• Arya, S. P., 1988: Introduction to Micrometeorology. Academic Press, 307 pp.

  • Beljaars, A. C. M., and A. A. M. Holtslag, 1991: Flux parameterization over land surfaces for atmospheric models. J. Appl. Meteor., 30 , 327341.

    • Search Google Scholar
    • Export Citation
  • Bridgman, P. W., 1931: Dimensional Analysis. Yale University Press, 113 pp.

  • Brutsaert, W., 2005: Hydrology: An Introduction. Cambridge University Press, 605 pp.

  • Buckingham, E., 1914: On physically similar systems: Illustrations of the use of dimensional equations. Phys. Rev., 4 , 345376.

  • Businger, J. A., J. Wyngaard, Y. Izumi, and E. F. Bradley, 1971: Flux-profile relationships in the atmospheric surface layer. J. Atmos. Sci., 28 , 181189.

    • Search Google Scholar
    • Export Citation
  • Busse, F. H., 1978: The optimum theory of turbulence. Adv. Appl. Mech., 18 , 77121.

  • Carl, D. M., T. C. Tarbell, and H. A. Panofsky, 1973: Profiles of wind and temperature from towers over homogeneous terrain. J. Atmos. Sci., 30 , 788794.

    • Search Google Scholar
    • Export Citation
  • Cheng, Y. M., M. B. Parlange, and W. Brutsaert, 2005: Pathology of Monin–Obukhov similarity in the stable boundary layer. J. Geophys. Res., 110 , D06101. doi:10.1029/2004JD004923.

    • Search Google Scholar
    • Export Citation
  • Dewar, R. C., 2003: Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states. J. Phys., 36 , 631641.

    • Search Google Scholar
    • Export Citation
  • Dewar, R. C., 2005: Maximum entropy production and the fluctuation theorem. J. Phys., 38 , L371L381. doi:10.1088/0305-4470/38/21/L01.

  • Dyer, A. J., 1964: The flux-gradient relation for turbulent heat transfer in the lower atmosphere. Quart. J. Roy. Meteor. Soc., 90 , 151157.

    • Search Google Scholar
    • Export Citation
  • Dyer, A. J., 1967: The turbulent transport of heat and water vapour in an unstable atmosphere. Quart. J. Roy. Meteor. Soc., 93 , 501508.

    • Search Google Scholar
    • Export Citation
  • Elliott, W. P., 1964: The height variation of vertical heat flux near the ground. Quart. J. Roy. Meteor. Soc., 90 , 260265.

  • Goodman, L. E., and W. H. Warner, 2001: Dynamics. Dover, 617 pp.

  • Handorf, D., T. Foken, and C. Kottmeier, 1999: The stable atmospheric boundary layer over an Antarctic ice sheet. Bound.-Layer Meteor., 91 , 165189.

    • Search Google Scholar
    • Export Citation
  • Irwin, J. S., and F. S. Binkowski, 1981: Estimation of the Monin–Obukhov scaling length using on-site instrumentation. Atmos. Environ., 15 , 10911094.

    • Search Google Scholar
    • Export Citation
  • Jaynes, E. T., 1957: Information theory and statistical mechanics. Phys. Rev., 106 , 620630.

  • Jaynes, E. T., 2003: Probability Theory: The Logic of Science. Cambridge University Press, 758 pp.

  • Johansson, C., A. Smedman, U. Högström, J. G. Brasseur, and S. Khanna, 2001: Critical test of the validity of Monin–Obukhov similarity during convective conditions. J. Atmos. Sci., 58 , 15491566.

    • Search Google Scholar
    • Export Citation
  • Kader, B. A., and A. M. Yaglom, 1990: Mean fields and fluctuation moments in unstably stratified turbulent boundary layers. J. Fluid Mech., 212 , 637662.

    • Search Google Scholar
    • Export Citation
  • Katul, G. G., 1994: A model for sensible heat flux probability density function for near-neutral and slightly-stable atmospheric flows. Bound.-Layer Meteor., 71 , 120.

    • Search Google Scholar
    • Export Citation
  • Kleidon, A., K. Fraedrich, E. Kirk, and F. Lunkeit, 2006: Maximum entropy production and the strength of boundary layer exchange in an atmospheric general circulation model. Geophys. Res. Lett., 33 , L06706. doi:10.1029/2005GL025373.

    • Search Google Scholar
    • Export Citation
  • Kondepudi, D., and I. Prigogine, 1998: Modern Thermodynamics. Wiley, 486 pp.

  • Lanczos, C., 1970: The Variational Principles of Mechanics. Dover, 418 pp.

  • Lorenz, R. D., and C. P. McKay, 2003: A simple expression for vertical convective fluxes in planetary atmospheres. Icarus, 165 , 407413.

    • Search Google Scholar
    • Export Citation
  • Malkus, W. V. R., 1954: The heat transport and spectrum of thermal turbulence. Proc. Roy. Soc. London, 225A , 196212.

  • Monin, A. S., and A. M. Obukhov, 1954: Basic turbulence mixing laws in the atmospheric surface layer. Tr. Inst. Teor. Geofiz. Akad. Nauk. SSSR, 24 , 163187. (English translation available in V. N. Bespalyi, Ed., 2001: Turbulence and Atmospheric Dynamics, J. L. Lumley, 164–194).

    • Search Google Scholar
    • Export Citation
  • Monin, A. S., and A. M. Yaglom, 1971: Statistical Fluid Mechanics: Mechanics of Turbulence. Vol. 1, The MIT Press, 782 pp.

  • Obukhov, A. M., 1946: Turbulence in an atmosphere with a non-uniform temperature. Tr. Inst. Teor. Geofiz. Akad. Nauk. SSSR, 1 , 95115. (English translation available in Obukhov, A. M., 1971: Turbulence in an atmosphere with a non-uniform temperature. Boundary-Layer Meteor.,2, 7–29).

    • Search Google Scholar
    • Export Citation
  • Ozawa, H., S. Shimokawa, and H. Sakuma, 2001: Thermodynamics of fluid turbulence: A unified approach to the maximum transport properties. Phys. Rev. E, 64 , 026303. doi:10.1103/PhysRevE.64.026303.

    • Search Google Scholar
    • Export Citation
  • Priestley, C. H. B., 1955: Free and forced convection in the atmosphere near the ground. Quart. J. Roy. Meteor. Soc., 81 , 139143.

  • Shannon, C. E., and W. Weaver, 1949: The Mathematical Theory of Communication. University of Illinois Press, 144 pp.

  • Taylor, R. J., 1956: Some measurements of heat flux at large negative Richardson number. Quart. J. Roy. Meteor. Soc., 82 , 8991.

  • Taylor, R. J., 1959: Similarity theory in the relation between fluxes and gradients in the lower atmosphere. Quart. J. Roy. Meteor. Soc., 85 , 6778.

    • Search Google Scholar
    • Export Citation
  • Townsend, A. A., 1962: Natural convection in the earth’s boundary layer. Quart. J. Roy. Meteor. Soc., 88 , 5156.

  • Wang, J., and R. L. Bras, 2009: A model of surface heat fluxes based on the theory of maximum entropy production. Water Resour. Res., 45 , W11422. doi:10.1029/2009WR007900.

    • Search Google Scholar
    • Export Citation
  • Wang, J., G. D. Salvucci, and R. L. Bras, 2004: An extremum principle of evaporation. Water Resour. Res., 40 , W09303. doi:10.1029/2004WR003087.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 285 99 10
PDF Downloads 248 95 7

An Extremum Solution of the Monin–Obukhov Similarity Equations

Jingfeng WangMassachusetts Institute of Technology, Cambridge, Massachusetts

Search for other papers by Jingfeng Wang in
Current site
Google Scholar
PubMed
Close
and
Rafael L. BrasUniversity of California, Irvine, Irvine, California

Search for other papers by Rafael L. Bras in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

An extremum hypothesis of turbulent transport in the atmospheric surface layer is postulated. The hypothesis has led to a unique solution of Monin–Obukhov similarity equations in terms of simple expressions linking shear stress (momentum flux) and heat flux to mean wind shear and temperature gradient. The extremum solution is consistent with the well-known asymptotic properties of the surface layer. Validation of the extremum solution has been made by comparison to field measurements of momentum and heat fluxes. Furthermore, a modeling test of predicting surface heat fluxes using the results of this work is presented. A critical reexamination of the interpretation of the Obukhov length is given.

* Current affiliation: University of California, Irvine, Irvine, California.

Corresponding author address: Jingfeng Wang, Department of Civil and Environmental Engineering, University of California, Irvine, E2167 Engineering Gateway, Irvine, CA 92697. Email: jingfenw@uci.edu

Abstract

An extremum hypothesis of turbulent transport in the atmospheric surface layer is postulated. The hypothesis has led to a unique solution of Monin–Obukhov similarity equations in terms of simple expressions linking shear stress (momentum flux) and heat flux to mean wind shear and temperature gradient. The extremum solution is consistent with the well-known asymptotic properties of the surface layer. Validation of the extremum solution has been made by comparison to field measurements of momentum and heat fluxes. Furthermore, a modeling test of predicting surface heat fluxes using the results of this work is presented. A critical reexamination of the interpretation of the Obukhov length is given.

* Current affiliation: University of California, Irvine, Irvine, California.

Corresponding author address: Jingfeng Wang, Department of Civil and Environmental Engineering, University of California, Irvine, E2167 Engineering Gateway, Irvine, CA 92697. Email: jingfenw@uci.edu

Save