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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
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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

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