Journal
JOURNAL OF FLUID MECHANICS
Volume 601, Issue -, Pages 189-198Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0022112008000773
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We propose a theory of a steady circular hydraulic jump based on the shallow-water model obtained from the depth-averaged Navier-Stokes equations. The flow structure both upstream and downstream of the jump is determined by considering the flow over a plate of finite radius. The radius of the jump is found using the far-field conditions together with the jump conditions that include the effects of surface tension. We show that a steady circular hydraulic jump does not exist if the surface tension is above a certain critical value. The solution of the problem provides a basis for the hydrodynamic stability analysis of the hydraulic jump. An analogy between the hydraulic jump and a detonation wave is pointed out.
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