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The effect of surface tension in porous wave maker problems

Published online by Cambridge University Press:  17 February 2009

A. Chakrabarti and
T. Sahoo
A. Chakrabarti
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
T. Sahoo
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
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Abstract

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Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 4 , April 1998, pp. 539 - 556
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Chakrabarti, A., “A note on the porous-wave maker problem”, Acta Mechanica 77 (1989) 121–129.Google Scholar
[2]Chakrabarti, A. and Sahoo, T., “Reflection of water waves by a nearly vertical porous wall”, J.Austral. Math. Soc. Series B 37 (1996) 417–29.Google Scholar
[3]Chakrabarti, A. and Sahoo, T., “Reflection of water waves in the presence of surface tension by a nearly vertical porous wall”, J. Austral. Math. Soc. Series B 39 (1998) 308–317.Google Scholar
[4]Chwang, A. T., “A porous wave maker theory”, J. Fluid Mech. 132 (1983) 395–406.Google Scholar
[5]Gorgui, M. A., Faltas, M. S. and Ahmed, A. Z., “Capillary gravity waves in the presence of infinite porous plates”, Il Nuovo Cimento, 15D, (1993) 793–808.Google Scholar
[6]Havelock, T. H., “Forced surface waves on water”, Phil. Mag. 8 (1929) 569–576.Google Scholar
[7]Hocking, L. M., “Capillary gravity waves produced by a heaving body”, J. Fluid Mech. 186 (1987) 337–349.Google Scholar
[8]Hocking, L. M. and Mahdmina, D., “Capillary gravity waves produced by a wave maker”, J. Fluid Mech. 224 (1991) 217–226.CrossRefGoogle Scholar
[9]Madsen, O. S., “Waves generated by a piston type wave maker” Proc. 12th Coastal Engng Conf., ASCE (1970), pp. 589–607.Google Scholar
[10]Mandal, B. N. and Bandyopadhyay, S., “A note on the plane vertical wave maker in the presence of surface tension”, Q. Appl. Math. 49, (1991) 627–633.Google Scholar
[11]Mandal, B. N. and Chakrabarti, A., “The plane vertical wave maker problem – revisited”, Appl.Math. Lett. 1, (1988) 255–258.Google Scholar
[12]Rhodes-Robinson, P. F., “On the forced surface waves due to a vertical wave maker in the presence of surface tension”, Proc. Camb. Phil. Soc. 76 (1971) 323–337.Google Scholar
[13]Rhodes-Robinson, P. F., “On surface waves in the presence of immersed vertical boundaries I”, Q. Jour. Mech. and Appl. Math. 32, (1979) 109–124.Google Scholar
[14]Rhodes-Robinson, P. F., “On surface waves in the presence of immersed vertical boundaries II”, Q. Jour. Mech. and Appl. Math. 32, (1979) 125–133.Google Scholar
[15]Rhodes-Robinson, P. F., “On waves at an interface between two liquids”, Math. Proc. Camb. Phil. soc. 88 (1980) 183–191.CrossRefGoogle Scholar
[16]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.Google Scholar
[17]Rhodes-Robinson, P. F., “On waves in the presence of vertical porous boundaries”, J. Austral. Math. Soc. Series B 39 (1997) 104–120.Google Scholar
[18]Williams, W. E., “Diffraction of surface waves on an incompressible fluid”, J. Fluid Mech. 22 (1965) 253–256.CrossRefGoogle Scholar