Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-19T05:15:25.187Z Has data issue: false hasContentIssue false
  • English
  • Français

Scattering of surface waves obliquely incident on a fixed half immersed circular cylinder

Published online by Cambridge University Press:  24 October 2008

B. N. Mandal  and
S. K. Goswami
B. N. Mandal
Affiliation:
Department of Applied Mathematics, University College of Science, Calcutta 700 009, India
S. K. Goswami
Affiliation:
Department of Mathematics, Presidency College, Calcutta 700 073, India
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of scattering of surface water waves obliquely incident on a fixed half immersed circular cylinder is solved approximately by reducing it to the solution of an integral equation and also by the method of multipoles. For different values of the angle of incidence and the wave number the reflection and transmission coefficients obtained by both methods are evaluated numerically and represented graphically to compare the results obtained by the respective methods.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 2 , September 1984 , pp. 359 - 369
Copyright
Copyright © Cambridge Philosophical Society 1984

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

REFERENCES

[1]Bai, K. J.. Diffraction of oblique waves by an infinite cylinder. J. Fluid Mech. 68 (1975), 513–535.CrossRefGoogle Scholar
[2]Bolton, W. E. and Ursell, F.. The wave force on an infinite long circular cylinder in an oblique sea. J. Fluid Mech. 57 (1973), 241–256.CrossRefGoogle Scholar
[3]Dean, W. R.. On the reflection of surface waves by a submerged plane barrier. Proc. Cambridge Philos. Soc. 41 (1945), 231–238.CrossRefGoogle Scholar
[4]Evans, D. V.. Diffraction of water waves by a submerged vertical plate. J. Fluid Mech. 40 (1970), 433–451.CrossRefGoogle Scholar
[5]Evans, D. V. and Morris, C. A. N.. The effect of a fixed vertical barrier on obliquely incident surface waves in deep water. J. Inst. Math. Appl. 9 (1972), 198–204.CrossRefGoogle Scholar
[6]Faulkner, T. R. Diffraction of an obliquely incident surface wave by a vertical barrier of finite depth. Proc. Cambridge Philos. Soc. 62 (1966), 829–838.Google Scholar
[7]Faulkner, T. R.. The diffraction of an obliquely incident surface wave by a submerged plane barrier. Z. Angew. Math. Phys. 17 (1966), 699–707.CrossRefGoogle Scholar
[8]Goswami, S. K.. A note on the problem of scattering of surface waves by a submerged fixed vertical barrier. Z. Angew. Math. Mech. 62 (1982), 637–639.CrossRefGoogle Scholar
[9]Garrison, C. J.. On the interaction of an infinite shallow draft cylinder oscillating at the free surface with a train of oblique waves. J. Fluid Mech. 39 (1969), 227–255.CrossRefGoogle Scholar
[10]Jarvis, R. J. and Taylor, B. S.. The scattering of surface waves by a vertical plane barrier. Proc. Cambridge Philos. Soc. 66 (1969), 417–422.CrossRefGoogle Scholar
[11]Levine, H.. Scattering of surface waves by a submerged circular cylinder. J. Math. Phys. 6 (1965), 1231–1243.CrossRefGoogle Scholar
[12]Macaskill, C.. Reflexion of water waves by a permeable barrier. J. Fluid. Mech. 95 (1979), 141–157.CrossRefGoogle Scholar
[13] Mandal, B. N. and Chakrabarti, R. N.. Scattering of surface waves by a submerged circular cylinder in a fluid of finite depth. J. Indian Inst. Sci. 64 (1983), 189–198.Google Scholar
[14]Mandal, B. N. and Goswami, S. K.. A note on the diffraction of an obliquely incident surface wave by a partially immersed fixed vertical barrier. Appl. Sci. Res. 40 (1983), 345–353.CrossRefGoogle Scholar
[15]Mandal, B. N. and Goswami, S. K.. The scattering of an obliquely incident surface wave by a submerged fixed vertical plate. J. Math. Phys. (1984), to appear.@@@@@CrossRefGoogle Scholar
[16]Ursell, F.. The effect of a fixed vertical barrier on surface waves in deep water. Proc. Cambridge Philos. Soc. 43 (1947), 374–382.CrossRefGoogle Scholar
[17]Ursell, F.. The transmission of surface waves under surface obstacles. Proc. Cambridge Philos. Soc. 57 (1961), 638–663.CrossRefGoogle Scholar
[18]Ursell, F.. The expansion of water-wave potentials at great distances. Proc. Cambridge Philos. Soc. 64 (1968), 811–826.CrossRefGoogle Scholar
[19]Watson, G. N.. Theory of Bessel Functions. (Cambridge University Press, 1948).Google Scholar
[20]Williams, W. E.. Note on the scattering of water waves by a vertical barrier. Proc. Cambridge Philos. Soc. 62 (1966), 507–509.CrossRefGoogle Scholar
[21]Yu, Y. S. and Ursell, F.. Surface waves generated by an oscillating circular cylinder on water of finite depth: theory and experiment. J. Fluid Mech. 11 (1961), 529–551.CrossRefGoogle Scholar