Wave-Breaking Model for Boussinesq-Type Equations Including Roller Effects in the Mass Conservation Equation
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 136, Issue 1
Abstract
We investigate the ability of a 1D fully nonlinear Boussinesq model including breaking to reproduce surf zone waves in terms of wave height and nonlinear intraphase properties such as asymmetry and skewness. An alternative approach for wave-breaking parameterization including roller effects through diffusive-type terms on both, the mass conservation and momentum equations is developed and validated on regular wave and solitary wave experiments as an attempt to improve wave height and left-right asymmetry estimates. The new approach is able to reproduce wave height decay, and intraphase nonlinear properties within the entire surf zone of spilling breakers without requiring temporal evolution of model parameters.
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Acknowledgments
This work has been supported by FONDECYT Research Grant No. UNSPECIFIED11060312 and was also performed within the framework of the IDAO/PATOM program (Interactions et Dynamique de l’Atmosphère et de l’Océan) sponsored by the CNRS/INSU. This work was accomplished during a sabbatical leave of Professor Eric Barthélemy at the Departamento de Ingeniería Hidráulica y Ambiental, Pontificia Universidad Católica de Chile (PUC). Financial support from the School of Engineering (PUC), the Institut National Polytechnique de Grenoble, the French Ministry of Education, and ECOS-Conicyt Research Grant No. UNSPECIFIEDC07U01 is gratefully acknowledged.
References
Andersen, O., and Fredsoe, J. (1983). “Transport of suspended sediment along the coast.” Progress Rep. No. 54, Institute of Hydrodynamics and Hydraulic Engineering, ISVA, Technical Univ. of Denmark, 33–46.
Barthélemy, E. (2004). “Nonlinear shallow water theories for coastal waves.” Surv. Geophys., 25(3–4), 315–337.
Bayram, A., and Larson, M. (2000). “Wave transformation in the nearshore zone: Comparison between a Boussinesq model and field data.” Coastal Eng., 39, 149–171.
Bonneton, P. (2001). “A note on wave propagation in the inner surf zone.” C. R. Acad. Sci. Paris, 329, Série IIb 27–33.
Bonneton, P. (2007). “Modelling of periodic wave transformation in the inner surf zone.” Ocean Eng., 34, 1459–1471.
Briganti, R., Musumeci, R. E., Bellotti, G., Brocchini, M., and Foti, E. (2004). “Boussinesq modeling of breaking waves: Description of turbulence.” J. Geophys. Res., 109, C07015.
Brocchini, M., Drago, M., and Iovenitti, L. (1992). “The modeling of short waves in shallow waters. Comparisons of numerical models based on Boussinesq and Serre equations.” Proc., 23rd Int. Conf. Coastal Eng., ASCE, Reston, Va., 76–88.
Cienfuegos, R. (2005). “Modélisation numérique des houles bidimensionnelles et du déferlement bathymétrique.” Ph.D. thesis, Institut National Polytechnique de Grenoble, Grenoble, France.
Cienfuegos, R., Barthélemy, E., and Bonneton, P. (2006a). “A fourth order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part I: Model development and analysis.” Int. J. Numer. Methods Fluids, 51(11), 1217–1253.
Cienfuegos, R., Barthélemy, E., and Bonneton, P. (2006b). “Nonlinear surf zone wave properties as estimated from Boussinesq modelling: Random waves and complex bathymetries.” Proc., 30th Int. Conf. Coastal. Eng., ASCE, Reston, Va.
Cienfuegos, R., Barthélemy, E., and Bonneton, P. (2007). “A fourth order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part II: Boundary conditions and validation.” Int. J. Numer. Methods Fluids, 53(9), 1423–1455.
Cointe, R., and Tulin, M. (1994). “A theory of steady breakers.” J. Fluid Mech., 276, 1–20.
Cox, D. (1995). “Experimental and numerical modeling of surf zone hydrodynamics.” Ph.D. thesis, Univ. of Delaware, Newark, Del.
Dally, W., and Brown, C. (1995). “A modeling investigation of the breaking wave roller with application to cross-shore currents.” J. Geophys. Res., 100(C12), 24873–24883.
Deigaard, R., and Fredsøe, J. (1989). “Shear stress distribution in dissipative water waves.” Coastal Eng., 13, 357–378.
Gaitonde, D., Shang, J., and Young, J. (1999). “Practical aspects of higher-order numerical schemes for wave propagation phenomena.” Int. J. Numer. Methods Eng., 45, 1849–1869.
Govender, K., Mocke, G. P., Alport, M. J. (2002). “Video-imaged surf zone wave and roller structures and flow fields.” J. Geophys. Res., 107(C7), 3072.
Hansen, J. B., and Svendsen, I. A. (1979). “Regular waves in shoaling water: Experimental data.” Technical Report, ISVA Series, Paper 21.
Karambas, T., and Koutitas, C. (1992). “A breaking wave propagation model based on the Boussinesq equations.” Coastal Eng., 18, 1–19.
Kennedy, A., Chen, Q., Kirby, J., and Dalrymple, R. (2000). “Boussinesq modeling of wave transformation, breaking and runup. I: 1D.” J. Waterway, Port, Coastal, Ocean Eng., 126(1), 39–48.
Kirby, J., and Kaihatu, J. (1996). “Structure of frequency domain models for random wave breaking.” Proc., 25th Int. Conf. Coastal Eng., ASCE, Reston, Va, 1114–1155.
Kobayashi, N., De Silva, G., and Watson, K. (1989). “Wave transformation and swash oscillation on gentle and steep slopes.” J. Geophys. Res., 94, 951–966.
Lynett, P. (2006). “Nearshore wave modeling with high-order Boussinesq-type equations.” J. Waterway, Port, Coastal, Ocean Eng., 132, 348–357.
Lynett, P., Wu, T., and Liu, P. (2002). “Modeling wave runup with depth-integrated equations.” Coastal Eng., 46, 89–107.
Madsen, P., Sørensen, O., and Schäffer, H. (1997a). “Surf zone dynamics simulated by a Boussinesq-type model: Part I. Model description and cross-shore motion of regular waves.” Coastal Eng., 32, 255–288.
Madsen, P., Sørensen, O., and Schäffer, H. (1997b). “Surf zone dynamics simulated by a Boussinesq-type model: Part II. Surf beat and swash oscillations for wave groups and irregular waves.” Coastal Eng., 32, 289–319.
Mignot, E., and Cienfuegos, R. (2009). “On the application of a Boussinesq model to river flows including shocks.” Coastal Eng., 56(1), 23–31.
Musumeci, R., Svendsen, I., and Veeramony, J. (2005). “The flow in the surf zone: A fully nonlinear Boussinesq-type approach.” Coastal Eng., 52, 565–598.
Okamoto, T., and Basco, D. (2006). “The relative trough Froude number for initiation of wave breaking: Theory, experiments and numerical model confirmation.” Coastal Eng., 53(8), 675–690.
Ozanne, F., Chadwick, A., Huntley, D., Simmonds, D., and Lawrence, J. (2000). “Velocity predictions for shoaling and breaking waves with a Boussinesq-type model.” Coastal Eng., 41, 361–397.
Raubenheimer, B., Guza, R., and Elgar, S. (1996). “Wave transformation across the inner surf zone.” J. Geophys. Res., 101(C11), 25589–25598.
Schäffer, H., Madsen, P., and Deigaard, R. (1993). “A Boussinesq model for waves breaking in shallow water.” Coastal Eng., 20, 185–202.
Seabra-Santos, F., Renouard, D., and Temperville, A. (1987). “Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle.” J. Fluid Mech., 176, 117–134.
Svendsen, I. (1984). “Mass flux and undertow in a surf zone.” Coastal Eng., 8, 347–365.
Svendsen, I., Madsen, P., and Hansen, J. (1978). “Wave characteristics in the surf zone.” Proc., 16th Int. Conf. Coastal Eng., ASCE, Reston, Va, 520–539.
Svendsen, I., Veeramony, J., Bakunin, J., and Kirby, J. (2000). “The flow in weak turbulent hydraulic jumps.” J. Fluid Mech., 418, 25–57.
Synolakis, C. (1987). “The runup of solitary waves.” J. Fluid Mech., 185, 523–545.
Ting, F., and Kirby, J. (1994). “Observation of undertow and turbulence in a laboratory surf zone.” Coastal Eng., 24, 51–80.
Veeramony, J., and Svendsen, I. (2000). “The flow in surf-zone waves.” Coastal Eng., 39, 93–122.
Vincent, S., Caltagirone, J. -P., and Bonneton, P. (2001). “Numerical modelling of bore propagation and run-up on sloping beaches using a MacCormack TVD scheme.” J. Hydraul. Res., 39(1), 41–49.
Zelt, J. (1991). “The run-up of nonbreaking and breaking solitary waves.” Coastal Eng., 15, 205–246.
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© 2010 ASCE.
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Received: Jul 24, 2008
Accepted: Mar 10, 2009
Published online: Dec 15, 2009
Published in print: Jan 2010
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