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On hydraulic control in a stratified fluid

Published online by Cambridge University Press:  26 April 2006

Peter D. Killworth
Peter D. Killworth
Affiliation:
Institute of Oceanographic Sciences, Deacon Laboratory, Wormley, Godalming, Surrey, GU8 5UB Present address: Robert Hooke Institute, The Observatory, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU.
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Abstract

The conditions for hydraulic control to occur in a continuously stratified fluid are discussed, using density as a vertical coordinate in place of height. A suitable definition of Froude number, which varies with depth, is given. Three conditions for control emerge. One is that the flow be everywhere well-behaved; another is that control occurs when the local long-wave speed vanishes. These are shown to be equivalent. The location of the control is determined indirectly by the Froude number, which occurs as the coefficient in an ordinary differential equation; the Froude number must be somewhere less than a critical value for control to occur. The third condition requires the coalescence of two different solutions for the same boundary conditions at the point of control. It is shown that this requirement is non-trivial: examples given include a simple control by topography, a virtual control, and a control by a constriction. A direct connection with layered theory is produced. Brief discussions of bidirectional flow (where the isopycnal surface of zero velocity must be flat) and weak shocks are given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 237 , April 1992 , pp. 605 - 626
Copyright
© 1992 Cambridge University Press

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