Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-01-09T22:18:11.408Z Has data issue: false hasContentIssue false
  • English
  • Français

The structure of strongly stratified flow over hills: dividing-streamline concept

Published online by Cambridge University Press:  20 April 2006

William H. Snyder ,
Roger S. Thompson ,
Robert E. Eskridge ,
Robert E. Lawson ,
Ian P. Castro ,
J. T. Lee ,
Julian C. R. Hunt  and
Yasushi Ogawa
William H. Snyder
Affiliation:
Meteorology and Assessment Division, Environmental Sciences Research Laboratory, U.S. Environmental Protection Agency, Research Triangle Park, NC 27711 USA
Roger S. Thompson
Affiliation:
Meteorology and Assessment Division, Environmental Sciences Research Laboratory, U.S. Environmental Protection Agency, Research Triangle Park, NC 27711 USA
Robert E. Eskridge
Affiliation:
Meteorology and Assessment Division, Environmental Sciences Research Laboratory, U.S. Environmental Protection Agency, Research Triangle Park, NC 27711 USA
Robert E. Lawson
Affiliation:
Meteorology and Assessment Division, Environmental Sciences Research Laboratory, U.S. Environmental Protection Agency, Research Triangle Park, NC 27711 USA
Ian P. Castro
Affiliation:
Department of Mechanical Engineering, University of Surrey, Guildford, Surrey, England GU2 5XH
J. T. Lee
Affiliation:
Los Alamos National Laboratory, Los Alamos, NM 87545 USA
Julian C. R. Hunt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, England CB3 9EW
Yasushi Ogawa
Affiliation:
Meteorology and Assessment Division, Environmental Sciences Research Laboratory, U.S. Environmental Protection Agency, Research Triangle Park, NC 27711 USA
Get access Rights & Permissions [Opens in a new window]

Abstract

In stably stratified flow over a three-dimensional hill, we can define a dividing streamline that separates those streamlines that pass around the hill from those that pass over the hill. The height Hs of this dividing streamline can be estimated by Sheppard's simple energy argument; fluid parcels originating far upstream of a hill at an elevation above Hs have sufficient kinetic energy to rise over the top, whereas those below Hs must pass around the sides. This prediction provides the basis for analysing an extensive range of laboratory observations and measurements of stably stratified flow over a variety of shapes and orientations of hills and with different upwind density and velocity profiles. For symmetric hills and small upwind shear, Sheppard's expression provides a good estimate for Hs. For highly asymmetric flow and/or in the presence of strong upwind shear, the expression provides a lower limit for Hs. As the hills become more nearly two-dimensional, these experiments become less well defined because steady-state conditions take progressively longer to be established. The results of new studies are presented here of the development of the unsteady flow upwind of two-dimensional hills in a finite-length towing tank. These measurements suggest that a very long tank would be required for steady-state conditions to be established upstream of long ridges with or without small gaps and cast doubt upon the validity of previous laboratory studies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 152 , March 1985 , pp. 249 - 288
Copyright
© 1985 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

Baines, P. G. 1977 Upstream influence and Long's model in stratified flows. J. Fluid Mech. 82, 147–59.Google Scholar
Baines, P. G. 1979a Observations of stratified flow past three-dimensional barriers. J. Geophys. Res. 84, 7834–8.Google Scholar
Baines, P. G. 1979b Observations of stratified flow over two-dimensional obstacles, in fluid of finite depth. Tellus 31, 351–71.Google Scholar
Brighton, P. W. M. 1978 Strongly stratified flow past three-dimensional obstacles. Q. J. R. Met. Soc. 104, 289–307.Google Scholar
Castro, I. P., Snyder, W. H. & Marsh, G. L. 1983 Stratified flow over three-dimensional ridges. J. Fluid Mech. 135, 261–82.Google Scholar
Drazin, P. G. 1961 On the steady flow of a fluid of variable density past an obstacle. Tellus 13, 239–51.Google Scholar
Foster, M. R. & Saffman, P. G. 1970 The drag of a body moving transversely in a confined stratified fluid. J. Fluid Mech. 43, 407–18.Google Scholar
Holzworth, G. C. 1980 The EPA program for dispersion model development for sources in complex terrain. Presented at 2nd Jt Conf. on Appl. of Air Poll. Meteorol., March 24–27. New Orleans, LA, 4p.
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, 1227–39.Google Scholar
Hunt, J. C. R. & Snyder, W. H. 1980 Experiments on stably and neutraly stratified flow over a model three-dimensional hill. J. Fluid Mech. 96, 671–704.Google Scholar
Hunt, J. C. R., Snyder, W. H. & Lawson, R. E. 1978 Flow structure and turbulent diffusion around a three-dimensional hill: fluid modeling study on effects of stratification. Part I. Flow structure. Environ. Prot. Agcy Rep. EPA-600/4-78–041, Res. Tri. Pk., NC.Google Scholar
Kitabayashi, K. 1977 Wind tunnel and field studies of stagnant flow upstream of a ridge. J. Met. Soc. Japan 55, 193–204.Google Scholar
Kitabayashi, K. 1981 On the stagnant zone upstream of an obstacle within a stably stratified flow in the atmosphere. J. Met. Soc. Japan 59, 373–86.Google Scholar
Lamb, V. R. & Britter, R. E. 1984 Shallow water flow over an isolated obstacle. J. Fluid Mech. 147, 291–313.Google Scholar
Lavery, T. F., Bass, A., Greene, B., Hatcher, R. V., Venkatram, A. & Egan, B. A. 1982a The Cinder Cone Butte dispersion experiment. In Proc. 3rd Jt. Conf. on Appl. of Air Poll. Meteorol, Jan 12–15, San Antonio, TX, Paper no. 11.3, Amer. Meteorol., Soc., Boston. MA.
Lavery, T. F., Bass, A., Strimaitis, D. G., Venkatram, A., Greene, B. R., Drivas, P. J. & Egan, B. A. 1982b EPA complex terrain modelling program: first milestone report 1981. Environ. Prot. Agcy Rep. EPA-600/3-82–036, Res. Tri. Pk., NC.Google Scholar
Long, R. R. 1953 Some aspects of the flow of stratified fluids: I. A theoretical investigation. Tellus 5, 42–57.Google Scholar
Long, R. R. 1954 Some aspects of the flow of stratified fluids: II. Experiments with a two-fluid system. Tellus 6, 97–115.Google Scholar
Long, R. R. 1955 Some aspects of the flow of stratified fluids: III. Continuous density gradients. Tellus 7, 341–57.Google Scholar
Long, R. R. 1972 Finite amplitude disturbances in the flow of in viscid rotating and stratified fluids over obstacles. Ann. Rev. Fluid Mech. 4, 69–92.Google Scholar
Mcintyre, M. E. 1972 On Long's hypothesis of no upstream influence in uniformly stratified or rotating fluid. J. Fluid Mech. 52, 209–243.Google Scholar
Ogawa, Y., Diosey, P. G., Uehara, K. & Ueda, H. 1981 A wind tunnel for studying the effects of thermal stratification in the atmosphere. Atmos. Environ. 15, 807–21.Google Scholar
Riley, J. J., Liu, H. T. & Geller, E. W. 1976 A numerical and experimental study of stably stratified flow around complex terrain. Environ. Prot. Agcy Rep. EPA-600/4-76–021, Res. Tri. Pk., NC.Google Scholar
Rowe, R. D., Benjamin, S. F., Chung, K. P., Havlena, J. J. & Lee, C. Z. 1982 Field studies of stable air flow over and around a ridge. Atmos. Environ. 16, 643–53.Google Scholar
Sheppard, P. A. 1956 Airflow over mountains. Q. J. R. Met. Soc., 82, 528–9.Google Scholar
Snyder, W. H., Britter, R. E. & Hunt, J. C. R. 1980 A fluid modeling study of the flow structure and plume impingement on a three-dimensional hill in stably stratified flow. In Proc. 5th Intl Conf. on Wind Engng (Ed. J. E. Cermak), pp. 319–29, Pergamon.
Snyder, W. H. & Hunt, J. C. R. 1984 Turbulent diffusion from a point source in stratified and neutral flows around a three-dimensional hill. Part II: Laboratory measurements of surface concentrations. Atmos. Environ. 18, 1969–2002.Google Scholar
Spangler, T. C. & Taylor, G. H. 1982 Flow simulation techniques used in the small hill impaction study. In Proc. 3rd Jt Conf. on Appl. of Air Poll. Meteorol., Jan. 12–15. San Antonio, TX, Paper no. 11.4, Amer. Meteorol. Soc., Boston, MA.
Thompson, R. S. & Snyder, W. H. 1976 EPA fluid modeling facility. In Proc. Conf. on Modeling and Simulation. Envir. Prot. Agcy Rep., EPA-600/9-76–016, Wash. D.C., July.
Turner, J. S. 1979 Buoyancy Effects in Fluids. Cambridge University Press. 368 p.
Wei, S. N., Kao, T. W. & Pao, H. P. 1975 Experimental study of upstream influence in the two-dimensional flow of a stratified fluid over an obstacle. Geophys. Fluid Dyn. 6. 315–36.Google Scholar
Weil, J. C., Traugott, S. C. & Wong, D. K. 1981 Stack plume interaction and flow characteristics for a notched ridge, Rep. PPRP-61, Maryland Power Plant Siting Program, Martin Marietta Corp., Baltimore, MD, 92p.