Skip to main content Accessibility help
×
Home

A unified approach to problems of scattering of surface water waves by vertical barriers

  • A. Chakrabarti (a1), Sudeshna Banerjea (a2), B. N. Mandal (a3) and T. Sahoo (a1)

Abstract

A unified analysis involving the solution of multiple integral equations via a simple singular integral equation with a Cauchy type kernel is presented to handle problems of surface water wave scattering by vertical barriers. Some well known results are produced in a simple and systematic manner.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      A unified approach to problems of scattering of surface water waves by vertical barriers
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      A unified approach to problems of scattering of surface water waves by vertical barriers
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      A unified approach to problems of scattering of surface water waves by vertical barriers
      Available formats
      ×

Copyright

References

Hide All
[1] Banerjea, S., “Scattering of water waves by a vertical wall with gaps”, J. Austral. Math. Soc. Ser. B 37 (1996) 512529.
[2] Chakrabarti, A. and Bharathi, L. Vijaya, “A new approach to the problem of scattering of water waves by vertical barriers”, ZAMM 72 (9) (1992) 415423.
[3] Erdelyi, A., Magnus, W., Oberhittenger, F. and Tricomi, F. G., Tables of integral transforms. Volume 1 (McGraw Hill, New York, 1954).
[4] Evans, D. V., “Diffraction of water waves by a submerged vertical plate”, J. Fluid Mech. 40 (1970) 433–151.
[5] Evans, D. V., “Vertical barriers, sloping beaches and submerged bodies”, in Wave Asymptotics (eds. Martin, P. A. and Wickham, G. K.), (Cambridge University Press, 1992) 202219.
[6] Gakhov, F. D., Boundary value problems (Addision Wesley, 1966).
[7] Gradshteyn, I. N. and Ryzhik, I. M., Tables of integrals, series and products (Acadamic press, 1980).
[8] Mandal, B. N. and Kundu, P. K., “Scattering of waterwaves by vertical barrier and associated mathematical methods”, Proc. Indian National Science Acadamy 53A (1987) 514530.
[9] Mei, C. C., “Radiation and scattering of transient gravity waves by vertical plates”, Q. J. Mech. Appl. Math. 19 (1966) 417440.
[10] Muskhelishvili, N. I., Singular integral equations (Noordhoff, 1963).
[11] Porter, D., “The transmission of surface waves through a gap in a vertical barrier”, Proc. Camb. Phil. Soc. 71 (1972) 411421.
[12] Ursell, F., “The effect of a fixed vertical barrier on surface waves in deep water”, Proc. Camb. Phil. Soc. 43 (1947) 374382.
[13] Bharathi, L. Vijaya and Chakrabarti, A., “Solution of a boundary value problem associated with diffraction of water waves by a nearly vertical barrier”, IMA J. App. Math. 47 (1991) 2332.
[14] Bharathi, L. Vijaya, Chakrabarti, A., Mandal, B. N. and Banerjea, S., “Solution of the problem of scattering of water waves by a nearly vertical plate”, J. Austral. Math. Soc. Ser. B 35 (1994) 382395.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed