Boussinesq Modeling of Wave Transformation, Breaking, and Runup. I: 1D
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 126, Issue 1
Abstract
Parts I and II of this paper describe the extension and testing of two sets of Boussinesq-type equations to include surf zone phenomena. Part I is restricted to 1D tests of shoaling, breaking, and runup, while Part II deals with two horizontal dimensions. The model uses two main extensions to the Boussinesq equations: a momentum-conserving eddy viscosity technique to model breaking, and a “slotted beach,” which simulates a shoreline while allowing computations over a regular domain. Bottom friction is included, using a quadratic representation, while the 2D implementation of the model also considers subgrid mixing. Comparisons with experimental results for regular and irregular wave shoaling, breaking and runup for both one and two horizontal dimensions show good agreement for a variety of wave conditions.
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References
1.
Carrier, G. F., and Greenspan, H. P. (1958). “Water waves of finite amplitude on a sloping beach.” J. Fluid Mech., Cambridge, England, 4, 97–109.
2.
Chen, Q., Kirby, J. T., Dalrymple, R. A., Kennedy, B. A., and Chawla, A. (2000). “Boussinesq modelling of wave transformation, breaking, and runup. II: 2D.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 126(1), 57–62.
3.
Chen, Q., Kirby, J. T., Dalrymple, R. A., Kennedy, A. B., and Haller, M. C. (1999). “Boussinesq modelling of a rip current system.” J. Geophys. Res., 104(9), 20,617–20,637.
4.
Heitner, K. L., and Housner, G. W. (1970). “Numerical model for tsunami runup.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 96, 701–719.
5.
Horikawa, K., and Kuo, C.-T. (1966). “A study on wave transformation inside surf zone.” Proc., Int. Conf. Coastal Eng., ASCE, New York, 217–233.
6.
Madsen, P. A., and Schäffer, H. A. (1998). “Higher order Boussinesq-type equations for surface gravity waves—Derivation and Analysis.” Philosophical Trans. Royal Soc., London, 356, 1–59.
7.
Madsen, P. A., and Sørensen, O. R. (1992). “A new form of the Boussinesq equations with improved linear dispersion characteristics. Part II: A slowly varying bathymetry.” Coast. Engrg., 18, 183–204.
8.
Madsen, P. A., Sørensen, O. R., and Schäffer, H. A. (1997a). “Surf zone dynamics simulated by a Boussinesq-type model. Part I: Model description and cross-shore motion of regular waves.” Coast. Engrg., 32, 255–287.
9.
Madsen, P. A., Sørensen, O. R., and Schäffer, H. A. (1997b). “Surf zone dynamics simulated by a Boussinesq-type model. Part II: Surf beat and swash oscillations for wave groups and irregular waves.” Coast. Engrg., 32, 289–319.
10.
Mase, H. (1995). “Frequency down-shift of swash oscillation compared to incident waves.”J. Hydr. Res., Delft, The Netherlands, 33(3), 397–411.
11.
Mase, H., and Kirby, J. T. (1992). “Hybrid frequency-domain KdV equation for random wave transformation.” Proc., 23rd Int. Conf. Coast. Eng., ASCE, New York, 474–487.
12.
Nwogu, O. (1993). “Alternative form of Boussinesq equations for near shore wave propagation.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 119(6), 618–638.
13.
Özkan-Haller, H. T., and Kirby, J. T. (1997). “A Fourier-Chebyshev collocation method for the shallow water equations including shoreline runup.” Appl. Ocean Rs., 19, 21–34.
14.
Peregrine, D. H. (1967). “Long waves on a beach.” J. Fluid Mech., 27, Cambridge, England, 815–827.
15.
Schäffer, H. A., Madsen, P. A., and Deigaard, R. A. (1993). “A Boussinesq model for waves breaking in shallow water.” Coast. Engrg., 20, 185–202.
16.
Svendsen, I. A., Yu, K., and Veeramony, J. (1996). “A Boussinesq breaking wave model with vorticity.” Proc., 25th Int. Conf. Coastal Engrg., ASCE, New York, 1192–1204.
17.
Tao, J. (1983). “Computation of wave run-up and wave breaking.” Internal Rep., Danish Hydraulics Institute, Horsholm, Denmark.
18.
Tao, J. (1984). “Numerical modelling of wave runup and breaking on the beach.” Acta Oceanologica Sinica, Beijing, 6(5), 692–700 (in Chinese).
19.
Wei, G., and Kirby, J. T. (1996). “A coastal processes model based on time-domain Boussinesq equations.” Res. Rep. No. CACR-96-01, Center for Applied Coastal Research, Newark, Del.
20.
Wei, G., Kirby, J. T., Grilli, S. T., and Subramanya, R. (1995). “A fully nonlinear Boussinesq model for surface waves. I: Highly nonlinear, unsteady waves.” J. Fluid Mech., Cambridge, England, 294, 71–92.
21.
Wei, G., Kirby, J. T., and Sinha, A. (1999). “Generation of waves in Boussinesq models using a source function model.” Coast. Engrg., 36, 271–299.
22.
Zelt, J. A. (1991). “The run-up of nonbreaking and breaking solitary waves.” Coast. Engrg., 15, 205–246.
Information & Authors
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 126 • Issue 1 • January 2000
Pages: 39 - 47
History
Received: Jan 28, 1999
Published online: Jan 1, 2000
Published in print: Jan 2000
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