Skip to main content
×
Home
    • Aa
    • Aa

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

  • ASLAN R. KASIMOV (a1)
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.

Copyright
References
Hide All
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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 14 *
Loading metrics...

Abstract views

Total abstract views: 67 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 18th October 2017. This data will be updated every 24 hours.