Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T15:11:06.648Z Has data issue: false hasContentIssue false
  • English
  • Français

Scattering of surface waves by a conical island

Published online by Cambridge University Press:  29 March 2006

Ronald Smith  and
T. Sprinks
Ronald Smith
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
T. Sprinks
Affiliation:
Department of Mathematics, University of Essex, Colchester, England
Get access Rights & Permissions [Opens in a new window]

Abstract

A model equation is derived which approximately describes the propagation of periodic surface waves in water of slowly varying depth. Numerical solutions to the model equation are obtained for the scattering of an incident plane wave by a conical island.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 72 , Issue 2 , 25 November 1975 , pp. 373 - 384
Copyright
© 1975 Cambridge University Press

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

Cohen, A. M. & Jones, D. E. 1974 A note on the numerical solution of some second order differential equations. J. Inst. Math. Appl. 13, 379–384.Google Scholar
Eckart, C. 1950 The ray particle analogy. J. Mar. Res. 9, 139–144.Google Scholar
Eckart, C. 1951 Surface waves on water of variable depth. Scripps Inst. Oceanog., Lecture Notes, Fall Semester 1950–51, Ref. 51–12, Wave Rep. no. 100.
Gill, S. 1951 A process for the step-by-step integration of differential equations in an automatic digital computing machine. Proc. Camb. Phil. Soc. 47, 96–108.Google Scholar
Homma, S. 1950 On the behaviour of seismic sea waves around a circular island. Geophys. Mag. 21, 199–208.Google Scholar
Keller, J. B. 1958 Surface waves on water of non-uniform depth. J. Fluid Mech. 4, 607–614.Google Scholar
Keller, J. B. & Rubinow, S. I. 1960 Asymptotic solution of eigenvalue problems. Ann. Phys. 9, 24–75. (Errata, pp. 303–305.)Google Scholar
Lautenbacher, C. 1970 Gravity wave refraction by islands. J. Fluid Mech. 41, 655–672.Google Scholar
Longuet-Higgins, M. S. 1967 On the trapping of wave energy round islands. J. Fluid Mech. 29, 781–821.Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill.
Newman, J. N. 1965 Propagation of water waves over an infinite step. J. Fluid Mech. 23, 399–415.Google Scholar
Shen, M. C., Meyer, R. E. & Keller, J. B. 1968 Spectra of water waves in channels and around islands. Phys. Fluids, 11, 2289–2304.Google Scholar
Smith, R. 1974 Edge waves on a beach of mild slope. Quart. J. Mech. Appl. Math. 27, 102–110.Google Scholar
Summerfield, W. 1972 Circular islands as resonators of long-wave energy. Phil. Trans. A 272, 361–402.Google Scholar
Ursell, F. 1952 Edge waves on a sloping beach. Proc. Roy. Soc. A 214, 79–97.Google Scholar
Vastano, A. C. & Reid, R. O. 1967 Tsunami response for islands: verification of a numerical procedure. J. Mar. Bee. 25, 129–139.Google Scholar