Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-25T07:12:05.921Z Has data issue: false hasContentIssue false
  • English
  • Français

The modified mild-slope equation

Published online by Cambridge University Press:  26 April 2006

P. G. Chamberlain  and
D. Porter
P. G. Chamberlain
Affiliation:
Department of Mathematics, The University of Reading, PO Box 220, Whiteknights, Reading, RG6 2AX, UK
D. Porter
Affiliation:
Department of Mathematics, The University of Reading, PO Box 220, Whiteknights, Reading, RG6 2AX, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

A modified version of the mild-slope equation is derived and its predictions of wave scattering by two-dimensional topography compared with those of other equations and with experimental data. In particular, the modified mild-slope equation is shown to be capable of describing known scattering properties of singly and doubly periodic ripple beds, for which the mild-slope equation fails. The new equation compares favourably with other models of scattering which improve on the mild-slope equation, in that it is widely applicable and computationally cheap.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 291 , 25 May 1995 , pp. 393 - 407
Copyright
© 1995 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

Berkhoff, J. C. W. 1973 Computation of combined refraction-diffraction. Proc. 13th Intl Conf. on Coastal Engng, July 1972, Vancouver, Canada, pp. 471–490. ASCE
Berkhoff, J. C. W. 1976 Mathematical models for simple harmonic linear water waves. Delft Hydr. Rep. W 154-IV.
Booij, N. 1983 A note on the accuracy of the Mild-Slope equation. Coastal Engng 7, 191–203.Google Scholar
Chamberlain, P. G. 1991 Wave propagation on water of uneven depth. PhD thesis, University of Reading.
Chamberlain, P. G. 1995 Symmetry relations and decomposition for the mild-slope equation. J. Engng Maths (to appear).Google Scholar
Chamberlain, P. G. & Porter, D. 1995 Decomposition methods for wave scattering by topography with application to ripple beds. Wave Motion (to appear).Google Scholar
Davies, A. G. & Heathershaw, A. D. 1984 Surface-wave propagation over sinusoidally varying topography. J. Fluid Mech. 144, 419–443.Google Scholar
Guazzelli, E., Rey, V. & Belzons, M. 1992 Higher-order Bragg reflection of gravity surface waves by periodic beds. J. Fluid Mech. 245, 301–317.Google Scholar
Kirby, J. T. 1986 A general wave equation for waves over rippled beds. J. Fluid Mech. 162, 171–186.Google Scholar
Luke, J. C. 1967 A variational principle for fluid with a free surface. J. Fluid Mech. 27, 395–397.Google Scholar
Massel, S. R. 1993 Extended refraction-diffraction equation for surface waves. Coastal Engng 19, 97–126.Google Scholar
Miles, J. 1991 Variational approximations for gravity waves in water of variable depth. J. Fluid Mech. 232, 681–688.Google Scholar
O'Hare, T. J. & Davies, A. G. 1993 A comparison of two models for surface-wave propagation over rapidly varying topography. Appl. Ocean Res. 15, 1–11.Google Scholar
Rey, V. 1992 Propagation and local behaviour of normally incident gravity waves over varying topography. Eur. J. Mech B 11, 213–232.Google Scholar