Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T22:36:48.265Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling rollers for shallow water flows

Published online by Cambridge University Press:  01 July 2013

O. Thual
O. Thual*
Affiliation:
Université de Toulouse; INPT, UPS; IMFT, Allée Camille Soula, F-31400 Toulouse, France CNRS; IMFT; F-31400 Toulouse, France
*
†Email address for correspondence: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Hydraulic jumps, roll waves or bores in open channel flows are often treated as singularities by hydraulicians while slowly varying shallow water flows are described by continuous solutions of the Saint-Venant equations. Richard & Gavrilyuk (J. Fluid Mech., vol. 725, 2013, pp. 492–521) have enriched this model by introducing an equation for roller vorticity in a very elegant manner. This new model matches several experimental results that have resisted theoretical approaches for decades. This is the case of the roller of a stationary hydraulic jump as well as the oscillatory instability that the jump encounters when the Froude number is increased. The universality of their approach as well as its convincing comparisons with experimental results open the way for significant progress in the modelling of open channel flows.

JFM classification

Waves/Free-surface Flows: Channel flow Geophysical and Geological Flows: Shallow water flows Turbulent Flows: Shear layer turbulence
Type
Focus on Fluids
Information
Journal of Fluid Mechanics , Volume 728 , 10 August 2013 , pp. 1 - 4
Copyright
©2013 Cambridge University Press 

References

Boutounet, M., Chupin, L., Noble, P. & Vila, J.-P. 2008 Shallow water viscous flows for arbitrary topography. Commun. Math. Sci. 1, 29–55.Google Scholar
Brock, R. R. 1969 Development of roll wave trains in open channels. J. Hydraul. Div. 95, 1401–1427.CrossRefGoogle Scholar
Brock, R. R. 1970 Periodic permanent roll waves. J. Hydraul. Div. 96, 2565–2580.Google Scholar
Chanson, H. 2011 Hydraulic jumps: turbulence and air bubble entrainment. La Houille Blanche 3, 5–16.CrossRefGoogle Scholar
Chow, V. T. 1959 Open-channel Hydraulics. McGraw-Hill.Google Scholar
Hager, W. H., Bremen, R. & Kawagoshi, N. 1990 Classical hydraulic jump: length of roller. J. Hydraul. Res. 28 (5), 591–608.CrossRefGoogle Scholar
Mok, K. M. 2004 Relation of surface roller eddy formation and surface fluctuation in hydraulic jumps. J. Hydraul. Res. 42, 207–212.CrossRefGoogle Scholar
Richard, G. L. & Gavrilyuk, S. L. 2012 A new model of roll waves: comparison with Brock’s experiments. J. Fluid Mech. 698, 374–405.Google Scholar
Richard, G. L. & Gavrilyuk, S. L. 2013 The classical hydraulic jump in a model of shear shallow water flows. J. Fluid Mech. 725, 492–521.CrossRefGoogle Scholar
Saint-Venant, B. 1871 Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et à l’introduction des marées dans leur lit. C. R. Séan. Acad. Sci., Paris 73, 147–154 and 237–240.Google Scholar
Svendsen, I. A., Veeramony, J., Bakunin, J. & Kirby, J. T. 2000 The flow in weak turbulent hydraulic jumps. J. Fluid Mech. 418, 25–57.CrossRefGoogle Scholar