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Hydraulic jumps in an incompressible stratified fluid

Published online by Cambridge University Press:  29 March 2006

C. H. Su
C. H. Su
Affiliation:
Advanced Study Program, National Center for Atmospheric Research, Boulder, Colorado 80303 Permanent address: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912.
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Abstract

A multi-layer model is used to describe a ‘two-dimensional’ continuously stratified fluid. We use a momentum theorem in each layer to derive an ordinary differential equation describing the vertical structure behind a jump. This equation is compared with the corresponding equation for continuous flow. As one would expect from the classical one-layer theory, they are identical up to second order for weak disturbances. The energy change across a jump is also derived. By requiring that energy be lost through a jump, we calculate when a weak jump is possible in general. Algorithms for computing jumps of arbitrary strength are given. To ensure that the flow after the jump is stable and also for a numerical reason to be stated in § 8, we require that the Richardson number after the jump be equal to or greater than S¼S. Numerical examples are given to show the range of parameters within which jumps are possible; the velocity profiles related to different kinds of jumps also appear. Since hydraulic jumps in a continuously stratified fluid have not yet been observed in any laboratory, it should be of interest to verify these calculations experimentally.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 73 , Issue 1 , 13 January 1976 , pp. 33 - 47
Copyright
© 1976 Cambridge University Press

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