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A free-streamline solution for stratified flow into a line sink

Published online by Cambridge University Press:  28 March 2006

Timothy W. Kao
Timothy W. Kao
Affiliation:
Department of Engineering Mechanics, The University of Michigan
Now at the W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, California.
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Abstract

An analysis is made of the two-dimensional flow under gravity of an inviscid non-diffusive stratified fluid into a line sink, involving a velocity discontinuity in the flow field. The fluid above the discontinuity is stagnant and hence is not drawn into the sink. At sufficiently low values of the modified Froude number, this is the only physically possible mode of flow, and is the cause of flow separation in many industrial and natural processes. A proper mathematical solution for flows with a stagnant zone has so far been lacking. This paper presents such a solution, after posing the problem as one involving a free-streamline, which is the line of velocity discontinuity. The solution to be given here is obtained by an inverse method. It is also found herein that the modified Froude number has a value of 0·345 for all separated flows of the kind in question.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 21 , Issue 3 , March 1965 , pp. 535 - 543
Copyright
© 1965 Cambridge University Press

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References

Debler, W. R. 1959 Proc. Amer. Soc. Civil Engrs, 85, No. EM 3, 51.
Kao, T. W. 1963 Phenomenon of Blocking in Stratified Flow. Ph.D. Thesis, University of Michigan, Ann Arbor, Michigan.
Long, R. R. 1953 Tellus, 5, 42.
Yih, C. S. 1958 Proc. Third U. S. Nat. Congress of Appl. Mech., pp. 857–861.
Yih, C. S. 1964 Dynamics of Non-Homogeneous Fluids. New York: McMillan Company (to be published).