Skip to main content
SpringerLink
Log in

Similarity Theory

  • Chapter
An Introduction to Boundary Layer Meteorology

Part of the book series: Atmospheric Sciences Library ((ATSL,volume 13))

Abstract

For a number of boundary layer situations, our knowledge of the governing physics is insufficient to derive laws based on first principles. Nevertheless, boundary layer observations frequently show consistent and repeatable characteristics, suggesting that we could develop empirical relationships for the variables of interest. Similarity theory provides a way to organize and group the variables to our maximum advantage, and in turn provides guidelines on how to design experiments to gain the most information.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 299.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 379.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 379.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • American Geophysical Union, 1969: Spectra of Meteorological Variables. Radio Science, 4, No. 12, 1099–1397.

    Article  Google Scholar 

  • André, J.-C., and C. Blondin, 1986: On the effective roughness length for use in numerical 3-D models. Bound.-Layer Meteor., 35, 231–245.

    Article  Google Scholar 

  • Arya, S.P.S., 1981: Parameterizing the height of the stable atmospheric boundary layer. J. Appi. Meteor., 20, 1192–1202.

    Article  Google Scholar 

  • Benoit, R., 1977: On the integral of the surface layer profile-gradient functions. J. Appi. Meteor., 16, 859–860.

    Article  Google Scholar 

  • Berkowicz, R. and L.P. Prahm, 1984: Spectral representation of the vertical structure of turbulence in the convective boundary layer. Quart. J. Roy. Meteor. Soc., 110, 35–52.

    Article  Google Scholar 

  • Brost, R.A., J.C. Wyngaard and D.H. Lenschow, 1982: Marine stratocumulus layers. Part II: Turbulence budgets. J. Atmos. Sci., 39, 818–836.

    Article  Google Scholar 

  • Buckingham, 1914: On physically similar systems: illustrations of the use of dimensional analysis, Phys. Rev., 4, 345.

    Article  Google Scholar 

  • Busch, N.E., 1973: On the mechanics of atmospheric turbulence. Workshop on Micrometeorology. (Ed. by D.A. Haugen). Amer. Meteor. Soc., Boston. 1–65.

    Google Scholar 

  • Businger, J.A., J.C. Wyngaard, Y. Izumi and E.F. Bradley, 1971: Flux profile relationships in the atmospheric surface layer. J. Atmos. Sci., 28, 181–189.

    Article  Google Scholar 

  • Caughey, S.J. and S.G. Palmer, 1979: Some aspects of turbulent structures through the depth of the convective boundary layer. Quart. J. Roy. Meteor. Soc., 105, 811–827.

    Article  Google Scholar 

  • Caughey, S.J. and C.J. Readings, 1974: The vertical component of turbulence in convective conditions. Adv. in Geophys., 18A, 125–130.

    Google Scholar 

  • Caughey, S.J. and C.J. Readings, 1975: Turbulent fluctuations in convective conditions. Quart. J. Roy. Meteor. Soc., 101, 537–542.

    Article  Google Scholar 

  • Caughey, S.J., J.C. Wyngaard and J.C. Kaimal, 1979: Turbulence in the evolving stable boundary layer. J. Atmos. Sci., 36, 1041–1052.

    Google Scholar 

  • Chamberlain, A.C., 1983: Roughness length of sea, sand and snow. Bound. Layer Meteor., 25, 405–409.

    Article  Google Scholar 

  • Charnock, H., 1955: Wind stress on a water surface. Quart. J. Roy. Meteor. Soc., 81, 639–640.

    Article  Google Scholar 

  • Deardorff, J.W., 1972: Numerical investigation of neutral and unstable planetary boundary layers. J. Atmos. Sci., 29, 91–115.

    Article  Google Scholar 

  • Deardorff, J.W., G.E. Willis and B.H. Stockton, 1980: Laboratory studies of the entrainment zone of a convectively mixed layer. J. Fluid Mech., 100, 41–64.

    Article  Google Scholar 

  • Dyer, A.J., 1974: A review of flux-profile relations. Bound. Layer Meteor., 1, 363–372.

    Article  Google Scholar 

  • Garratt, J.R., 1977: Review of drag coefficients over oceans and continents. Mon. Wea. Rev., 105, 915–929.

    Article  Google Scholar 

  • Gossard, E.E., R.B. Chadwick, W.D. Neff, and K.P. Moran, 1982: The use of ground-based Doppler radars to measure gradients, fluxes and structure parameters in elevated layers. J. Appi. Meteor., 21, 211–226.

    Article  Google Scholar 

  • Grant, A.L.M., 1986: Observations of boundary layer structure made during the 1981 KONTUR experiment. Quart. J. Roy. Meteor. Soc., 112, 825–841.

    Article  Google Scholar 

  • Hicks, B.B., P. Hyson and C.J. Moore, 1975: A study of eddy fluxes over a forest.J. Appi. Meteor., 14, 58–66.

    Article  Google Scholar 

  • Holtslag, A.A.M. and F.T.M. Nieuwstadt, 1986: Scaling the atmospheric boundary layer. Bound.-Layer Meteor., 36, 201–209.

    Article  Google Scholar 

  • Kaimal, J.C., J.C. Wyngaard, D.A. Haugen, O.R. Coté, Y. Izumi, S.J. Caughey, and C.J. Readings, 1976: Turbulence structure in the convective boundary layer. J. Atmos. Sci., 33, 2152–2169.

    Article  Google Scholar 

  • Kaimal, J.C, J.C. Wyngaard, Y. Izumi and O.R. Coté, 1972: Spectral characteristics of surface layer turbulence. Quart. J. Roy. Meteor. Soc., 98, 563–589.

    Article  Google Scholar 

  • Kolmogorov, A.N., 1941: Energy dissipation in locally isotropic turbulence. Doklady AN SSSR, 32, No. 1, 19–21.

    Google Scholar 

  • Kondo, J. and H. Yamazawa, 1986: Aerodynamic roughness over an inhomogeneous ground surface. Bound.-Layer Meteor., 35, 331–348.

    Article  Google Scholar 

  • Lascer, A. and S.P.S. Arya, 1986: A numerical model study of the structure and similarity scaling of the nocturnal boundary layer. Bound.-Layer Meteor., 35, 369–386.

    Article  Google Scholar 

  • LeMone, M.A. and W.T. Pennell, 1976: The relationship of the trade wind cumulus distribution to subcloud layer fluxes and structure. Mon. Wea. Rev., 104, 524–539.

    Article  Google Scholar 

  • Lenschow, D.H., 1974: Model of the height variation of the turbulence kinetic energy in the unstable planetary boundary layer. J. Atmos. Sci., 31, 465–474.

    Article  Google Scholar 

  • Lenschow, D.H., J.C. Wyngaard, and W.T. Pennell, 1980: Mean field and second moment budgets in a baroclinic convective boundary layer. J. Atmos. Sci., 37, 1313–1326.

    Article  Google Scholar 

  • Lettau, H., 1969: Note on aerodynamic roughness-parameter estimation on the basis of roughness-element description. J. Appi. Meteor., 8, 828–832.

    Article  Google Scholar 

  • Mahrt, L. and J.-C. André, 1983: On the stratification of turbulent mixed layer. J. Geophys. Res., 88, 2662–2666.

    Article  Google Scholar 

  • Merry, M. and H.A. Panofsky, 1976: Statistics of vertical motion over land and water. Quart. J. Roy. Meteor. Soc., 102, 225–260.

    Article  Google Scholar 

  • Moeng, C.-H. and J.C. Wyngaard, 1984: Statistics of conservative scalars in the convective boundary layer. J. Atmos. Sci., 51, 3161–3169.

    Article  Google Scholar 

  • Monin, A.S. and A.M. Obukhov, 1954: Basic laws of turbulent mixing in the atmosphere near the ground. Tr. Akad. Nauk., SSSR Geophiz. Inst., No. 24 (151), 1963–1987.

    Google Scholar 

  • Nappo, C.J., Jr., 1977: Mesoscale flow over complex terrain during the Eastern Tennessee Trajectory Experiment (ETTEX). J. Appi. Meteor., 16, 1186–1196.

    Article  Google Scholar 

  • Nicholls, S., and C.J. Readings, 1979: Aircraft observations of the structure of the lower boundary layer over the sea. Quart. J. Roy. Meteor. Soc., 105, 785–802.

    Article  Google Scholar 

  • Nickerson, E.C. and V.E. Smiley, 1975: Surface layer and energy budget parameterizations for mesoscale models. J. Appi. Meteor., 14, 297–300.

    Article  Google Scholar 

  • Nieuwstadt, F.T.M., 1984: The turbulent structure of the stable, nocturnal boundary layer. J. Atmos. Sci., 41, 2202–2216.

    Article  Google Scholar 

  • Obukhov, A.M., 1941: Energy distribution in the spectrum of a turbulent flow. Izvestiya AN SSSR, Ser. Geogr. Geofiz., No. 4–5, 453–466.

    Google Scholar 

  • Panofsky, H.A., D. Larko, R. Lipschutz, G. Stone, E.F. Bradley, A.J. Bowen and J. Hojstrup, 1982: Spectra of velocity components over complex terrain. Quart. J. Roy. Meteor. Soc., 108, 215–230.

    Article  Google Scholar 

  • Panofsky, H.A., H. Tennekes, D.H. Lenschow, and J.C. Wyngaard, 1977: the characteristics of turbulent velocity components in the surface layer under convective conditions. Bound.-Layer Meteor., 11, 355–361.

    Article  Google Scholar 

  • Paulson, C.A., 1970: The mathematical representation of wind speed and temperature in the unstable atmospheric surface layer. J. Appi. Meteor., 9, 857–861.

    Article  Google Scholar 

  • Perry, R.H., C.H. Chilton and S.D. Kirkpatrick, (Eds.), 1963:Perry’s Chemical Engineer’s Handbook, 4th Ed.. Mraw Hill, NY. 2–87 to 2–90.

    Google Scholar 

  • Smedman-Högström, A.-S., and U. Högström, 1978: A practical method for determining wind frequency distributions for the lowest 200 m from routine meteorological data. J. Appi. Meteor., 17, 942–954.

    Article  Google Scholar 

  • Smith, S.D., 1980: Wind stress and heat flux over the ocean in gale force winds. J. Phys. Ocean., 10, 709–726.

    Article  Google Scholar 

  • Sorbjan, Z., 1986: On similarity in the atmospheric boundary layer. Bound. Layer Meteor., 34, 377–397.

    Article  Google Scholar 

  • Sorbjan, Z., 1987: An examination of local similarity theory in the stably stratified boundary layer. Bound.-Layer Meteor., 38, 63–71.

    Article  Google Scholar 

  • Stull, R.B., 1983: Integral scales for the nocturnal boundary layer. Part I: Empirical depth relationships. J. Clim. Appi. Meteor., 22, 673–686.

    Article  Google Scholar 

  • Taylor, P.A., 1987: Comments and further analysis on effective roughness lengths for use in numerical 3-D models. Bound.-Layer Meteor., 39, 403–418.

    Article  Google Scholar 

  • Tennekes, H., 1973: Similarity laws and scale relations in planetary boundary layers. Workshop on Micrometeorology (Ed., D.A. Haugen), Am. Meteor. Soc., 177–216.

    Google Scholar 

  • Tennekes, H., 1976: Fourier-transform ambiguity in turbulence dynamics. J. Atmos. Sci., 33, 1660–1663.

    Article  Google Scholar 

  • Tennekes, H., 1982: Similarity relations, scaling laws and spectral dynamics. Atmospheric Turbulence and Air Pollution Modelling. (Ed. by F.T.M. Nieuwstadt and H.van Dop). Reidel. 37–68.

    Google Scholar 

  • Thompson, R. S., 1978: Note on the aerodynamic roughness length for complex terrain, J. Appi. Meteor., 17, 1402–1403.

    Article  Google Scholar 

  • Webb, E.K., 1982: Profile relationships in the superadiabatic surface layer. Quart. J. Roy. Meteor. Soc., 108, 661–688.

    Article  Google Scholar 

  • Whitaker, S., 1968: Introduction to Fluid Mechanics. Prentice-Hall, Englewood Cliffs. 457pp.

    Google Scholar 

  • Wyngaard, J.C., 1973: On surface layer turbulence. Workshop on Micrometeorology. (Ed. D.A. Haugen). Am. Meteor. Soc. 101–148.

    Google Scholar 

  • Wyngaard, J.C. and R.A. Brost, 1984: Top-down and bottom-up diffusion of a scalar in the convective boundary layer. J. Atmos. Sci., 41, 102–112.

    Article  Google Scholar 

  • Wyngaard, J.C. and O.R. Coté, 1971: Budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer. J. Atmos. Sci., 28, 190–201.

    Article  Google Scholar 

  • Wyngaard, J.C., O.R. Coté, and Y. Izumi, 1971: Local free convection, similarity, and the budgets of shear stress and heat flux. J. Atmos. Sci., 28, 1171–1182.

    Article  Google Scholar 

  • Yamada, T., 1976: On the similarity functions A, B, and C of the planetary boundary layer. J. Atmos. Sci., 33, 781–793.

    Article  Google Scholar 

  • Zhou, M.Y., D.H. Lenschow, B.B. Stankov, J.C. Kaimal, and J.E. Gaynor, 1985: Wave and turbulence structure in a shallow baroclinic convective boundary layer and overlying inversion. J. Atmos. Sci., 42, 47–57.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Atmospheric Science Programme, Department of Geography, The University of British Columbia, Vancouver, Canada

    Roland B. Stull

Authors
  1. Roland B. Stull
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Atmospheric Science Programme, Department of Geography, The University of British Columbia, Vancouver, Canada

    Roland B. Stull

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Kluwer Academic Publishers

About this chapter

Cite this chapter

Stull, R.B. (1988). Similarity Theory. In: Stull, R.B. (eds) An Introduction to Boundary Layer Meteorology. Atmospheric Sciences Library, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3027-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-3027-8_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-277-2769-5

  • Online ISBN: 978-94-009-3027-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation