Journal ArticleDOI
A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry
Per A. Madsen,Ole R. Sørensen +1 more
TLDR
In this paper, a new form of the Boussinesq equations applicable to irregular wave propagation on a slowly varying bathymetry from deep to shallow water is introduced, which incorporate excellent linear dispersion characteristics, and are formulated and solved in two horizontal dimensions.About:
This article is published in Coastal Engineering.The article was published on 1992-12-01. It has received 783 citations till now. The article focuses on the topics: Boussinesq approximation (water waves) & Shallow water equations.read more
Citations
More filters
Journal ArticleDOI
A third-generation wave model for coastal regions: 1. Model description and validation
TL;DR: In this article, a third-generation numerical wave model to compute random, short-crested waves in coastal regions with shallow water and ambient currents (Simulating Waves Nearshore (SWAN)) has been developed, implemented, and validated.
Journal ArticleDOI
Alternative form of Boussinesq equations for nearshore wave propagation
TL;DR: In this paper, a new form of the Boussinesq equations is derived using the velocity at an arbitrary distance from the still water level as the velocity variable instead of the commonly used depth-averaged velocity.
Book
Waves in Oceanic and Coastal Waters
TL;DR: The SWAN wave model as discussed by the authors is a wave model based on linear wave theory (SWAN) for oceanic and coastal waters, and it has been shown to be effective in detecting ocean waves.
Journal ArticleDOI
Boussinesq modeling of wave transformation, breaking, and runup. ii: 2d
TL;DR: In this article, an extended Boussinesq model for surf zone hydrodynamics in two horizontal dimensions is implemented and verified using an eddy viscosity term.
Journal ArticleDOI
A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation
TL;DR: A high-order adaptive time-stepping TVD solver for the fully nonlinear Boussinesq model of Chen (2006), extended to include moving reference level as in Kennedy et al. (2001).
References
More filters
Book
The applied dynamics of ocean surface waves
TL;DR: In this article, the authors present selected theoretical topics on ocean wave dynamics, including basic principles and applications in coastal and offshore engineering, all from a deterministic point of view, and the bulk of the material deals with the linearized theory.
Journal ArticleDOI
Long waves on a beach
TL;DR: In this paper, the Boussinesq equations for long waves in water of varying depth are derived for small amplitude waves, but do include non-linear terms, and solutions have been calculated numerically for a solitary wave on a beach of uniform slope, which is also derived analytically by using the linearized long-wave equations.
Journal ArticleDOI
A new form of the Boussinesq equations with improved linear dispersion characteristics
TL;DR: In this paper, a new form of the Boussinesq equations is introduced in order to improve their dispersion characteristics, and a numerical method for solving the new set of equations in two horizontal dimensions is presented.
Journal ArticleDOI
Bound waves and triad interactions in shallow water
Per A. Madsen,Ole R. Sørensen +1 more
TL;DR: Boussinesq type equations with improved linear dispersion characteristics are derived and applied to study wave-wave interaction in shallow water in this article, where weakly nonlinear solutions are formulated in terms of Fourier series with constant or spatially varying coefficients for two purposes: to derive higher order boundary conditions for regular and irregular wave trains and to derive evolution equations on constant or variable water depth.
A unified model for the evolution of nonlinear water waves
TL;DR: In this article, a model of water waves that describes wave propagation over long distances accurately, at low cost, and for a wide variety of physical situations are given, using exact prognostic equations, and a high-order expansion to relate variables at each time step.