Abstract
Low frequency motion in and outside the surf zone generated by grouping in the incident short waves is considered in a two-dimensional model. This groupiness has two primary effects, which are shown to be of the same order of magnitude. One is the long forced wave bound to the incident short waves, and the other is a time-varying position of the break point, which also contributes to the forcing of low frequency motion (or long waves).
Free, long waves are formed where the short-wave forcing undergoes changes due to shoaling or breaking or by reflection of bound waves. Mathematically this is a consequence of imposed boundary and matching conditions.
The presence of the induced long waves significantly changes the bottom velocities in a way that suggests a close connection with the formation of longshore sand bars.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramowitz, M. and I. A. Stegun (1974). Handbook of Mathematical Functions. Dover, New York.
Bowers, E. C. (1977). Harbour resonance due to set-down beneath wave groups. J. Fluid Mech. 79, 71–93.
Carrier, C. F. and H. P. Greenspan (1958). Water waves of finite amplitude on a sloping beach. J. Fluid Mech., 4, 97–109.
Carrier, C. F. and H. P. Greenspan (1958). Water waves of finite amplitude on a sloping beach. J. Fluid Mech., 4, 97–109.
Chu, V. H. and C. C. Mei (1970). On slowly varying Stokes waves. J. Fluid Mech., 41, 873–87.
Foda, M. A. and C. C. Mei (1981). Nonlinear excitation of long-trapped waves by a group of short swells. 0J. Fluid Mech., 111. 319–45.
Goda, Y. (1970). A synthesis on breaker indices. Trans. Jap. Soc. Civ. Engrs. 2, Part 2.
Guza, R. T. and E. B. Thornton (1982). Swash oscillations on a natural beach. J. Geophys. Res., 87, CI, 483–491.
Guza, R. T. and E. B. Thornton (1985). Observations of surf beat. J. Geophys. Res., 90, C2, 3161–3171.
Kostense, J. K. (1984). Measurements of surf beat and set-down beneath wave groups. Proc. 19th Int.Conf.Coast.Eng.,Houston,Texas, 724–40.
Liu, Philip L.-F. (1988). A note on long waves induced by short-wave groups over a shelf. Submitted to J. Fluid Mech. May 1988.
Longuet-Higgins, M. S., and R. W. Stewart (1962). Radiation stress and mass transport in gravity waves with application to ‘surf beats’. J. Fluid Mech., 13, 481–504.
Longuet-Higgins, M. S., and R. W. Stewart (1964). Radiation stresses in water waves: A physical discussion with applications. Deep Sea Research, 11, 529–562.
Mei, C. C. (1983). The Applied Dynamics of Ocean Surface Waves. Wiley. Mei, C. C. and C. Benmoussa (1984). Long waves induced by short-wave groups over an uneven bottom. J. Fluid Mech. 139. 219–35.
Molin, B. (1982). On the generation of long-period second-order free-waves due to changes in the bottom profile. Ship. Res. Inst. Papers 68, Tokyo, Japan.
Munk, W. H. (1949). Surf beats. Trans. Am. Geophys. Union 30, 849–854.
Ottesen Hansen, N.-E. et al. (1980). Correct reproduction of group-induced long waves. Proc. 17th Int.Conf.Coast.Eng.,Sydney, 784–800.
Ottesen Hansen, N.-E. (1978). Long period waves in natural wave trains. Prog. Rep. 46, Inst. Hydrodyn. Hydr. Eng.,Tech.Univ.Denmark, 13–24.
Phillips, 0. M. (1977). The Dynamics of the Upper Ocean. 2nd Ed. Cambridge Univ. Press.
Sand, S. E. (1982). Long wave problems in laboratory models. J. Waterway, Port, Coastal and Ocean Div., Proc. ASCE, WW 4. 492–503.
Schäffer, H. A. and I. A. Svendsen (1988). Surf beat generation on a mild slope beach. Proc. 21st Int. conf. Coastal Eng.,Malaga, Spain.
Symonds, G., G. A. Huntley and A. J. Bowen (1982). Two dimensional surf beat: Long wave generation by a time-varying break point. J. Geophys. Res., 87, CI, 492–498.
Tucker, M. J. (1950). Surf beats: Sea waves of 1 to 5 min. period. Proc. Roy. Soc. London. A 202, 565–573.
Wright L. D., R. T. Guza and A. D. Short (1982). Surf zone dynamics on a high energy dissipative beach. Mar. Geol., 45, 41–62.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Kluwer Academic Publisher
About this chapter
Cite this chapter
Schäffer, H.A., Jonsson, I.G., Svendsen, I.A. (1990). Free and Forced Cross-Shore Long Waves. In: Tørum, A., Gudmestad, O.T. (eds) Water Wave Kinematics. NATO ASI Series, vol 178. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0531-3_23
Download citation
DOI: https://doi.org/10.1007/978-94-009-0531-3_23
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6725-6
Online ISBN: 978-94-009-0531-3
eBook Packages: Springer Book Archive