Skip to main content
SpringerLink
Log in

A simple model for the adjustment of velocity spectra in unstable conditions downstream of an abrupt change in roughness and heat flux

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

Abstract

A simple model for the equilibrium spectra of velocity fluctuations in the unstable surface layer is developed. All three component spectra are written as a sum of two spectra For the horizontal spectra, the two parts scale with % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaacIcacaWGUb% GaamOEamaaBaaaleaacaWGPbaabeaakiaac+cacaWG1bGaaiilaiaa% dQhadaWgaaWcbaGaamyAaaqabaGccaGGVaGaamitaiaacMcaaaa!4232!\[(nz_i /u,z_i /L)\]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gacaWG6b% Gaai4laiaadwhaaaa!3B5E!\[nz/u\], respectively; the vertical spectrum can be written entirely as a function of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gacaWG6b% Gaai4laiaadwhaaaa!3B5E!\[nz/u\] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadQhacaGGVa% Gaamitaaaa!3A42!\[z/L\].

The equilibrium spectra are utilized as part of a model describing the development of velocity spectra downwind of a change in surface roughness and heat flux.

Results are shown for the streamwise component and compared with hotwire measurements from the RISØ 78 experiment. The model shows excellent agreement with the measurements.

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

  • Caughey, S. J. and Wyngaard, J. C.: 1979, ‘The Turbulence Kinetic Energy Budget in Convective Conditions’, Quart. J. Roy. Meteorol. Soc. 105, 231–239.

    Google Scholar 

  • Elliott, W. P.: 1958, ‘The Growth of the Atmospheric Internal Boundary-Layer’, Trans. Amer. Geophys. Union 39, 1048–1054.

    Google Scholar 

  • Jensen, N. O.: 1978, ‘Change of Surface Roughness and the Planetary Boundary-Layer’, Quart. J. Roy. Meteorol. Soc. 104, 351–356.

    Google Scholar 

  • Kaimal, J. C., Wyngaard, J. C., Izumi, Y., and Coté, O. R.: 1972, ‘Spectral Characteristics of Surface Layer Turbulence’, Quart. J. Roy. Meteorol. Soc. 98, 653–689.

    Google Scholar 

  • Kaimal, J. C., Wyngaard, J. C., Haugen, D. A., Coté, O. R., Izumi, Y., Caughey, S. J., and Readings, C. J.: 1976, ‘Turbulence Structure in the Convective Boundary-Layer’, J. Atmos. Sci. 33, 2152–2169.

    Google Scholar 

  • Kaimal, J. C.: 1978, ‘Horizontal Velocity Spectra in an Unstable Surface Layer’, J. Atmos. Sci. 35, 18–23.

    Google Scholar 

  • Panofsky, H. A., Larko, D., Lipshutz, R., Stone, G., Bradley, E. F., Bowen, A. J., and Højstrup, J.: 1981

  • Panofsky, H. A., Tennekes, H., Lenschow, D. H., and Wyngaard, J. C.: 1977, ‘The Characteristics of Turbulent Velocity Components in the Surface Layer under Convective Conditions’, Boundary-Layer Meteorol. 11, 355–361.

    Google Scholar 

  • Panofsky, H. A.: 1973, ‘Tower Micrometeorology’, In: Workshop of Micrometeorology (ed.), D. A. Haugen.

  • Panofsky, H. A. and Townsend, A. A.: 1964, ‘Change of the Terrain Roughness and the Wind Profile’, Quart. J. Roy. Meteorol. Soc. 90, 147–155.

    Google Scholar 

  • Paulson, C. A.: 1970, ‘The Mathematical Representation of Wind Speed and Temperature Profiles in the Unstable Surface Layer’, J. Appl. Meteorol. 9, 857–861.

    Google Scholar 

  • Peterson, E. W., Taylor, P. A., Højstrup, J., Jensen, N. O., Kristensen, L., and Petersen, E. L.: 1980, ‘RISØ 78: Further Investigations into the Effects of Local Terrain Irregularities on Tower-Measured Wind Profiles’, Boundary-Layer Meteorol. 19, 303–313.

    Google Scholar 

  • Peterson, E. W., Jensen, N. O., and Højstrup, J.: 1979, ‘Observations of Downwind Development of Wind Speed and Variance Profiles at Bognaes and Comparison with Theory’, Quart. J. Roy. Meteorol. Soc. 105, 527–529.

    Google Scholar 

  • Peterson, E. W.: 1969, ‘Modification of Mean Flow and Turbulent Energy by a Change in Surface Roughness under Conditions of Neutral Stability’, Quart J. Roy. Meteorol. Soc. 95, 561–575.

    Google Scholar 

  • Rao, K. S.: 1975, ‘Effect of Thermal Stratification on the Growth of the Internal Boundary-Layer’, Boundary-Layer Meteorol. 8, 227–234.

    Google Scholar 

  • Rao, K. S., Wyngaard, J. C., and Coté, O. R.: 1974, ‘The Structure of the Two-Dimensional Internal Boundary-Layer over a Sudden Change in Surface Roughness’, J. Atmos. Sci. 31, 738–746.

    Google Scholar 

  • Shir, C. C.: 1972, ‘A Numerical Computation of Air Flow over a Sudden Change of Surface Roughness’, J. Atmos. Sci. 29, 304–310.

    Google Scholar 

  • Shirer, N. H. and Rossi, R.: 1981, Private communication.

  • Taylor, P. A.: 1969, ‘On Wind and Shear Stress Profiles above a Change in Surface Roughness’, Quart. J. Roy. Meteorol. Soc. 95, 77–91.

    Google Scholar 

  • Taylor, P. A.: 1970, ‘A Model of Airflow above Changes in Surface Heat, Flux Temperature and Roughness for Neutral and Unstable Conditions’, Boundary-Layer Meteorol. 1, 18–39.

    Google Scholar 

  • Tennekes, H. and Lumley, J. L.: 1972, ‘A First Course in Turbulence’, MIT Press.

  • Thomson, D. W.: 1979, ‘RISØ 78: Mean Profile and Turbulence Measurements at a Shoreline Escarpment’, RISØ Report No. 410, RISØ National Laboratory, DK4000, Roskilde, Denmark.

    Google Scholar 

  • Townsend, A. A.: 1966, ‘The Flow in a Turbulence Boundary-Layer after a Change in Surface Roughness’, J. Fluid Mech. 26, 255–266.

    Google Scholar 

  • Townsend, A. A.: 1966, ‘The Flow in a Turbulence Boundary-Layer after a Change in Surface Roughness’, J. Fluid Mech. 26, 255–266.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Meteorology, Naval Postgraduate School, Monterey, California, USA

    Jørgen Højstrup

  2. Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania, USA

    Jørgen Højstrup

Authors
  1. Jørgen Højstrup
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

on leave of absence from RISØ National Laboratory Roskilde, Denmark.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Højstrup, J. A simple model for the adjustment of velocity spectra in unstable conditions downstream of an abrupt change in roughness and heat flux. Boundary-Layer Meteorol 21, 341–356 (1981). https://doi.org/10.1007/BF00119278

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00119278

Keywords

Search

Navigation