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A stationary circular hydraulic jump, the limits of its existence and its gasdynamic analogue

Published online by Cambridge University Press:  25 April 2008

ASLAN R. KASIMOV
ASLAN R. KASIMOV*
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
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Abstract

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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 601 , 25 April 2008 , pp. 189 - 198
Copyright
Copyright © Cambridge University Press 2008

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References

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