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Reflection of water waves in the presence of surface tension by a nearly vertical porous wall

Published online by Cambridge University Press:  17 February 2009

A. Chakrabarti  and
T. Sahoo
A. Chakrabarti
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore560 012, India
T. Sahoo
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore560 012, India
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Abstract

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In the present paper the problem of reflection of water waves by a nearly vertical porous wall in the presence of surface tension has been investigated. A perturbational approach for the first-order correction has been employed as compared with the corresponding vertical wall problem. A mixed Fourier transform together with the regularity property of the transformed function along the positive real axis has been used to obtain the potential functions along with the reflection coefficients up to first order. Whilst the problem of water of infinite depth is the subject matter of the present paper, a similar approach is applicable to problems associated with water of finite depth.

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 3 , January 1998 , pp. 308 - 317
Copyright
Copyright © Australian Mathematical Society 1998

References

[1] Chakrabarti, A., “A note on the porous-wavemaker problem”, Acta Mechanica 77 (1989) 121–129.CrossRefGoogle Scholar
[2] Chakrabarti, A. and Sahoo, T., “Reflection of water waves by a nearly vertical porous wall”, J. Aust. Math. Soc. Series. B 37 (1996), 417–429.CrossRefGoogle Scholar
[3] Chwang, A. T., “A porous wavemaker theory”, J. Fluid Mechanics 132 (1983) 395–406.CrossRefGoogle Scholar
[4] Kachoyan, P. J. and McKee, W. D., “Wave forces on steeply sloping sea walls”, J. Engin. Maths. 19 (1985) 351–362.CrossRefGoogle Scholar
[5] Mandal, B. N. and Chakrabarti, A., “A note on diffraction of water waves by a nearly vertical barrier”, IMA J. Appl. Maths. 43 (1989) 157–165.CrossRefGoogle Scholar
[6] Mandal, B. N. and Kar, S. K., “Reflection of water waves by a nearly vertical wall”, Int. J. Math. Educ. Science and Technology 23 (1992) 665–670.CrossRefGoogle Scholar
[7] Packham, B. A., “Capillary gravity waves against a vertical cliff”, Proc. Camb. Phil. Soc. 64 (1968) 833–847.CrossRefGoogle Scholar
[8] Rhodes-Robinson, P. F., “On surface waves in the presence of immersed vertical boundaries I”, Q. J. Mech. Appl. Math. 32 (1979) 109–124.CrossRefGoogle Scholar
[9] Rhodes-Robinson, P. F., “Note on the reflection of water waves at a wall in the presence of surface tension”, Proc. Camb. Phil. Soc. 92 (1982) 369–373.CrossRefGoogle Scholar
[10] Rhodes-Robinson, P. F., “On waves in the presence of vertical porous boundaries”, J. Aust. Math. Soc. Ser. B (1996), 39 (1997), 104–120.CrossRefGoogle Scholar
[11] Shaw, D. S., “Perturbational results for diffraction of water waves by nearly vertical barriers”, IMA J. Appl. Math. 33 (1985) 99–117.CrossRefGoogle Scholar
[12] Sneddon, I. N., The Use of Integral Transforms (Tata McGraw Hill, New Delhi, 1974).Google Scholar