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Shallow-water approach to the circular hydraulic jump

Published online by Cambridge University Press:  26 April 2006

Tomas Bohr ,
Peter Dimon  and
Vakhtang Putkaradze
Tomas Bohr
Affiliation:
The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
Peter Dimon
Affiliation:
The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
Vakhtang Putkaradze
Affiliation:
The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark Moscow Physico-Technical Institute, Institutsky per. 9, 141700 Moscow (Dolgoprudny), Russia
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Abstract

We show that the circular hydraulic jump can be qualitatively understood using simplified equations of the shallow-water type which include viscosity. We find that the outer solutions become singular at a finite radius and that this lack of asymptotic states is a general phenomenon associated with radial flow with a free surface. By connecting inner and outer solutions through a shock, we obtain a scaling relation for the radius Rj of the jump, Rj ∼ Q⅝v⅜g⅛, where Q is the volume flux, v is the kinematic viscosity and g is the gravitational acceleration. This scaling relation is valid asymptotically for large Q. We discuss the corrections appearing at smaller Q and compare with experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 254 , September 1993 , pp. 635 - 648
Copyright
© 1993 Cambridge University Press

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