Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves

Madsen, Peter Hauge; Sørensen, Ole R.; Schäffer, Hemming A.

doi:10.1016/s0378-3839(97)00028-8

Cited by 288 publications

(176 citation statements)

References 27 publications

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“…Their derivation makes use of the NLSW equations, and thus for consistency the dispersive (l 2 ) terms will be ignored in the numerical simulations for this comparison. The wave and slope parameters for this test case are identical to those used by Madsen et al (1997) and Kennedy et al (2000). A wave train with height 0.006 m and period of 10 s travels in a onedimensional channel with a depth of 0.5 m and a slope of 1:25.…”

Section: Sine Wave Runupmentioning

confidence: 99%

“…Another treatment of moving boundary problem is employing a slot or permeable-seabed technique (Tao, 1983(Tao, , 1984. The first application of the permeable slot with a Boussinesq-type model (Madsen et al, 1997) yielded runup errors on the order of 10% of the maximum. Modifications have been made to this permeable slot technique , increasing the accuracy, but it was also shown that the empirical coefficients that govern the technique cannot be universally determined, due to numerical stability problems .…”

Section: Introductionmentioning

confidence: 99%

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Modeling wave runup with depth-integrated equations

Lynett

Liu

2002

Coastal Engineering

362

212

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In this paper, a moving boundary technique is developed to investigate wave runup and rundown with depth-integrated equations. Highly nonlinear and weakly dispersive equations are solved using a high-order finite difference scheme. An eddy viscosity model is adopted for wave breaking so as to investigate breaking wave runup. The moving boundary technique utilizes linear extrapolation through the wet -dry boundary and into the dry region. Nonbreaking and breaking solitary wave runup is accurately predicted by the proposed model, yielding a validation of both the wave breaking parameterization and the moving boundary technique. Two-dimensional wave runup in a parabolic basin and around a conical island is investigated, and agreement with published data is excellent. Finally, the propagation and runup of a solitary wave in a trapezoidal channel is examined. D

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Section: Sine Wave Runupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling wave runup with depth-integrated equations

Lynett

Liu

2002

Coastal Engineering

362

212

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“…These parameters were given by Madsen et al (1997a). However, the calibration of <t > B and to some extent t 1/2 is related to the accuracy of the computed surface elevation before the breaking occurs.…”

Section: -Bid (C -«) (4)mentioning

confidence: 99%

“…Wave breaking is introduced in the Boussinesq equations on the basis of the surface roller concept for spilling breakers as described by Schaffer et al (1993) and Madsen et al (1997aMadsen et al ( , 1997b. The basic principle is that the surface roller is considered as a volume of water carried by the wave with the wave celerity.…”

Section: Breaker Model Based On the Roller Conceptmentioning

confidence: 99%

Nearshore Wave Dynamics Simulated by Boussinesq Type Models

Sørensen¹,

Madsen²,

Schäffer³

1999

Coastal Engineering 1998

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This paper presents a numerical study of nearshore wave dynamics including the surf zone. Two different time-domain Boussinesq type formulations are applied for this purpose. The first model incoporates Pade [2,2] dispersion characteristics and lowest order nonlinearity. The second and more sophisticated model incorporates Pade [4,4] characteristics and higher-order nonlinearity in the dispersive terms. The models are validated on the shoaling and breaking of regular and irregular waves with and without an ambient current.

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“…Further a linear shoaling analysis of the new equations and a verification of the numerical model with respect to shoaling and refraction-diffraction in deep and shallow water are generalized. In nineties the model evolved to two-dimensional form of equations of the Boussinesq type (Madsen et al, 1997a;1997b). It's features improved linear dispersion characteristics, possibility of wave breaking, and a moving boundary at the shoreline.…”

Section: Review Of Short Wave Modelingmentioning

confidence: 99%