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


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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C. Ellegaard , A. E. Hansen , A. Haaning , K. Hansen , A. Markussen , T. Bohr , J. L. Hansen & S. Watanabe 1998 Creating corners in kitchen sinks. Nature 392, 767768.

C. Ellegaard , A. E. Hansen , A. Haaning , K. Hansen , A. Markussen , T. Bohr , J. L. Hansen & S. Watanabe 1999 Cover illustration: Polygonal hydraulic jumps. Nonlinearity 12, 17.

F. R. Gilmore , M. S. Plesset & H. E. Crossley Jr 1950 The analogy between the hydraulic jumps in liquids and shock waves in gases. J. Appl. Phys. 21, 243249.

Lord Rayleigh 1914 On the theory of long waves and bores. Proc. R. Soc. Lond. A 90, 324.

I. Tani 1949 Water jump in the boundary layer. J. Phys. Soc. Japan 4, 212215.

F. White 2006 Fluid Mechanics. McGraw-Hill.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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