Skip to main content
SpringerLink
Log in

50 Years of the Monin–Obukhov Similarity Theory

  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

Abstract

This historical survey shows that Obukhov’s 1946 fundamental paper on a universal length scale for exchange processes in the surface layer was the basis for the derivation of the similarity theory by Monin and Obukhov in 1954. A brief overview of the experiments and findings used to formulate the universal functions in the presently used form is given. Finally, the current status of the theory is described, covering topics such as the accuracy of the universal functions and the turbulent Prandtl number.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Albrecht, F.: 1940, ‘Untersuchungen über den Wärmehaushalt der Erdoberfläche in verschiedenen Klimagebieten’, Reichsamt f. Wetterdienst, Wiss. Abh. Bd. VIII, Nr. 2, 1–82.

  • Andreas, E. L., Claffey, K. J., Fairall, C. W., Grachev, A. A., Guest, P. S., Jordan, R. E., and Persson, P. O. G.: 2004, ‘Measurements of the von Kármán Constant in the Atmospheric Surface Layer – Further Discussions’, in 16th Conference on Boundary Layers and Turbulence, Portland ME, Amer. Meteorol. Soc., paper 7.2, pp. 1–7.

  • Barrett E.W. and Suomi V.E. (1949). ‘Preliminary Report on Temperature Measurement by Sonic Means’. J. Meteorol. 6: 273–276

    Google Scholar 

  • Bernhardt K.-H. (1995). ‘Zur Interpretation der Monin–Obuchovschen Länge’. Meteorol. Z. 4:81–82

    Google Scholar 

  • Bovscheverov V.M. and Voronov V.P. (1960). ‘Akustitscheskii fljuger (Acoustic rotor)’. Izv. AN SSSR, ser. Geofiz. 6: 882–885

    Google Scholar 

  • Bradley E.F. (1968). ‘A Shearing Stress Meter for Micrometeorological Studies’. Quart. J. Roy. Meteorol. Soc. 94:380–387

    Article  Google Scholar 

  • Businger J.A., Miyake M., Inoue E., Mitsuta Y., and Hanafusa T. (1969). ‘Sonic Anemometer Comparison and Measurements in the Atmospheric Surface Layer’. J. Meteorol. Soc. Japan 47:1–12

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Businger J.A. and Yaglom A.M. (1971). ‘Introduction to Obukhov’s Paper “Turbulence in an Atmosphere with a Non-Uniform Temperature” ’. Boundary-Layer Meteorol. 2:3–6

    Article  Google Scholar 

  • Businger J.A. (1988). ‘A Note on the Businger–Dyer Profiles’. Boundary-Layer Meteorol. 42:145–151

    Article  Google Scholar 

  • Culf A.D., Foken T., and Gash J.H.C. (2004). ‘The Energy Balance Closure Problem’. In: Kabat P., Claussen M. et al. (eds). Vegetation, Water, Humans and the Climate A New Perspective on an Interactive System. Springer, Berlin, Heidelberg, pp. 159–166

    Google Scholar 

  • Denmead D.T. and Bradley E.F. (1985). ‘Flux–Gradient Relationships in a Forest Canopy’. In: Hutchison B.A., Hicks B.B.(eds). The Forest-Atmosphere Interaction. D. Reidel Publ. Comp., Dordrecht, Boston, London, pp. 421–442

    Google Scholar 

  • Dyer A.J., Hicks B.B., and King K.M. (1967). ‘The Fluxatron – A Revised Approach to the Measurement of Eddy Fluxes in the Lower Atmosphere’. J. Appl. Meteorol. 6:408–413

    Article  Google Scholar 

  • Dyer A.J. and Hicks B.B. (1970). ‘Flux–Gradient Relationships in the Constant Flux Layer’. Quart. J. Roy. Meteorol. Soc. 96:715–721

    Article  Google Scholar 

  • Dyer A.J. (1974). ‘A Review of Flux-Profile-Relationships’. Boundary-Layer Meteorol. 7:363–372

    Article  Google Scholar 

  • Dyer A.J., Garratt J.R., Francey R.J., McIlroy I.C., Bacon N.E., Hyson P., Bradley E.F., Denmead D.T., Tsvang L.R., Volkov J.A., Kaprov B.M., Elagina L.G., Sahashi K., Monji N., Hanafusa T., Tsukamoto O., Frenzen P., Hicks B.B., Wesely M., Miyake M., and Shaw W.J. (1982). ‘An International Turbulence Comparison Experiment (ITCE 1976)’. Boundary-Layer Meteorol. 24:181–209

    Article  Google Scholar 

  • Foken T., Kitajgorodskij S.A., and Kuznecov O.A. (1978). ‘On the Dynamics of the Molecular Temperature Boundary Layer above the Sea’. Boundary-Layer Meteorol. 15:289–300

    Article  Google Scholar 

  • Foken T. and Kuznecov O.A. (1978). ‘Die wichtigsten Ergebnisse der gemeinsamen Expedition “KASPEX-76” des Institutes für Ozeanologie Moskau und der Karl-Marx-Universität Leipzig’. Beitr. Meeresforsch. 41:41–47

    Google Scholar 

  • Foken T. and Skeib G. (1983). ‘Profile Measurements in the Atmospheric Near-Surface Layer and the Use of Suitable Universal Functions for the Determination of the Turbulent Energy Exchange’. Boundary-Layer Meteorol. 25:55–62

    Article  Google Scholar 

  • Foken T. (1990). ‘Turbulenter Energieaustausch zwischen Atmosphäre und Unterlage – Methoden, meßtechnische Realisierung sowie ihre Grenzen und Anwendungsmöglichkeiten’. Ber. Dt. Wetterdienstes 180:287

    Google Scholar 

  • Foken T. and Bernhardt K. (1994). ‘Atmospheric Boundary Layer Research in Central and East European Countries with KAPG, 1981–1990’. Geophys. Rep. 01:1–58

    Google Scholar 

  • Foken T. and Oncley S.P. (1995). ‘Results of the Workshop “Instrumental and Methodical Problems of Land Surface Flux Measurements”’. Bull. Amer. Meteorol. Soc. 76:1191–1193

    Google Scholar 

  • Foken T. (2003). Angewandte Meteorologie, Mikrometeorologische Methoden. Springer, Heidelberg, 289 pp.

    Google Scholar 

  • Garratt J.R. (1980). ‘Surface Influence upon Vertical Profiles in the Atmospheric Near Surface Layer’. Quart. J. Roy. Meteorol. Soc. 106:803–819

    Article  Google Scholar 

  • Garratt J.R. and Hicks B.B. (1990). ‘Micrometeorological and PBL Experiments in Australia’. Boundary-Layer Meteorol. 50:11–32

    Article  Google Scholar 

  • Garratt J.R. (1992). The Atmospheric Boundary Layer. Cambridge University Press, Cambridge, 316 pp.

    Google Scholar 

  • Geiger R. (1927). Das Klima der bodennahen Luftschicht. Friedr. Vieweg & Sohn, Braunschweig, 246 pp.

    Google Scholar 

  • Geiger R., Aron R.H., and Todhunter P. (1995). The Climate Near the Ground. Friedr. Vieweg & Sohn Verlagsges. mbH, Braunschweig, Wiesbaden, 528 pp.

    Google Scholar 

  • Hanafusa T., Fujitana T., Kobori Y., and Mitsuta Y. (1982). ‘A New Type Sonic Anemometer–Thermometer for Field Operation’. Papers in Meteorol. & Geophys. 33:1–19

    Article  Google Scholar 

  • Handorf D., Foken T., and Kottmeier C. (1999). ‘The Stable Atmospheric Boundary Layer over an Antarctic Ice Sheet’. Boundary-Layer Meteorol. 91:165–186

    Article  Google Scholar 

  • Haugen D.H. (eds) (1973). ‘Workshop on Micrometeorology’. Amer. Meteorol. Soc., Boston, 392 pp.

    Google Scholar 

  • Hess G.D., Hicks B.B., and Yamada T. (1981). ‘The Impact of the Wangara Experiment’. Boundary-Layer Meteorol. 20: 135–174

    Article  Google Scholar 

  • Hicks B.B. (1986). ‘Book Review: ‘“International Turbulence Comparison Experiment ITCE 1981”’. Boundary-Layer Meteorol. 34:417–419

    Article  Google Scholar 

  • Högström U. (1974). ‘A Field Study of the Turbulent Fluxes of Heat Water Vapour and Momentum at a ‘Typical’ Agricultural Site’. Quart. J. Roy. Meteorol. Soc. 100:624–639

    Google Scholar 

  • Högström U. (1985). ‘Von Kármán Constant in Atmospheric Boundary Flow: Reevaluated’. J. Atmos. Sci. 42: 263–270

    Article  Google Scholar 

  • Högström U. (1988). ‘Non-dimensional Wind and Temperature Profiles in the Atmospheric Surface Layer: A Re-evaluation’. Boundary-Layer Meteorol. 42:55–78

    Article  Google Scholar 

  • Högström U. (1990). ‘Analysis of Turbulence Structure in the Surface Layer with a Modified Similarity Formulation for Near Neutral Conditions’. J. Atmos. Sci. 47:1949–1972

    Article  Google Scholar 

  • Högström U. (1996). ‘Review of Some Basic Characteristics of the Atmospheric Surface Layer’. Boundary-Layer Meteorol. 78:215–246

    Article  Google Scholar 

  • Högström U. and Bergstrom H. (1996). ‘Organized Turbulence Structures in the Near-Neutral Atmospheric Surface Layer’. J. Atmos. Sci. 53:2452–2464

    Article  Google Scholar 

  • Izumi, Y.: (1971), Kansas 1968 Field Program Data Report. Bedford, MA, Air Force Cambridge Research Papers, No. 379, 79 pp.

  • Johansson C., Smedman A., Högström U., Brasseur J.G., and Khanna S. (2001). ‘Critical Test of Monin–Obukhov Similarity During Convective Conditions’. J. Atmos. Sci. 58:1549–1566

    Article  Google Scholar 

  • Kader B.A. and Yaglom A.M. (1972). ‘Heat and Mass Transfer Laws for Fully Turbulent Wall Flows’. Int. J. Heat Mass Transfer 15:2329–2350

    Article  Google Scholar 

  • Kader B.A. and Yaglom A.M. (1990). ‘Mean Fields and Fluctuation Moments in Unstably Stratified Turbulent Boundary Layers’. J. Fluid Mech. 212:637–662

    Article  Google Scholar 

  • Kaimal J.C. and Businger J.A. (1963). ‘A Continuous Wave Sonic Anemometer–Thermometer’. J. Climate Appl. Meteorol. 2:156–164

    Article  Google Scholar 

  • Kaimal J.C. and Wyngaard J.C. (1990). ‘The Kansas and Minnesota Experiments’. Boundary-Layer Meteorol. 50:31–47

    Article  Google Scholar 

  • Kantha L.H. and Clayson C.A. (2000). Small Scale Processes in Geophysical Fluid Flows. Academic Press, San Diego, 883 pp.

    Google Scholar 

  • von Kármán T. and Howarth L. (1938). ‘On the Statistical Theory of Isotropic Turbulence’. Proc. Roy. Soc. London A 164:192–215

    Article  Google Scholar 

  • Kleinschmidt E. (eds) (1935). Handbuch der meteorologischen Instrumente und ihrer Auswertung. Springer, Berlin, 733 pp.

    Google Scholar 

  • Kolmogorov A.N. (1941a). ‘Lokalnaja struktura turbulentnosti v neschtschimaemoi schidkosti pri otschen bolschich tschislach Reynoldsa (The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers)’. Dokl. AN SSSR 30:299–303

    Google Scholar 

  • Kolmogorov A.N. (1941b). ‘Rassejanie energii pri lokolno-isotropoi turbulentnosti (Dissipation of Energy in Locally Isotropic Turbulence)’. Dokl. AN SSSR 32:22–24

    Google Scholar 

  • Kondo J. and Sato T. (1982). ‘The Determination of the von Kármán Constant’. J. Meteorol. Soc. Japan 60:461–471

    Google Scholar 

  • Lee X., Massman W.J. and Law B. (eds) (2004). Handbook of Micrometeorology: A Guide for Surface Flux Measurement and Analysis. Kluwer, Dordrecht, 250 pp.

    Google Scholar 

  • Lettau H. (1939). Atmosphärische Turbulenz. Akad. Verlagsges., Leipzig, 283 pp.

    Google Scholar 

  • Lettau H. (1949). ‘Isotropic and Non-Isotropic Turbulence in the Atmospheric Surface Layer’. Geophys. Res. Pap. 1:86

    Google Scholar 

  • Lettau H.H. (eds) (1957). Exploring the Atmosphere’s First Mile, Vol1. Pergamon Press, London, New York, 376 pp.

    Google Scholar 

  • Lumley J.L. and Yaglom A.M. (2001). ‘A Century of Turbulence’. Flow Turbulence Combust. 66:241–286

    Article  Google Scholar 

  • McBean G.A., Bernhardt K., Bodin S., Litynska Z., van Ulden A.P., and Wyngaard J.C. (1979). ‘The Planetary Boundary Layer’. WMO, Note 530:201

    Google Scholar 

  • Mitsuta Y. (1966). ‘Sonic Anemometer-Thermometer for General Use’. J. Meteorol. Soc. Japan Ser. II 44:12–24

    Google Scholar 

  • Miyake M., Stewart R.W., Burling R.W., Tsvang L.R., Kaprov B.M., and Kuznecov O.A. (1971). ‘Comparison of Acoustic Instruments in an Atmospheric Flow Over Water’. Boundary-Layer Meteorol. 2:228–245

    Article  Google Scholar 

  • Monin A.S. and Obukhov A.M. (1954). ‘Osnovnye zakonomernosti turbulentnogo peremeshivanija v prizemnom sloe atmosfery (Basic Laws of Turbulent Mixing in the Atmosphere Near the Ground)’. Trudy geofiz. inst. AN SSSR 24(151): 163–187

    Google Scholar 

  • Monin A.S. and Yaglom A.M. (1973). Statistical Fluid Mechanics: Mechanics of Turbulence, Vol 1. MIT Press, Cambridge, London, 769 pp.

    Google Scholar 

  • Monin A.S. and Yaglom A.M. (1975). Statistical Fluid Mechanics: Mechanics of Turbulence, Vol 2. MIT Press, Cambridge, London, 874 pp.

    Google Scholar 

  • Montgomery R.B. (1948). ‘Vertical Eddy Flux of Heat in the Atmosphere’. J. Meteorol. 5:265–274

    Google Scholar 

  • Obukhov A.M. (1946). ‘Turbulentnost’ v temperaturnoj–neodnorodnoj atmosfere (Turbulence in an Atmosphere with a Non-uniform Temperature)’. Trudy Inst. Theor. Geofiz. AN SSSR 1:95–115

    Google Scholar 

  • Obukhov A.M. (1951). ‘Charakteristiki mikrostruktury vetra v prizemnom sloje atmosfery (Characteristics of the Micro-structure of the Wind in the Surface Layer of the Atmosphere)’. Izv. AN SSSR, ser. Geofiz. 3:49–68

    Google Scholar 

  • Obukhov A.M. (1960). ‘O strukture temperaturnogo polja i polja skorostej v uslovijach konvekcii (Structure of the Temperature and Velocity Fields Under Conditions of Free Convection)’. Izv. AN SSSR, ser. Geofiz. 9:1392–1396

    Google Scholar 

  • Obukhov A.M. (1971). ‘Turbulence in an Atmosphere with a Non-uniform Temperature’. Boundary-Layer Meteorol. 2:7–29

    Article  Google Scholar 

  • Oncley S.P., Friehe C.A., Larue J.C., Businger J.A., Itsweire E.C., and Chang S.S. (1996). ‘Surface-layer Fluxes, Profiles, and Turbulence Measurements over Uniform Terrain Under Near-neutral Conditions’. J. Atmos. Sci. 53:1029–1054

    Article  Google Scholar 

  • Paeschke W. (1937). ‘Experimentelle Untersuchungen zum Rauhigkeitsproblem in der bodennahen Luftschicht’. Z. Geophys. 13:14–21

    Google Scholar 

  • Panin G.N., Tscherevitinov F.O., and Piacena C. (1982). ‘O vlijanii stratifikacii vozducha na processy vzaimodejsvija vodoema s atmosfery (About the Influence of the Stability on Air–Sea Interaction)’. Acta Hydrophys. 27:229–244

    Google Scholar 

  • Panofsky H.A. (1963). ‘Determination of Stress from Wind and Temperature Measurements’. Quart. J. Roy. Meteorol. Soc. 89: 85–94

    Article  Google Scholar 

  • Prandtl L. (1925). ‘Bericht über Untersuchungen zur ausgebildeten Turbulenz’. Z. angew. Math. Mech. 5:136–139

    Google Scholar 

  • Priestley C.H.B. and Swinbank W.C. (1947). ‘Vertical Transport of Heat by Turbulence in the Atmosphere’. Proc. Roy. Soc. London A 189:543–561

    Google Scholar 

  • Pruitt W.O., Morgan D.L., and Lourence F.J. (1973). ‘Momentum and Mass Transfer in the Surface Boundary Layer’. Quart. J. Roy. Meteorol. Soc. 99:370–386

    Article  Google Scholar 

  • Raupach M.R., Thom A.S., and Edwards I. (1980). ‘A Wind-Tunnel Study of Turbulent Flow Close to Regularly Arrayed Rough Surface’. Boundary-Layer Meteorol. 18:373–379

    Article  Google Scholar 

  • Raupach M.R., Finnigan J.J., and Brunet Y. (1996). ‘Coherent Eddies and Turbulence in Vegetation Canopies: The Mixing-layer Analogy’. Boundary-Layer Meteorol. 78:351–382

    Article  Google Scholar 

  • Reynolds O. (1894). ‘On the Dynamical Theory of Turbulent Incompressible Viscous Fluids and the Determination of the Criterion’. Phil. Trans. R. Soc. London A 186:123–161

    Google Scholar 

  • Richardson L.F. (1920). ‘The Supply of Energy from and to Atmospheric Eddies’. Proc. Roy. Soc. A 97:354–373

    Article  Google Scholar 

  • Schmidt W. (1925). Der Massenaustausch in freier Luft und verwandte Erscheinungen. Henri Grand Verlag, Hamburg, 118 pp.

    Google Scholar 

  • Schotland R.M. (1955). ‘The Measurement of Wind Velocity by Sonic Waves’. J. Meteorol. 12:386–390

    Google Scholar 

  • Sheppard P.A. (1947). ‘The Aerodynamic Drag of the Earth’s Surface and the Value of von Karman’s Constant in the Lower Atmosphere’. Proc. Roy. Soc. A 188:208

    Article  Google Scholar 

  • Stull R.B. (1988). An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, Dordrecht, 666 pp.

    Google Scholar 

  • Suomi V.E. (1957). ‘Sonic Anemometer – University of Wisconsin’. In: Lettau H.H. and Davidson B. (eds). Exploring the Atmosphere’s First Mile. Pergamon Press, London, New York, pp. 256–266

    Google Scholar 

  • Swinbank W.C. (1951). ‘The Measurement of Vertical Transfer of Heat and Water Vapor by Eddies in the Lower Atmosphere’. J. Meteorol. 8:135–145

    Google Scholar 

  • Swinbank W.C. (1964). ‘The Exponential Wind Profile’. Quart. J. Roy. Meteorol. Soc. 90:119–135

    Article  Google Scholar 

  • Swinbank W.C. (1968). ‘A Comparison between Prediction of the Dimensional Analysis for the Constant-Flux Layer and Observations in Unstable Conditions’. Quart. J. Roy. Meteorol. Soc. 94:460–467

    Article  Google Scholar 

  • Swinbank W.C. and Dyer A.J. (1968). ‘An Experimental Study on Mircrometeorology’. Quart. J. Roy. Meteorol. Soc. 93: 494–500

    Article  Google Scholar 

  • Taylor G.I. (1915). ‘Eddy Motion in the Atmosphere’. Phil. Trans. Roy. Soc. London A 215:1–26

    Article  Google Scholar 

  • Taylor G.I. (1938). ‘The Spectrum of Turbulence’. Proc. Roy. Soc. London A 164:476–490

    Google Scholar 

  • Tschalikov D.V. (1968). ‘O profilja vetra i temperatury v prizemnom sloe atmosfery pri ustojtschivoj stratifikacii (About the Wind and Temperature Profile in the Surface Layer for Stable Stratification)’. Trudy GGO 207:170–173

    Google Scholar 

  • Tsvang L.R., Kaprov B.M., Zubkovskij S.L., Dyer A.J., Hicks B.B., Miyake M., Stewart R.W., and McDonald J.W. (1973). ‘Comparison of Turbulence Measurements by Different Instuments; Tsimlyansk Field Experiment 1970’. Boundary-Layer Meteorol. 3:499–521

    Article  Google Scholar 

  • Tsvang L.R., Zubkovskij S.L., Kader B.A., Kallistratova M.A., Foken T., Gerstmann W., Przandka Z., Pretel J., Zelený J., and Keder J. (1985). ‘International Turbulence Comparison Experiment (ITCE-81)’. Boundary-Layer Meteorol. 31:325–348

    Article  Google Scholar 

  • Webb E.K. (1970). ‘Profile Relationships: The Log-Linear Range, and Extension to Strong Stability’. Quart. J. Roy. Meteorol. Soc. 96:67–90

    Article  Google Scholar 

  • Wieringa J. (1980). ‘A Revaluation of the Kansas Mast Influence on Measurements of Stress and Cup Anemometer Overspeeding’. Boundary-Layer Meteorol. 18:411–430

    Article  Google Scholar 

  • Wyngaard J.C., Businger J.A., Kaimal J.C., and Larsen S.E. (1982). ‘Comments on “A Revaluation of the Kansas Mast Influence on Measurements of Stress and Cup Anemometer Overspeeding”’. Boundary-Layer Meteorol. 22:245–250

    Article  Google Scholar 

  • Yaglom A.M. (1977). ‘Comments on Wind and Temperature Flux-Profile Relationships’. Boundary-Layer Meteorol. 11: 89–102

    Article  Google Scholar 

  • Yaglom A.M. (1990). ‘Alexander Mikhailovich Obukhov, 1918–1989’. Boundary-Layer Meteorol. 53:v–xi

    Article  Google Scholar 

  • Zilitinkevich S.S. and Tschalikov D.V. (1968). ‘Opredelenie universalnych profilej skorosti vetra i temperatury v prizemnom sloe atmosfery (Determination of Universal Profiles of Wind Velocity and Temperature in the Surface Layer of the Atmosphere)’. Izv. AN SSSR, Fiz. Atm. i Okeana 4:294–302

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Micrometeorology, University of Bayreuth, D-95440, Bayreuth, Germany

    Thomas Foken

Authors
  1. Thomas Foken
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Foken.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Foken, T. 50 Years of the Monin–Obukhov Similarity Theory. Boundary-Layer Meteorol 119, 431–447 (2006). https://doi.org/10.1007/s10546-006-9048-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10546-006-9048-6

Keywords

Search

Navigation