Skip to main content
×
Home
    • Aa
    • Aa

Steady free surface flows induced by a submerged ring source or sink

  • T. E. Stokes (a1), G. C. Hocking (a2) and L. K. Forbes (a3)
Abstract
Abstract

The steady axisymmetric flow induced by a ring sink (or source) submerged in an unbounded inviscid fluid is computed and the resulting deformation of the free surface is obtained. Solutions are obtained analytically in the limit of small Froude number (and hence small surface deformation) and numerically for the full nonlinear problem. The small Froude number solutions are found to have the property that if the non-dimensional radius of the ring sink is less than , there is a central stagnation point on the surface surrounded by a dip which rises to the stagnation level in the far distance. However, as the radius of the ring sink increases beyond , a surface stagnation ring forms and moves outward as the ring sink radius increases. It is also shown that as the radius of the sink increases, the solutions in the vicinity of the ring sink/source change continuously from those due to a point sink/source () to those due to a line sink/source (). These properties are confirmed by the numerical solutions to the full nonlinear equations for finite Froude numbers. At small values of the Froude number and sink or source radius, the nonlinear solutions look like the approximate solutions, but as the flow rate increases a limiting maximum Froude number solution with a secondary stagnation ring is obtained. At large values of sink or source radius, however, this ring does not form and there is no obvious physical reason for the limit on solutions. The maximum Froude numbers at which steady solutions exist for each radius are computed.

Copyright
Corresponding author
Email address for correspondence: G.Hocking@murdoch.edu.au
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

5. L. K. Forbes & G. C. Hocking 2003 On the computation of steady axi-symmetric withdrawal from a two-layer fluid. Comput. Fluids 32, 385401.

15. J. Imberger & P. F. Hamblin 1982 Dynamics of lakes, reservoirs and cooling ponds. Annu. Rev. Fluid Mech. 14, 153187.

16. J. Imberger & J. C. Patterson 1990 Physical limnology. In Advances in Applied Mechanics (ed. J. W. Hutchinson & T. Wu ). vol. 27. pp. 303475. Academic.

18. G. H. Jirka & D. S Katavola 1979 Supercritical withdrawal from two-layered fluid systems. Part 2. Three dimensional flow into a round intake. J. Hydraul. Res. 17 (1), 5362.

20. H. Mekias & J.-M. Vanden-Broeck 1991 Subcritical flow with a stagnation point due to a source beneath a free surface. Phys. Fluids A 3, 26522658.

23. T. E. Stokes , G. C. Hocking & L. K. Forbes 2002 Unsteady free surface flow induced by a line sink. J. Engng Maths 47, 137160.

27. P. A. Tyvand 1992 Unsteady free-surface flow due to a line source. Phys. Fluids A 4, 671676.

29. J.-M. Vanden Broeck , L. W. Schwartz & E. O. Tuck 1978 Divergent low-Froude-number series expansion of nonlinear free-surface flow problems. Proc. R. Soc. Lond. Ser. A 361, 207224.

30. I. R. Wood & K. K. Lai 1972 Selective withdrawal from a two-layered fluid. J. Hydraul. Res. 10 (4), 475496.

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

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 11 *
Loading metrics...

Abstract views

Total abstract views: 88 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 27th May 2017. This data will be updated every 24 hours.