Boundary-Layer Meteorology

, Volume 32, Issue 3, pp 257–279 | Cite as

Two-dimensional stratified fluid flow over valleys: Linear theory and a laboratory investigation

  • Francesco Tampieri
  • J. C. R. Hunt
Article
Revised:

Abstract

The problem of two-dimensional, non-rotating, stably stratified fluid flow over a pair of ridges has been investigated by means of a linearized laminar boundary-layer theory and laboratory visualization experiments.

The theory allows for a description of the interaction between the main body of the flow, driven by inertial and bouyancy forces, and a thin viscous layer near the hump. In the linear frame, it leads to an evaluation of some conditions for having separation in the valley.

The experiments have been performed in a small recirculating channel. In the approach flow, there is a well-developed laminar boundary layer with a height of the same order of that of the obstacle, and constant stable stratification. The Froude number (based on obstacle height) has been varied from 0.25 to 1.8.

The two ridges are of small to moderate slope (between 1\4 and 1\2); the distance D between them varies between being slightly less than to much greater than the wavelength of internal gravity waves or lee waves.

The experimental results confirm the general prediction of linear theory that for typical valley slopes, some separated or recirculating flow generally occurs in the valley between the ridges. Both theory and the experiments suggest that over a narrow range of Froude number F L (based on the hump half length L) such that the natural lee wavelength is about equal to the valley width D, and for a particular ratio D/L of about 6, the valley is ‘ventilated’, i.e., there is no significant region of separation. This result is different if strong resonant modes are excited, associated with an elevated inversion. In general, the surface winds are expected to be greatest on the lee slope of the second hump. These results extend and confirm previous estimates for valley flows in stably stratified airstreams.

Keywords

Froude Number Laminar Boundary Layer Internal Gravity Wave Recirculate Flow Stable Stratification 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramowitz, M. and Stegun, I. A.: 1972, Handbook of Mathematical Functions. Dover Publications, New York, 1045 pp.Google Scholar
  2. Bell, R. C. and Thompson, R. O. R. Y.: 1980, ‘Valley Ventilation by Cross Winds’, J. Fluid Mech. 96, 757–767.Google Scholar
  3. Brighton, P. W. M.: 1977, Ph. D. Thesis, Cambridge University.Google Scholar
  4. Brighton, P. W. M.: 1978, ‘Strongly Stratified Flow Past Three-Dimensional Obstacles and Mesoscale Vortex Streets in the Atmosphere’, Quart. J. Roy. Meteorol. Soc. 104, 289–307.Google Scholar
  5. Egger, J.: 1981, ‘Thermally Forced Circulations in a Valley’, Geophys. Astrophys. Fluid Dyn. 17, 255–279.Google Scholar
  6. Hunt, J. C. R., Richards, K. J., and Brighton, P. W. M.: 1985, ‘atStratified Shear Flow over low Hills. II: Stratification Effects in the Outer Flow Region’, To be published in Quart. J. Roy. Meteorol. Soc. Google Scholar
  7. Hunt, J. C. R. and Simpson, J. E.: 1982, ‘Atmospheric Boundary Layers and Non-Homogeneous Terrain’, in E. J. Plate (ed.), Engineering Meteorology, Elsevier, Amsterdam, 269–318.Google Scholar
  8. Hunt, J. C. R. and Snyder, W. H.: 1980, ‘Experiments on Stably and Neutrally Stratified Flow over a Model Three-Dimensional Hill’, J. Fluid Mech. 96, 671–704.Google Scholar
  9. Lighthill, J.: 1978, Waves in Fluids, Cambridge University Press, Cambridge, 504 pp.Google Scholar
  10. Long, R. R.: 1955, ‘Some Aspects of the Flow of Stratified Fluids. III: Continuous Density Gradients’, Tellus 7, 341–357.Google Scholar
  11. Merkine, L. O.: 1975, ‘Steady Finite Amplitude Baroclinic Flow over Long Topography in a Rotating Stratified Atmosphere’, J. Atmos. Sci. 32, 1881–1893.Google Scholar
  12. Miles, J. W.: 1968, ‘Lee Waves in a Stratified Flow. I: Thin Barrier’, J. Fluid Mech. 32, 549–567.Google Scholar
  13. Odell, Kovasznay: 1971, ‘A New Type of Water-Channel with Density Stratification’, J. Fluid Mech. 50, 535–543.Google Scholar
  14. Oster, Yamamoto: 1963, ‘Density Gradient Technique’, Chem. Rev. 63, 257–268.Google Scholar
  15. Scorer, R. S.: 1972, Clouds of the World, David and Charles Ltd. 176 pp.Google Scholar
  16. Smith, F. T.: 1973, ‘Laminar Flow over a Small Hump on a Flat Plate’, J. Fluid Mech. 57, 803–824.Google Scholar
  17. Smith, R. B.: 1979, ‘The Influence of Mountains on the Atmosphere’, Adv. Geophys. 21, 87–230.Google Scholar
  18. Smith, F. T., Sykes, R. I., and Brighton, P. W. M.: 1977, ‘A Two-Dimensional Boundary Layer Encountering a Three-Dimensional Hump’, J. Fluid Mech. 83, 163–176.Google Scholar
  19. Smith, F. T., Brighton, P. W. M., Jackson, P. S., and Hunt, J. C. R.: 1981, ‘On Boundary Layer Flow Past Two-Dimensional Obstacles’, J. Fluid Mech. 113, 123–152.Google Scholar
  20. Snyder, W. H., Britter, R. E., and Hunt, J. C. R.: 1979, ‘A Fluid Modelling Study of the Flow Structure and Plume Inpingement on a Three-Dimensional Hill in a Stably Stratified Flow’, Proc. 5th Int. Conf. on Wind Energy, Fort Collins, Co., Pergamon.Google Scholar
  21. Taylor, P. A. and Gent, P. R.: 1980, ‘Modification of the Boundary Layer by Orography’, in Orographic Effects in Planetary Flows, GARP Publ. Ser. No. 23, 145–168.Google Scholar
  22. Wallace, J. M., Tibaldi, S., and Symmons, A. J.: 1983, ‘Reduction of Systematic Forecast Errors in the ECMWF Model Through the Introduction of an Envelope Topography’, Quart. J. Roy. Meteorol. Soc. 109, 683–717.Google Scholar

Copyright information

© D. Reidel Publishing Company 1985

Authors and Affiliations

  • Francesco Tampieri
    • 1
  • J. C. R. Hunt
    • 2
  1. 1.FISBAT-CNRBolognaItaly
  2. 2.Dept. of Applied Math. and Theor. PhysicsCambridgeUK

Personalised recommendations