Boundary-Layer Meteorology

, Volume 11, Issue 3, pp 363–373 | Cite as

Drag and heat transfer relations for the planetary boundary layer

  • Robert R. Long
  • Larry J. Guffey


A theory is offered for the drag and heat transfer relations in the statistically steady, horizontally homogeneous, diabatic, barotropic planetary boundary layer. The boundary layer is divided into three regionsR1,R2, andR3, in which the heights are of the order of magnitude ofz0,L, andh, respectively, wherez0 is the roughness length for either momentum or temperature,L is the Obukhov length, andh is the height of the planetary boundary layer. A matching procedure is used in the overlap zones of regionsR1 andR2 and of regionsR2 andR3, assuming thatz0Lh. The analysis yields the three similarity functionsA(μ),B(μ), andC(μ) of the stability parameter, μ = ϰu*/fL, where ϰ is von Kármán's constant,u* is the friction velocity at the ground andf is the Coriolis parameter. The results are in agreement with those previously found by Zilitinkevich (1975) for the unstable case, and differ from his results only by the addition of a universal constant for the stable case. Some recent data from atmospheric measurements lend support to the theory and permit the approximate evaluation of universal constants.


Heat Transfer Boundary Layer Planetary Boundary Layer Friction Velocity Roughness Length 
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  1. Arya, S. P. S.: 1975, ‘Geostrophic Drag and Heat Transfer Relations for the Atmospheric Boundary layer’,Quart. J. Roy. Meteorol. Soc.,101, 147–161.Google Scholar
  2. 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.Google Scholar
  3. Businger, J. A. and Arya, S. P. S.: 1974, ‘Height of the Mixed Layer in the Stably Stratified Planetary Boundary Layer’,Adv. Geophy. 18A, Academic Press, pp. 73–92.Google Scholar
  4. Csanady, G. T.: 1972, ‘Geostrophic Drag, Heat and Mass Transfer Coefficients for the Diabatic Ekman Layer’,J. Atmos. Sci.,29, 488–496.Google Scholar
  5. Izakson, A. A.: 1937, ‘On the Formula for Velocity Distributions Near Walls’,Tech. Phys. USSR,4, 27–37.Google Scholar
  6. Long, R. R.: 1976, ‘Relation between Nusselt Number and Rayleigh Number in Turbulent Thermal Convection’,J. Fluid Mech.,73, 445–451.Google Scholar
  7. Long, R. R.: 1977, ‘Some Aspects of Turbulence in Geophysical Systems’, (To appear inAppl. Mech. Rev.).Google Scholar
  8. Millikan, C. B.: 1937, ‘A Critical Discussion of Turbulent Flows in Channels and Circular Tubes’,Proc. 5th Inter. Congr. Appl. Mech., pp. 386–392.Google Scholar
  9. Monin, A. S. and Yaglom, A. M.: 1971,Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 1, MIT Press.Google Scholar
  10. Obukhov, A. M.: 1946, ‘Turbulence in Thermally Inhomogeneous Atmosphere’,Trudy In-ta Teoret. Geofiz. AN SSSR,1, 95–115.Google Scholar
  11. Prandtl, L.: 1932, ‘Meteorologische Andwendungen der Strömungslehre’,Beitr. Phys. Atmos. 19, 188–202.Google Scholar
  12. Priestley, C. H. B.: 1959,Turbulent Transfer in the Lower Atmosphere, Univ. of Chicago Press, Chicago, Ill.Google Scholar
  13. Tennekes, H. and Lumley, J. L.: 1972,A First Course in Turbulence, MIT Press, Cambridge, Mass.Google Scholar
  14. Townsend, A. A. : 1976,The Structure of Turbulent Shear Flow, Cambridge Univ. Press (Second Edition).Google Scholar
  15. Wyngaard, J. C., Arya, S. P. S., and Coté, O. R.: 1974, ‘Some Aspects of the Structure of Convective Planetary Boundary Layers’,J. Atmos. Sci. 31, 747–754.Google Scholar
  16. Yamada, T.: 1976, ‘On the Similarity FunctionsA, B, C of the Planetary Boundary Layer’.J. Atmos. Sci. 33, 781–793.Google Scholar
  17. Yamada, T., and Mellor, G. L.: 1975, ‘A Simulation of the Wangara Atmospheric Boundary Layer Data’.J. Atmos. Sci. 32, 2309–2329.Google Scholar
  18. Zilitinkevich, S. S.: 1972, ‘On the Determination of the Height of the Ekman Boundary Layer’,Boundary-Layer Meteorol.,3, 141–145.Google Scholar
  19. Zilitinkevich, S. S.: 1975 ‘Resistance Laws and Prediction Equations for the Depth of the Planetary Boundary Layer’,J. Atmos. Sci.,32, 741–752.Google Scholar
  20. Zilitinkevich, S. S. and Chalikov, D. V.: 1968, ‘The Laws of Resistance and of Heat and Moisture Exchange in the interaction between the Atmosphere and Underlying Surface’,Izv. Atmos. Ocean. Phys. 4, 438–441 (English ed.).Google Scholar

Copyright information

© D. Reidel Publishing Company 1977

Authors and Affiliations

  • Robert R. Long
    • 1
  • Larry J. Guffey
    • 1
  1. 1.Departments of Earth Sciences and Mechanics and Materials ScienceThe Johns Hopkins UniversityBaltimoreUSA

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