometeorological and microclimatological applications. In a historic survey ranging from the sixties of the past century down to the present days, we present integral similarity functions for momentum, sensible heat, and water vapor for both unstable and stable stratification, where on the one hand free convection condition and on the other hand strongly stable stratification are addressed.

KeywordsProfile FunctionsMonin-Obukhov ScalingPrandtl-Obukhov-Priestley ScalingLocal Similarity FunctionIntegral Similarity FunctionObukhov NumberGradient Richardson NumberFlux Richardson Number

H. A. Panofsky, “Determination of Stress from Wind and Temperature Measurements,” Quarterly Journal of the Royal Meteorological Society, Vol. 89, No. 379, 1963, pp. 85-94. http://dx.doi.org/10.1002/qj.49708937906
A. S. Monin and A. M. Obukhov, “Osnovnye Zakonomernosti Turbulentnogo Peremesivanija v Prizemnom sloe Atmosfery,” Trudy Geofizicheskogo Instituta Akademiya Nauk SSSR, Vol. 24, 1954, pp. 163-187. (in Russian)
O. Reynolds, “On the Dynamical Theory of Incompressible Viscous Fluids and the Determination of the Criterion,” Philosophical Transactions of the Royal Society, Vol. 186, 1895, pp. 123-164. http://dx.doi.org/10.1098/rsta.1895.0004
T. Hesselberg, “Die Gesetze der Ausgeglichenen Atmospharischen Bewegungen,” Beitrage zur Physik der Atmosphare, Vol. 12, 1926, pp. 141-160. (in German)
J. van Mieghem, “Atmospheric Energetics,” Clarendon Press, Oxford, 1973.
G. Cox, “Basic Considerations,” In: G. Cox, Ed., Combustion Fundamentals of Fire, Academic Press, London, San Diego, New York, pp. 3-30.
G. Kramm, R. Dlugi and D. H. Lenschow, “A Re-Evaluation of the Webb-Correction Using Density-Weighted Averages,” Journal of Hydrology, Vol. 166, No. 3-4, 1995, pp. 283-292. http://dx.doi.org/10.1016/0022-1694(94)05088-F
F. Herbert, “A Re-Evaluation of the Webb Correction Using Density-Weighted Averages—Comment,” Journal of Hydrology, Vol. 173, No. 1-4, 1995, pp. 343-344. http://dx.doi.org/10.1016/0022-1694(95)02867-O
G. Kramm and F. X. Meixner, “On the Dispersion of Trace Species in the Atmospheric Boundary Layer: A Re-Formulation of the Governing Equations for the Turbulent Flow of the Compressible Atmosphere,” Tellus, Vol. 52A, 2000, pp. 500-522.
A. S. Kowalski, “Exact Averaging of Atmospheric State and Flow Variables,” Journal of the Atmospheric Sciences, Vol. 69, No. 5, 2012, pp. 1750-1757. http://dx.doi.org/10.1175/JAS-D-11-0299.1
E. Buckingham, “On Physically Similar Systems; Illustrations of the Use of Dimensional Equations,” Physical Review, Vol. 4, No. 4, 1914, pp. 345-376. http://dx.doi.org/10.1103/PhysRev.4.345
G. I. Barenblatt, “Similarity, Self-Similarity, and Intermediate Asymptotics,” Cambridge University Press, Cambridge, 1996.
G. Kramm and F. Herbert, “Similarity Hypotheses for the Atmospheric Surface Layer Expressed by Dimensional π Invariants Analysis—A Review,” The Open Atmospheric Science Journal, Vol. 3, 2009, pp. 48-79.

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Hans A. Panofsky’s Integral Similarity Function—At Fifty

Abstract

References (71)