Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T06:50:27.996Z Has data issue: false hasContentIssue false

Experimental observations of edge waves

Published online by Cambridge University Press:  26 April 2006

S. J. Buchan
Affiliation:
Steedman Science & Engineering, 31 Bishop St., Jolimont, Western Australia, 6014
W. G. Pritchard
Affiliation:
Department of Mathematics, Penn State University, University Park, PA 16802, USA

Abstract

The main purpose of this paper is to provide some carefully documented experimental observations of the subharmonic generation of edge waves over a plane beach by waves normally incident on the beach from the distant ocean. In order to establish experimentally the details of the subharmonic instability mechanism, it is important first to determine the properties of the primary wave field whose stability is to be investigated. Thus, a detailed appraisal has been made of the wave field established in the tank and over the beach in the absence of edge waves. These data have been particularly useful in defining the amplitudes of the incident- and reflected-wave fields at the toe of the beach, the magnitudes of which are central to the triggering of the edge-wave instability. Details are presented of the edge-wave field over the beach, as well as marginal stability curves and initial growth rates of the instability, the latter two of which are compared with theoretical estimates obtained from extant theories of the instability mechanism. Some experiments are also described in which edge waves were established as modes forced by topographical imperfections at the beach.

Type
Research Article
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

Benjamin, T. B., Boczar-Karakiewicz, B. & Pritchard, W. G. 1987 Reflection of water waves in a channel with corrugated bed. J. Fluid Mech. 185, 249.Google Scholar
Benjamin, T. B., Bona, J. L. & Mahony, J. J. 1972 Model equations for long waves in nonlinear dispersive systems. Phil. Trans. R. Soc. Lond. A 272, 47.Google Scholar
Birchfield, G. E. & Galvin, C. J. JR 1975 Generation of edge waves through nonlinear subharmonic resonance. Geol. Soc. Am. Mem. 142, 15.Google Scholar
Bona, J. L., Pritchard, W. G. & Scott, L. R. 1981 An evaluation of a model equation for water waves. Phil. Trans. R. Soc. Lond. A 302, 457.Google Scholar
Galvin, C. J. JR 1965 Resonant edge waves on laboratory beaches. Eos Trans. Am. Geophys. Union 436, 112.Google Scholar
Guza, R. T. & Bowen, A. J. 1976 Finite amplitude edge waves. J. Mar. Res. 34, 268.Google Scholar
Guza, R. T. & Davis, R. E. 1974 Excitation of edge waves by waves incident on a beach. J. Geophys. Res. 79, 1285.Google Scholar
Guza, R. T. & Inman, D. L. 1975 Edge waves and beach cusps. J. Geophys. Res. 80, 4529.Google Scholar
Lin, N. K. 1988 Excitation of coastal edge waves. Ocean Phys. Engng 12, 65.Google Scholar
Mahony, J. J. & Pritchard, W. G. 1980 Wave reflexion from beaches. J. Fluid Mech. 101, 809.Google Scholar
Mathew, J. & Akylas, T. R. 1990 On the radiation damping of finite-amplitude progressive edge waves. Proc. R. Soc. Lond. A 431, 419.Google Scholar
Miles, J. W. 1990a Parametrically excited standing edge waves. J. Fluid Mech. 214, 43.Google Scholar
Miles, J. W. 1990b Wave reflection from a gently sloping beach. J. Fluid Mech. 214, 59.Google Scholar
Minzoni, A. A. & Whitham, G. B. 1977 On the excitation of edge waves on beaches. J. Fluid Mech. 79, 273.Google Scholar
Rockliff, N. 1978 Finite amplitude effects in free and forced edge waves. Math. Proc. Camb. Philos. Soc. 83, 463.Google Scholar
Ursell, F. 1952 Edge waves on a sloping beach. Proc. R. Soc. Lond. A 214, 79.Google Scholar
Ursell, F., Dean, R. G. & Yu, Y. S. 1960 Forced small-amplitude water waves: a comparison of theory and experiment. J. Fluid Mech. 7, 33.Google Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. In Handbuch der Physik (ed. W. Flügge) vol. 9, pp. 446778. Springer.
Yeh, H. H. 1986 Experimental study of standing edge waves. J. Fluid Mech. 168, 291.Google Scholar