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

  • A. Chakrabarti (a1) and T. Sahoo (a1)

Abstract

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.

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Copyright

References

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[1] Chakrabarti, A., “A note on the porous-wavemaker problem”, Acta Mechanica 77 (1989) 121129.
[2] Chakrabarti, A. and Sahoo, T., “Reflection of water waves by a nearly vertical porous wall”, J. Aust. Math. Soc. Series. B 37 (1996), 417429.
[3] Chwang, A. T., “A porous wavemaker theory”, J. Fluid Mechanics 132 (1983) 395406.
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[8] Rhodes-Robinson, P. F., “On surface waves in the presence of immersed vertical boundaries I”, Q. J. Mech. Appl. Math. 32 (1979) 109124.
[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) 369373.
[10] Rhodes-Robinson, P. F., “On waves in the presence of vertical porous boundaries”, J. Aust. Math. Soc. Ser. B (1996), 39 (1997), 104120.
[11] Shaw, D. S., “Perturbational results for diffraction of water waves by nearly vertical barriers”, IMA J. Appl. Math. 33 (1985) 99117.
[12] Sneddon, I. N., The Use of Integral Transforms (Tata McGraw Hill, New Delhi, 1974).
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