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Internal hydraulic jumps in two-layer systems

Published online by Cambridge University Press:  07 December 2015

Peter G. Baines
Peter G. Baines*
Affiliation:
Department of Infrastructure Engineering, University of Melbourne, Melbourne 3010, Australia
*
†Email address for correspondence: [email protected]
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Abstract

This paper describes a new model of internal hydraulic jumps in two-layer systems that places no restrictions (such as the Boussinesq approximation) on the densities of the two fluids. The model is based on that of Borden and Meiburg (J. Fluid Mech., vol. 276, 2013, R1) for Boussinesq jumps, and has the appropriate behaviour in various limits (single-layer, small amplitude, Boussinesq, infinite depth). The energy flux loss in each layer across the jump is positive for all realistic jumps, reaching a maximum for the jump with maximum speed. Larger-amplitude jumps are possible, with decreasing energy loss, down to the ‘conjugate state’ of zero energy loss. However, it is argued that such states may be difficult to realise in practice, and if formed, will tend to the jump with maximum speed. The energy loss is mostly in the contracting layer unless the density there is small. The two-layer model is extended to incorporate mixing between the layers within the jump, with mixing based on the Richardson number.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Waves/Free-surface Flows: Hydraulics Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 787 , 25 January 2016 , pp. 1 - 15
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Copyright
© 2015 Cambridge University Press 

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