BORE PROPAGATION SPEED AT THE TERMINATION OF WAVE BREAKING

Takashi Okamoto, Conceição Juana Fortes, David R. Basco

Abstract


Wave breaking is the most important event in nearshore hydrodynamics because of the energy exertion and mass transportation during the event drive all the nearshore phenomena, such as wave set-up/down, long shore current, and nearshore circulation. Wave celerity is a key parameter in wave breaking especially for the mass transportation, the energy dissipation during the wave breaking event, and the wave breaking index calculation, for example. There are many models to calculate the wave celerity during the breaking event (bore propagation speed) and it is well known that the bore propagation speed is faster than that is given by linear wave theory. But Okamoto et al. (2008) found the bore propagation speed at the termination location of wave breaking becomes much slower than the theoretical estimation when the termination of wave breaking occurs on inversely sloped bottom. In this paper, the bore propagation speed at the termination location of wave breaking is examined with the experimental data collected in a wave tank with simplified bar-trough beach settings. Comparisons with theoretical models are presented. Fourier analysis is performed to investigate the evolution of higher harmonics and synthesized time series, which is a simple summation of linear wave components, is constructed by using the obtained information to calculate the wave celerity during and after the wave breaking. Calculation result reveals that as the breaking wave approaches to the termination, the bore propagation speed decreases towards the value which can be explained by the existence of slowly and independently propagating higher harmonics.

Keywords


wave breaking; bore propagation speed; wave tank experiments; harmonics composition

References


Bonneton, P. 2004. Wave Celerity in the Inner Surf Zone, Proceedings of 29th International conference on Coastal Engineering (Lisbon), ASCE, 392-401.

Catalan, P.A. and M.C. Haller. 2008. Remote sensing of breaking wave phase speeds with application of non-linear depth inversions, Coastal Engineering, 55, 93-111 http://dx.doi.org/10.1016/j.coastaleng.2007.09.010

Kirby, J.T. and R.A. Dalrymple. 1986. An approximate model for nonlinear dispersion in monochromatice wave propagation models, Coastal Engineering, 9, 545-561 http://dx.doi.org/10.1016/0378-3839(86)90003-7

Madsen, P.A., O.R. Sørensen, and H.A. Schäffer. 1997. Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves, Coastal Engineering, 32, 255-287 http://dx.doi.org/10.1016/S0378-3839(97)00028-8

Misra, S.K., A.B. Kennedy, and J.T. Kirby. 2003. An approach to determining nearshore bathymetry using remotely sensed ocean surface dynamics, Coastal Engineering, 47, 265-293 http://dx.doi.org/10.1016/S0378-3839(02)00118-7

Okamoto, T., D.R. Basco, and C.J. Fortes. 2006. The Relative Trough Froude Number for Termination of Wave Breaking, Proceedings of 30th International Conference on Coastal Engineering (San Diego), ASCE, 180-192

Okamoto, T., C.J. Fortes, and D.R. Basco. 2008. Wave Breaking Termination on Bar-trough Shaped Beaches, Proceedings of the 18th International Offshore and Polar Engineering Conference (Vancouver), 811-819

Schäffer, H.A., P.A. Madsen, and R.A. Deigaard. 1993. A Boussinesq Model for Wave Breaking in Shallow Water, Coastal Engineering, 20, 185-202 http://dx.doi.org/10.1016/0378-3839(93)90001-O

Stive, M.J.F. 1984. Energy dissipation in waves breaking on gentle slopes, Coastal Engineering, 8, 99-127 http://dx.doi.org/10.1016/0378-3839(84)90007-3

Svendsen, I.A., 1984. Wave heights and set-up in a surf zone, Coastal Engineering, 8, 303-329 http://dx.doi.org/10.1016/0378-3839(84)90028-0

Svendsen, I.A., P.A. Madsen, and J.B. Hansen. 1979. Wave Characteristics in the Surf Zone, Proceedings of 16th International Conference on Coastal Engineering (Hamburg), ASCE, 520-539

Svendsen, I.A., W. Qin, and B.A. Ebersole. 2003. Modeling waves and currents at the LSTF and other laboratory facilities, Coastal Engineering, 50, 19-45 http://dx.doi.org/10.1016/S0378-3839(03)00077-2


Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.