Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-08T16:20:36.971Z Has data issue: false hasContentIssue false
  • English
  • Français

Experiments on stably and neutrally stratified flow over a model three-dimensional hill

Published online by Cambridge University Press:  19 April 2006

J. C. R. Hunt  and
W. H. Snyder
J. C. R. Hunt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
W. H. Snyder
Affiliation:
Meteorology and Assessment Division, Environmental Sciences Research Laboratory, U.S. Environmental Protection Agency, Research Triangle Park, NC 27711
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper describes the flow structure observed over a bell-shaped hill with height h (the profile of which is the reciprocal of a fourth-order polynomial) when it was placed first in a large towing tank containing stratified saline solutions with uniform stable density gradients and second in an unstratified wind tunnel. (A similarly shaped model hill was also studied in a small towing tank.) Observations were made at values of the Froude number F (≃ U/Nh) in the range 0·1 to 1·7 and at F = ∞, where U is the towing speed and N is the Brunt-Väisälä frequency, and at values of the Reynolds number from 400 to 275000. For F ≲ 0·4, the observations verify Drazin's (1961) theory for low-Froude-number flow over three-dimensional obstacles and establish limits of applicability. For Froude numbers of the order of unity, it is found that a classification of the lee-wave patterns and separated-flow regions observed in two-dimensional flows also appears to apply to three-dimensional hills.

Flow-visualization techniques were used extensively in obtaining both qualitative and quantitative information on the flow structure around the hill. Representative photographs of dye tracers, potassium permanganate dye streaks, shadowgraphs, surface dye smears, and hydrogen-bubble patterns are included here. While emphasis is centred on obtaining a basic understanding of the flow around three-dimensional hills, the results are applicable to the estimation of air pollutant dispersion around hills.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 96 , Issue 4 , 27 February 1980 , pp. 671 - 704
Copyright
Copyright © 1980 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brighton, P. W. M. 1977 Boundary layer and stratified flow over obstacles. Ph.D. dissertation, University of Cambridge, England.Google Scholar
Brighton, P. W. M. 1978 Strongly stratified flow past three-dimensional obstacles. Quart. J. Boy. Met. Soc. 104, 289–307.CrossRefGoogle Scholar
Burt, E. W. & Slater, H. H. 1977 Evaluation of the valley model. AMS-APCA Joint Conf. on Appl. of Air Poll. Meteorology, Salt Lake City, Utah.Google Scholar
Clutter, D. W. & Smith, A. M. O. 1961 Flow visualization by electrolysis of water. Aerospace Engng 20, 24–27, 74–76.Google Scholar
Connell, J. R. 1976 Wind and turbulence in the planetary boundary layer around an isolated 3-D mountain as measured by a research aircraft. Int. Conf. on Mountain Met. and Biomet., Interlaken, Switz.Google Scholar
Crapper, G. D. 1959 A three-dimensional solution for waves in the lee of mountains. J. Fluid Mech. 6, 51–76.CrossRefGoogle Scholar
Crapper, G. D. 1962 Waves in the lee of a mountain with elliptical contours. Phil. Trans. Boy. Soc. A 254, 601–623.Google Scholar
Davis, R. E. 1969 The two-dimensional flow of a fluid of variable density over an obstacle. J. Fluid Mech. 36, 127–143.CrossRefGoogle Scholar
Drazin, P. G. 1961 On the steady flow of a fluid of variable density past an obstacle. Tellus 8, 239–251.Google Scholar
Hunt, J. C. R., Abell, C. J., Peterka, J. A. & Woo, H. 1978 Kinematical studies of the flows around free or surface mounted obstacles; applying topology to flow visualization. J. Fluid Mech. 86, 179–200; corrigendum J. Fluid Mech. 95, (1979), 796.CrossRefGoogle Scholar
Hunt, J. C. R. & Mulhearn, P. J. 1973 Turbulent dispersion from sources near two-dimensional obstacles. J. Fluid Mech. 61, 254–74.CrossRefGoogle Scholar
Hunt, J. C. R., Puttock, J. S. & Snyder, W. H. 1979 Turbulent diffusion from a point source in stratified and neutral flows around a three-dimensional hill. Part I. Diffusion equation analysis. Atmos. Environ. 13, 1227–1239.CrossRefGoogle Scholar
Hunt, J. C. R., Snydek, W. H. & Lawson, R. K. 1978 Flow structure and turbulent diffusion around a three-dimensional hill: fluid modelling study on effects of stratification. Part I: flow structure. U.S. EPA Env. Monitoring Ser. Rep. EPA-600/4-78-041. Res. Tri. Pk., N.C.Google Scholar
Huppert, H. K. 1968 Appendix to paper by J. W. Miles. J. Fluid Mech. 33, 803–814.Google Scholar
Kitabayashi, K., Orgill, M. M. & Cermak, J. E. 1971 Laboratory simulation of airflow and atmospheric transport-dispersion over Elk Mountain, Wyoming. Fluid Dyn. and Diff. Lab. Rep. no. CER 70–71 KK-MMO-JEC-65, Colorado State University, Fort Collins.Google Scholar
Larrson, L. 1954 Observation of lee waves in the Jamt Land Mountains. Sweden. Tellus 6, 124–138.Google Scholar
Liu, H. T. & Lin, J. T. 1975 Laboratory simulation of plume dispersion from lead smelter in Glover, Missouri, in neutral and stable atmosphere. U.S. EPA Res. no. EPA-450/3-75-066, Res. Tri. Pk., NC.Google Scholar
Liu, H. T. & Lin, J. T. 1976 Plume dispersion in stably stratified flows over complex terrain; Phase 2. U.S. EPA Env. Monitoring Ser. Rep. no. EPA-600/4-76-022. Res. Tri. Pk., NC.Google Scholar
Long, R. K. 1955 Some aspects of the flow of stratified flows. III. Continuous density gradients. Tellus 7, 342–357.CrossRefGoogle Scholar
Long, R. K. 1972 Finite amplitude disturbances in the flow of inviscid rotating and stratified fluids over obstacles. Ann. Rev. Fluid Mech. 4, 69–92.CrossRefGoogle Scholar
Marwitz, J. D., Veal, D. L., Auer, A. H. & Middleton, J. R. 1969 Prediction and verification of the air flow over a three-dimensional mountain. Natural Resources Res. Inst. Tech. Rep. no. 60. University of Wyo.Google Scholar
Milne-Thompson, L. M. 1960 Theoretical Hydrodynamics, 4th ed. Macmillan.Google Scholar
Oster, G. & Yamamoto, M. 1963 Density gradient techniques. Chem. Rev. 63, 257–268.CrossRefGoogle Scholar
Pad, Y. H., Lin, J. T., Carlsen, R. L. & Smithmeyer, L. P. C. 1971 The design and construction of a stratified towing tank with an oil-lubricated carriage. Flow Res. Rep. no. 4, Flow Res., Kent, Wash.Google Scholar
Queney, P., Corby, G. A., Gerbier, N., Koschmieder, H. & Zierep, J. 1960 The airflow over mountains. World Met. Org. Tech. Note no. 34. Geneva, Switz.Google Scholar
Riley, J. J., Liu, H. T. & Geller, E. W. 1976 A numerical and experimental study of stably stratified flow around complex terrain. U.S. EPA Env. Monitoring Ser. Rep. no. EPA-600/4-76-021. Res. Tri. Pk., NC.Google Scholar
Schraub, F. A., Kline, S. J., Henry, J., Runstadler, P. W. & Littel, A. 1965 Basic Engng 87, 429–444.CrossRefGoogle Scholar
Scorer, R. S. 1954 Theory of airflow over mountains, III: Air stream characteristics. Quart. J. Roy. Met. Sac. 80, 417–428.CrossRefGoogle Scholar
Scorer, R. S. 1968 Air Pollution. Pergamon.Google ScholarPubMed
Snyder, W. H., 1979 The EPA meteorological wind tunnel; its design, construction and operating characteristics. U.S. EPA Env. Mon. Ser. Rep. EPA 600/4-79-051, RG. Tri. Pk, N.C.Google Scholar
Snyder, W. H., Britter, R. E. & Hunt, J. C. R. 1979 A fluid modelling study of the flow structure and plume impingement on a three dimensional hill in stably stratified flow. Proc. 5th Int. Conf. on Wind Engng, Fort Collins. Pergamon.Google Scholar
Sykes, R. I. 1978 Stratification effects in boundary layer flow over hills. Proc. Roy. Soc. A 361, 225.Google Scholar
Thompson, R. S. & Snyder, W. H. 1976 EPA fluid modeling facility. Proc. Conf. on Envir. Modeling and Simulation, Cincinnati, Ohio. EPA-600/9-76-016. U.S. Environmental Protection Agency, Washington, D.C.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.CrossRefGoogle Scholar