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The classical hydraulic jump in a model of shear shallow-water flows

Published online by Cambridge University Press:  16 May 2013

G. L. Richard  and
S. L. Gavrilyuk
G. L. Richard
Affiliation:
Aix-Marseille Université, UMR CNRS 7343, IUSTI, 5 rue E. Fermi, 13453 Marseille CEDEX 13, France
S. L. Gavrilyuk*
Affiliation:
Aix-Marseille Université, UMR CNRS 7343, IUSTI, 5 rue E. Fermi, 13453 Marseille CEDEX 13, France
*
†Email address for correspondence: [email protected]
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Abstract

A conservative hyperbolic two-parameter model of shear shallow-water flows is used to study the classical turbulent hydraulic jump. The parameters of the model, which are the wall enstrophy and the roller dissipation coefficient, are determined from measurements of the roller length and the deviation from the Bélanger equation of the sequent depth ratio (experimental data by Hager & Bremen, J. Hydraul. Res., vol. 27, 1989, pp. 565–585; and Hager, Bremen & Kawagoshi, J. Hydraul. Res., vol. 28, 1990, pp. 591–608). Stationary solutions to the model describe with a good accuracy the free-surface profile of the hydraulic jump. The model is also capable of predicting the oscillations of the jump toe. We show that if the upstream Froude number is larger than ${\sim }1. 5$, the jump toe oscillates with a particular frequency, while for the Froude number smaller than 1.5 the solution becomes stationary. In particular, we show that for a given flow discharge, the oscillation frequency is a decreasing function of the Froude number.

JFM classification

Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Shear waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 725 , 25 June 2013 , pp. 492 - 521
Copyright
©2013 Cambridge University Press 

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