Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T06:50:26.264Z Has data issue: false hasContentIssue false
  • English
  • Français

Smoothly attaching bow flows with constant vorticity

Published online by Cambridge University Press:  17 February 2009

S. W. McCue  and
L. K. Forbes
S. W. McCue
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom; e-mail: [email protected]
L. K. Forbes
Affiliation:
School of Mathematics and Physics, University of Tasmania, GPO Box 252-37, Hobart, Tas 7001, Australia; e-mail: [email protected]
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 free surface flow of a finite depth fluid past a semi-infinite body is considered. The fluid is assumed to have constant vorticity throughout and the free surface is assumed to attach smoothly to the front face of the body. Numerical solutions are found using a boundary integral method in the physical plane and it is shown that solutions exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a comer is also considered. Vorticity is included in the flow and it is shown that the behaviour of the solutions is qualitatively the same as that found in the problem described above.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 3 , January 2001 , pp. 354 - 371
Copyright
Copyright © Australian Mathematical Society 2001

References

[1] Farrow, D. E. and Tuck, E. O., “Further studies of stem wavemaking”, J. Austral Math. Soc. Ser. B 36 (1995) 424–437.CrossRefGoogle Scholar
[2] Forbes, L. K., “On the effects of non-linearity in free-surface flow about a submerged point vortex”, J. Engng Maths 19 (1985) 139–155.CrossRefGoogle Scholar
[3] Forbes, L. K. and Belward, S. R., “Atmospheric solitary waves: some applications to the morning glory of the Gulf of Carpentaria”, J. Fluid Mech. 321 (1996) 137–155.CrossRefGoogle Scholar
[4] Hocking, G. C., “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. Ser. B 26 (1985) 470–486.CrossRefGoogle Scholar
[5] Hocking, G. C., “Critical withdrawal from a two-layer fluid through a line sink”, J. Engng Maths 25 (1991) 1–11.CrossRefGoogle Scholar
[6] Hocking, G. C., “Flow from a vertical slot into a layer of finite depth”. Applied Math. Modelling 16 (1992) 300–306.CrossRefGoogle Scholar
[7] Hocking, G. C., “Bow flows with smooth separation in water of finite depth”, J. Austral. Math. Soc. Ser. B 35 (1993) 114–126.CrossRefGoogle Scholar
[8] Hocking, G. C. and Vanden-Broeck, J. M., “Withdrawal of a fluid of finite depth through a line sink with a cusp in the free surface”, Computers and Fluids 27 (1998) 797–806.CrossRefGoogle Scholar
[9] King, A. C. and Bloor, M. I. G., “A note on the free surface induced by a submerged source at infinite Froude number”, J. Austral. Math. Soc. Ser. B 30 (1988) 147–156.CrossRefGoogle Scholar
[10] Madurasinghe, M. A., “Splashless ship bows with stagnant attachment”, J. Ship Res. 32 (1988) 194–202.CrossRefGoogle Scholar
[11] Madurasinghe, M. A. and Tuck, E. O., “Ship bows with continuous and splashless flow attachment”, J. Austral. Math. Soc. Ser. B 27 (1986) 442–452.CrossRefGoogle Scholar
[12] McCue, S. W. and Forbes, L. K., “Bow and stem flows with constant vorticity”, J. Fluid Mech. 399 (1999) 277–300.CrossRefGoogle Scholar
[13] Teles da Silva, A. F. and Peregrine, D. H., “Steep, steady surface waves on water of finite depth with constant vorticity”, J. Fluid Mech. 195 (1988) 281–302.CrossRefGoogle Scholar
[14] Vanden-Broeck, J. M., “Bow flows in water of finite depth”, Phys. Fluids A 1 (1989) 1328–1330.CrossRefGoogle Scholar
[15] Vanden-Broeck, J. M., “Steep solitary waves in water of finite depth with constant vorticity”, J. Fluid Mech. 274 (1994) 339–348.CrossRefGoogle Scholar
[16] Vanden-Broeck, J. M., “Cusp flow due to a submerged source with a free surface partially covered by a lid”, European J. Mech. B, (Fluids), 16 (1997) 249–255.Google Scholar
[17] Vanden-Broeck, J. M. and Keller, J. B., “Free surface flow due to a sink”, J. Fluid Mech. 175 (1987) 109–117.CrossRefGoogle Scholar
[18] Vanden-Broeck, J. M., Schwartz, L. W. and Tuck, E. O., “Divergent low-Froude-number series expansion in nonlinear free-surface flow problems”, Proc. R. Soc. Lond. A 361 (1978) 207–224.Google Scholar
[19] Vanden-Broeck, J. M. and Tuck, E. O., “Computation of near-bow or stem flows, using series expansion in the Froude number”, in Proc. 2nd Intl Conf. Numerical Ship Hydrodynamics, Berkeley, CA (University Extension Publications, 1977), pp. 371–381.Google Scholar