Journal of Fluid Mechanics

Shallow-water approach to the circular hydraulic jump

Tomas  Bohr a1, Peter  Dimon a1 and Vakhtang  Putkaradze a1a2
a1 The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
a2 Moscow Physico-Technical Institute, Institutsky per. 9, 141700 Moscow (Dolgoprudny), Russia

Article author query
bohr t   [Google Scholar] 
dimon p   [Google Scholar] 
putkaradze v   [Google Scholar] 


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 [similar] Q[fraction five-eighths]v[fraction three-eighths]g, 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.

(Published Online April 26 2006)
(Received March 17 1992)
(Revised February 16 1993)