Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-27T17:30:31.600Z Has data issue: false hasContentIssue false
  • English
  • Français

The time-dependent free surface flow induced by a submerged line source or sink

Published online by Cambridge University Press:  26 April 2006

E. M. Sozer  and
M. D. Greenberg
E. M. Sozer
Affiliation:
Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA
M. D. Greenberg
Affiliation:
Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The unsteady nonlinear potential flow induced by a submerged line source or sink is studied by a vortex sheet method, both to trace the free surface evolution and to explore the possible existence of steady-state solutions. Only steady-state flows have been considered by other investigators, and these flows have been insensitive to whether they are generated by a source or sink, except with respect to the flow direction along the streamlines. The time-dependent solution permits an assessment of the stability of previously found steady solutions, and also reveals differences between source and sink flows: for the infinite-depth case, steady stagnation-point-type solutions are found both for source flows and sink flows, above the critical value reported by other investigators; finally, it is shown that streamline patterns of steady stagnation-point flows are identical for source and sink flows only in the limiting case of infinite depth.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 284 , 10 February 1995 , pp. 225 - 237
Copyright
© 1995 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. Washington: US Govt. Printing Office.
Baker, G. R., Meiron, D. I. & Orszag, S. A. 1982 Generalized vortex methods for free surface problems. J. Fluid Mech. 123, 477–501.Google Scholar
Craya, A. 1949 Theoretical research on the flow of nonhomogeneous fluids. La Houille Blanche 4, 44–55.Google Scholar
Forbes, L. K. & Hocking, G. C. 1993 Flow induced by a line sink in a quiescent fluid with surface-tension effects. J. Austral. Math. Soc. B 34, 377–391.Google Scholar
Hocking, G. C. 1985 Cusp-like free-surface flows due to a submerged source or sink in the presence of a flat or sloping bottom. J. Austral. Math. Soc. B 26, 470–486.Google Scholar
Hocking, G. C. 1991 Critical withdrawal from a two-layer fluid through a line sink. J. Engng Maths 25, 1–11.Google Scholar
Hocking, G. C. & Forbes, L. K. 1991 A note on the flow induced by a line sink beneath a free surface. J. Austral. Math. Soc. B 32, 251–260.Google Scholar
Hocking, G. C. & Forbes, L. K. 1992 Subcritical free-surface flows caused by a line source in a fluid of finite depth. J. Engng Maths 26, 455–466.Google Scholar
Longuet-Higgins, M. S. & Cokelet, E. D. 1976 The deformation of steep surface waves. I. A numerical method of computation. Proc. R. Soc. Lond. A 350, 1–26.Google Scholar
Peregrine, D. H. 1972 A line source beneath a free surface. Mathematics Research Center, Univ. Wisconsin Rep. 1248.
Shapiro, R. 1975 Linear filtering. Maths Comput. 29, 1094–1097.Google Scholar
Sozer, E. M. 1994 Vortex sheet approach to the nonlinear flow induced by a moving object below a free surface. (tentative title) PhD dissertation, Mech. Eng. Dept. University of Delaware.
Sozer, E. M. & Greenberg, M. D. 1993 A vortex sheet approach to the nonlinear flow induced by a line soure or sink. In Boundary Elements XV, Proc. 15th Intl Conf. on BEM (ed. C. A. Brebbia & J. J. Rencis). Elsevier.
Telste, J. G. 1987 Inviscid flow about a cylinder rising to a free surface. J. Fluid Mech. 182, 149–168.Google Scholar
Tuck, E. O. & Vanden-Broeck, J. M. 1984 A cusp-like free-surface flow due to a submerged source or sink. J. Austral. Math. Soc. B 25, 443–450.Google Scholar
Vanden-Broeck, J. M. & Keller, J. B. 1987 Free surface flow due to a sink. J. Fluid Mech. 175, 109–117.Google Scholar
Vanden-Broeck, J. M., Schwartz, L. W. & Tuck, E. O. 1978 Divergent low-Froude number series expansion of nonlinear free-surface problems. Proc. R. Soc. Lond. A 361, 207–224.Google Scholar
Zaroodny, S. J. & Greenberg, M. D. 1973 On a vortex sheet approach to the numerical calculation of water waves. J. Comput. Phys. 11, 440–446.Google Scholar