Hostname: page-component-7479d7b7d-qs9v7 Total loading time: 0 Render date: 2024-07-10T11:25:36.635Z Has data issue: false hasContentIssue false

Reflection of a high-amplitude solitary wave at a vertical wall

Published online by Cambridge University Press:  10 July 1997

M. J. COOKER
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
P. D. WEIDMAN
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309, USA
D. S. BALE
Affiliation:
Department of Physics, University of Colorado, Boulder, CO 80309, USA

Abstract

The collision of a solitary wave, travelling over a horizontal bed, with a vertical wall is investigated using a boundary-integral method to compute the potential fluid flow described by the Euler equations. We concentrate on reporting new results for that part of the motion when the wave is near the wall. The wall residence time, i.e. the time the wave crest remains attached to the wall, is introduced. It is shown that the wall residence time provides an unambiguous characterization of the phase shift incurred during reflection for waves of both small and large amplitude. Numerically computed attachment and detachment times and amplitudes are compared with asymptotic formulae developed using the perturbation results of Su & Mirie (1980). Other features of the flow, including the maximum run-up and the instantaneous wall force, are also presented. The numerically determined residence times are in good agreement with measurements taken from a cine film of solitary wave reflection experiments conducted by Maxworthy (1976).

Type
Research Article
Copyright
© 1997 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.)