Hostname: page-component-6bf8c574d5-685pp Total loading time: 0 Render date: 2025-03-06T19:30:11.224Z Has data issue: false hasContentIssue false
  • English
  • Français

Water wave diffraction by a surface strip

Published online by Cambridge University Press:  04 January 2007

RUPANWITA GAYEN ,
B. N. MANDAL  and
A. CHAKRABARTI
RUPANWITA GAYEN
Affiliation:
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700 108, India
B. N. MANDAL*
Affiliation:
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700 108, India
A. CHAKRABARTI
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
*
†Author to whom correspondence should be addressed: biren@isical.ac.in
Get access Rights & Permissions [Opens in a new window]

Abstract

The two-dimensional problem of wave diffraction by a strip of arbitrary width is investigated here in the context of linearized theory of water waves by reducing it to a pair of Carleman-type singular integral equations. These integral equations have been solved earlier by an iterative process which is valid only for a sufficiently wide strip. A new method is described here by which solutions of these integral equations are determined by solving a set of four Fredholm integral equations of the second kind, and the process is valid for a strip of arbitrary width. Numerical solutions of these Fredholm integral equations are utilized to obtain fairly accurate numerical estimates for the reflection and transmission coefficients. Previous numerical results for a wide strip are recovered from the present analysis. Additional results for the reflection coefficient are presented graphically for moderate values of the strip width which exhibit a less oscillatory nature of the curve than the case of a wide strip.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 571 , 25 January 2007 , pp. 419 - 438
Copyright
Copyright © Cambridge University Press 2007

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

Chakrabarti, A. 2000 On the solution of the problem of scattering of surface water waves by a sharp discontinuity in the surface boundary conditions. ANZIAM J. 42, 277–286.CrossRefGoogle Scholar
Chung, H. & Linton, C. M. 2005 Reflection and transmission across a finite gap in an infinite elastic plate on water. Q. J. Mech. Appl. Maths 58, 1–15.CrossRefGoogle Scholar
Evans, D. V. 1985 The solution of a class of boundary value problems with smoothly varying boundary conditions. Q. J. Mech. Appl. Maths 38, 521–536.CrossRefGoogle Scholar
Gabov, S. A., Sveshnikov, A. G. & Shatov, A. K. 1989 Dispersion of internal waves by an obstacle floating on the boundary separating two liquids. Prikl. Mat. Mech. 53, 727–730 (in Russian).Google Scholar
Gakhov, F. D. 1966 Boundary Value Problems. Pergamon.CrossRefGoogle Scholar
Gayen(Chowdhury), R., Mandal, B. N. & Chakrabarti, A. 2005 Water wave scattering by an ice-strip. J. Engng Maths 53, 21–37.CrossRefGoogle Scholar
Goldshtein, R. V. & Marchenko, A. V. 1989 The diffraction of plane gravitational waves by the edge of an ice-cover. Prikl. Mat. Mech. 53, 731–736.Google Scholar
Jones, D. S. 1964 The Theory of Electromagnetism. Pergamon.Google Scholar
Kanoria, M., Mandal, B. N. & Chakrabarti, A. 1999 The Wiener-Hopf solution of a class of mixed boundary value problems arising in surface water wave phenomena. Wave Motion 29, 267–292.CrossRefGoogle Scholar
Linton, C. M. 2001 The finite Dock problem. Z. Angew. Math. Phys. 52, 640–656.CrossRefGoogle Scholar
Noble, B. 1958 Methods Based on the Wiener-Hopf Technique. Pergamon.Google Scholar
Peters, A. S. 1950 The effect of a floating mat on water waves. Commun. Pure. Appl. Maths 3, 319–354.CrossRefGoogle Scholar
Shanin, A. V. 2001 Three theorems concerning diffraction by a strip or a slit. Q. J. Mech. Appl. Maths 54, 107–137.CrossRefGoogle Scholar
Shanin, A. V. 2003 Diffraction of a plane wave by two ideal strips. Q. J. Mech. Appl. Maths 56, 187–215.CrossRefGoogle Scholar
Stoker, J. J. 1957 Water Waves. Interscience.Google Scholar
Ursell, F. 1947 The effect of a fixed vertical barrier on surface water waves in deep water. Proc. Comb. Phil. Soc. 42, 374–382.CrossRefGoogle Scholar
Varley, E. & Walker, J. D. A. 1989 A method for solving singular integro-differential equations. IMA J. Appl. Maths 43, 11–45.CrossRefGoogle Scholar
Weitz, M. & Keller, J. B. 1950 Reflection of water waves from floating ice in water of finite depth. Commun. Pure. Appl. Maths 3, 305–318.CrossRefGoogle Scholar
Williams, M. H. 1982 Diffraction by a finite strip. Q. J. Mech. Appl. Maths 35, 103–124.CrossRefGoogle Scholar