Keywords
Boussinesq-type equations
breaker depth index
numerical models
How to Cite
Abstract
The breaker depth index, γb, is commonly used to determine the wave height to water depth ratio where the wave will break (Horikawa, 1988). In the present study, γb has been calculated using a fully nonlinear Boussinesq Type Equations (BTE) wave model with implemented BCI (Breaking Celerity Index). The BCI is a phase-resolving type breaking criterion for calculating the incipient wave breaking conditions (D'Alessandro and Tomasicchio, 2008). The model suitability in predicting γb has been verified against physical data from an experimental investigation conducted with incident regular waves propagating along uniform 1:20 and 1:50 slope beaches (G.V. dos Reis, 1992), and estimates of γb from five existing empirical formulae (Battjes, 1974; Ostendorf and Madsen, 1979; Singamsetti and Wind, 1980; Smith and Kraus, 1990; Goda, 2010). The comparisons showed that BCI presents a better agreement with the physical data with respect to the other investigated formulae in determining the value of γb, independently from the breaker type. In addition, the verification of the BCI in determining γb has been extended to the observed data from a large-scale laboratory experiment on wave hydrodynamics performed over a fixed-bed barred beach (Tomasicchio and Sancho, 2002).References
Battjes, J. 1974. Surf similarity, Proceedings 14th Int. Conf. Coastal Engineering, Copenhagen, ASCE, 1050-1061.
Battjes, J.A., M.J.F. Stive. 1985. Calibration and verification of a dissipation model for random breaking waves, Journal of Geophysical Research 90(C5), 9159-9167.
Brunone, B., G.R. Tomasicchio. 1997. Wave kinematics at steep slopes: Second-order model. Journal of Waterway, Port, Coastal and Ocean Engineering, 123, 223-232.
Camenen, B., and M. Larson. 2007. Predictive formulas for breaker depth index and breaker type, Journal of Coastal Research, 23(4), 1028-1041.
D'Alessandro, F., G.R. Tomasicchio. 2008. The BCI criterion for the initiation of breaking process in Boussinesq type equations wave models, Coastal Engineering, 55, 1174-1184.
Galvin, C.J.Jr. 1969. Breaker travel and choice of design wave height, Journal of Waterways and Harbors Div., ASCE, 95 (WW2): 175-200.
Goda, Y. 1964. Wave forces on a vertical circular cylinder: experiments and proposed method of wave force computation, Report Port and Harbour Res. Inst., 8: 1-74.
Goda, Y. 1970. A synthesis of breaker indices, Trans. Jap. Soc. of Civil Engineers, 2, 39-49.
Goda, Y. 1974. New wave pressure formulae for composite breakwaters, Proceedings 14th Int. Conf. Coastal Engineering, Copenhagen, ASCE, 1702-1720.
Goda, Y. 2010. Reanalysis of regular and random breaking wave statistics, Coastal Engineering Journal, 52(1), 71-106.
Gonsalves Veloso dos Reis, M.T.L. 1992. Characteristics of waves in the surfzone, MS Thesis, Department of Civil Engineering, University of Liverpool, Liverpool.
Horikawa, K. 1988. Nearshore Dynamics and Coastal Processes, Theory, Measurement and Predictive Models, University of Tokyo Press, Tokyo, Japan.
Iversen, H.W. 1951. Laboratory study of breakers, Gravity Waves Proc. NBS Semicentennial Symp., NBS Circular 521: 9-32.
Kamphuis, J.W. 1991. Incipient wave breaking, Coastal Engineering, 15, 185-203.
Kennedy, A.B., Q. Chen, J.T. Kirby, and R.A. Dalrymple. 2000. Boussinesq modeling of wave transformation, breaking and run-up. I: 1D, Journal of Waterway, Port, Coastal and Ocean Engineering, 126, 39-47.
Kirby, J.T., G. Wei, Q. Chen, A.B. Kennedy, and R.A. Dalrymple. 1998. FUNWAVE 1.0 Fully Nonlinear Boussinesq Wave Model Documentation and User's Manual, Research Report N0 CACR-98-06, Center for Applied Coastal Res., University of Delaware, Newark.
Kishi, T., and S. Iohara. 1958. Researches on coastal dikes (7) - experimental study on wave transformation and breaking waves, Rept. Public Works Res. Inst., 95: 185-197 (in Japanese).
Kobayashi, N., M.D. Orzech, B.D. Johnson, M.N. Herrman. 1997. Probability modeling of surf zone and swash dynamics, Proceedings Int. Symp. on Ocean Wave Measurement and Analysis - Waves' 97. ASCE, Reston, VA, pp. 107-121.
Kobayashi, N., M.N. Herrman, B.D. Johnson, M.D. Orzech. 1998. Probability distribution of surface elevation in surf and swash zones, Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE 124(3), 99-107.
Kobayashi, N., G.R. Tomasicchio, B. Brunone. (2000). Partial standing waves at a steep slope, Journal of Coastal Research, 16(2), pp. 379-384.
Lara, J.L., I.J. Losada, and P. L.-F. Liu. 2006. Breaking waves over a mild gravel slope: Experimental and numerical analysis, J. Geophys. Res., 111 (C11019), 1-26.
Li, Y.C., G.H. Dong, and B. Teng. 1991. Wave breaker indices in finite water depth, China Ocean Engineering, 5 (1): 51-64.
Liu, P.L.-F., I.J. Losada. 2002. Wave propagation modeling in coastal engineering, Journal of Hydraulic Research, 40(3), 229-240.
Madsen, P.A., R. Murray, and O.R. Sørensen. 1991. A new form of the Boussinesq equations with improved linear dispersion characteristics, Coastal Engineering, 15, 371-388.
McCowan, J. 1894. On the highest waves in water, Phil. Mag. Ser., 5, 36: 351-358.
Miche, R. 1944. Mouvements ondulatoires de l'ocean pour une eau profonde constante et d´ecroissante, Ann. des Ponts et Chaussèes, 25-78, 131-164, 270-292, 369-406.
Munk, W.H. 1949. The solitary wave theory and its applications to surf problem, Ann. New York Acad. Sci., 51: 376-423.
Nwogu, O. 1993. Alternative form of Boussinesq equations for nearshore wave propagation, Journal of Waterway, Port, Coastal and Ocean Engineering, 119, 618-638.
Okamoto, T., and D.R. Basco. 2006. The Relative Trough Froude Number for initiation of wave breaking: Theory, experiments and numerical model confirmation, Coastal Engineering, 53, 675-690.
Ostendorf, D., and O. Madsen. 1979. An analysis of longshore current and associated sediment transport in the surf zone, Technical Report no 241, Dep. Civil Eng., MIT, USA, 169.
Peregrine, D.H. 1967. Long waves on a beach, Journal of Fluid Mechanics, 27(4), 815-827.
Peregrine, D.H. 1983. Breaking waves on beaches, Annu. Rev. Fluid Mech., 15: 149-178.
Rattanapitikon, W. and T. Shibayama. 2000. Verification and modification of breaker height formulas, Coastal Engineering Journal, 42(4), 389-406.
Sancho, F. 2002. Surface wave statistics past a barred beach, Proceedings of 6th Congress of SIMAI, Chia Laguna.
Schäffer, H.A., P.A. Madsen, and R. Deigaard. 1993. A Boussinesq model for waves breaking in shallow water, Coastal Engineering, 20, 185-202.
Singamsetti, S. and H. Wind. 1980. Characteristics of breaking and shoaling periodic waves normally incident on to plane beaches of constant slope, Technical Report M1371, Delft Univ. Tech., The Netherlands.
Smith, J.W., and N.C. Kraus. 1991. Laboratory study of wave-breaking over bars and artificial reefs. Journal of Waterway, Port, Coastal, and Ocean Engineering, ASCE, 117(4): 307-325.
Tomasicchio, G.R., F. Sancho. 2002. On wave induced undertow at a barred beach, Proceedings of 28th International Conference on Coastal Engineering, ASCE, pp. 557-569.
Utku, M. 1999. The Relative Trough Froude Number. A new criteria for wave breaking, Ph.D. Dissertation, Dept. of Civil and Enviromental Engineering, Old Dominion University, Norfolk, VA.
Van Rijn, L. 1990. Principles of fluid flow and surface waves in river, estuaries, seas and ocean. Aqua Publications, The Netherlands.
Yamada, H., and T. Shiotani. 1968. On the highest water waves of permanent type. Bull. Disaster Prevention Res. Inst., Kyoto Univ., 18-2(135): 1-22.
Wei, G., J.T. Kirby, S.T. Grilli, and R. Subramanya. 1995. A fully nonlinear Boussinesq model for surface waves. I: highly non linear, unsteady waves. Journal of Fluid Mechanics, 294, 71-92.