Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T07:18:09.575Z Has data issue: false hasContentIssue false
  • English
  • Français

Bow flows with smooth separation in water of finite depth

Published online by Cambridge University Press:  17 February 2009

G. C. Hocking
G. C. Hocking
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, W.A., 6009.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The bow flow generated by a wide flat-bottomed ship moving in water of finite depth is examined. Solutions obtained using an integral equation technique are presented for a range of different depths and for a range of angles of the front of the bow. The solution for the limiting case of infinite Froude number is obtained as an integral, and numerical solutions are found for the nonlinear problem in which the Froude number is finite. Solutions with smooth separation are shown to exist for all values of Froude number greater than unity, for any bow slope.

Type
Research Article
Information
The ANZIAM Journal , Volume 35 , Issue 1 , July 1993 , pp. 114 - 126
Copyright
Copyright © Australian Mathematical Society 1993

References

[1] Forbes, L. K and Hocking, G. C, “Subcritical free-surface flow caused by a line source in a fluid of finite depth–Part 1”, Report 1991/01, Dept of Maths, Univ. of Western Aust., Nedlands, Australia 6009, 1991.Google Scholar
[2] Hocking, G. C., “Infinite Froude number solutions to the problem of a submerged source or sink”, J. Aust. Math Soc. Ser. B 29 (1988) 401–409.CrossRefGoogle Scholar
[3] Hocking, G. C., “Critical withdrawal from a two-layer fluid through a line sink”, J. Eng. Math. 25 (1991) 1–11.CrossRefGoogle Scholar
[4] Hocking, G. C and Forbes, L. K, “Subcritical free-surface flow caused by a line source in a fluid of finite depth”, J. Eng. Math. 26 (1992) 455–466.CrossRefGoogle Scholar
[5] King, A. C. and Bloor, M. I. G., “A note on the free surface induced by a submerged source at infinite Froude number”, J. Aust. Math Soc. Ser. B 30 (1988) 147–156.CrossRefGoogle Scholar
[6] Madurasinghe, M. A. D. and Tuck, E. O., “Ship bows with continuous and splashless flow attachment”, J. Aust. Math. Soc. Ser. B 27 (1986) 442–452.CrossRefGoogle Scholar
[7] Mekias, H. and Vanden-Broeck, J. M., “Supercritical free-surface flow with a stagnation point due to a submerged source”, Phys. Fluids A 1 (1989) 1694–1697.CrossRefGoogle Scholar
[8] Mekias, H. and Vanden-Broeck, J. M., “Subcritical flow with a stagnation point due to a source beneath a free surface”, Phys. Fluids A 3 (1991) 2652–2658.CrossRefGoogle Scholar
[9] Tricomi, F. G., Integral Equations (Interscience, 1957).Google Scholar
[10] Tuck, E. O., “Application and solution of singular integral equations”, in The application and numerical solution of integral equations (eds. Anderssen, R.S. et al. ), (Sijthoff and Noordhoff, 1980).Google Scholar
[11] Tuck, E. O. and Vanden-Broeck, J. M., “Splashless bow flows in two dimensions?”, in Proc. 15th Symp. Naval Hydro., Hamburg, September 1984, (National Academy Press, Washington D.C., 1985) 293–302.Google Scholar
[12] Vanden-Broeck, J. M., “Nonlinear free-surface flows past two-dimensional bodies”, in Advances in Nonlinear waves (ed. Debnath, L.), (Pitmann, Boston, 1985) Vol. 2, 31–42.Google Scholar
[13] Vanden-Broeck, J. M., “Bow flows in water of finite depth”, Phys. Fluids 1 (1989) 1328–1330.CrossRefGoogle Scholar
[14] Vanden-Broeck, J. M. and Keller, J. B., “Free surface flow due to a sink”, J. Fluid Mech 175 (1987) 109–117.CrossRefGoogle Scholar
[15] Vanden-Broeck, J. M., Schwartz, L. W. and Tuck, E. O., “Divergent low-Froude number series expansion of non-linear free-surface flow problems”, Proc. Roy. Soc. London Ser. A 361 (1978) 207–224.Google Scholar
[16] Vanden-Broeck, J. M. and Tuck, E. O., “Computation of near-bow or stern flows, using series expansion in the Froude number”, in Proc. 2nd Int. Conf. Num. Ship Hydro., (Berkely, California, 1977) 371–381.Google Scholar