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Edge waves forced by short-wave groups

Published online by Cambridge University Press:  26 April 2006

Hemming A. Schäuffer
Hemming A. Schäuffer
Affiliation:
Danish Hydraulic Institute, Agern Allé5, DK-2970 Hørsholm, Denmark
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Abstract

On the basis of the theory for infragravity waves induced by short-wave groups developed by Schäffer (1993), three-dimensional infragravity waves are analysed. The theory relies on the linearized depth-integrated conservation equations for mass and momentum combined to give a second-order long-wave equation with forcing expressions in terms of the radiation stress. This forcing gives a dynamic set-up originating from oscillations of the break-point position and a dynamic set-down bound to the short-wave groups. For small angles of incidence leaky-mode solutions are found while trapped modes appear when the primary waves are sufficiently oblique. In the latter case resonant edge-wave excitation may occur. A semi-analytical steady-state solution for the infragravity motion is presented. The solution is restricted to periodicity along a plane beach connected to a shelf and valid only for small primary-wave modulations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 259 , 25 January 1994 , pp. 125 - 148
Copyright
© 1994 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions. Dover.
Bowen, A. J. & Guza, R. R. 1978 Edge waves and surf beat. J. Geophys. Res. 83, 1913–1920.Google Scholar
Eckart, C. 1951 Surface waves on water of variable depth. Wave Rep. 100. Scripps Inst. of Oceanogr., Univ. of California, La Jolla.
Erdélyi, A. 1953 Higher Transcendental Functions, vol. 1. McGraw-Hill.
Foda, M. A. & Mei, C. C. 1981 Nonlinear excitation of long-trapped waves by a group of short swells. J. Fluid Mech. 111, 319–345.Google Scholar
Gallagher, B. 1971 Generation of surf beat by non-linear wave interactions. J. Fluid Mech. 49, 1–20.Google Scholar
Huntley, G. A., Guza, R. T. & Thornton, E. B. 1981 Field observations of surf beat. 1. Progressive edge waves. J. Geophys. Res. 86, C7, 6451–6466.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1962 Radiation stress and mass transport in gravity waves with application to ‘surf beats’. J. Fluid Mech. 13, 481–504.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1964 Radiation stresses in water waves: A physical discussion with applications. Deep-Sea Res. 11, 529–562.Google Scholar
Mei, C. C. & Benmoussa, C. 1984 Long waves induced by short-wave groups over an uneven bottom. J. Fluid Mech. 139, 219–235.Google Scholar
Munk, W. H., Snodgrass, F. E. & Carrier, G. F. 1956 Edge waves on the continental shelf. Science 123, 127–132.Google Scholar
Schäffer, H. A. 1990 Infragravity water waves induced by short-wave groups. Series Paper 50. Inst. Hydrodyn. Hydr. Eng. (ISVA), Techn. Univ. Denmark.
Schäffer, H. A. 1993 Infragravity waves induced by short-wave groups. J. Fluid Mech. 247, 551–588 (referred to herein as I).Google Scholar
Schäffer, H. A. & Jonsson, I. G. 1992 Edge waves revisited. Coastal Engng 16, 349–368.Google Scholar
Symonds, G., Huntley, G. A. & Bowen, A. J. 1982 Two dimensional surf beat: Long wave generation by a time-varying break point. J. Geophys. Res. 87, C1, 492–498.Google Scholar