A new Boussinesq method for fully nonlinear waves from shallow to deep water

By P. A. Madsen, Harry B. Bingham, Hua Liu. Journal of Fluid Mechanics, 2002

366 citations recorded by the source corpus.

Subfields: Earth-Surface Processes, Ocean Engineering, Oceanography

View Paper: https://www.semanticscholar.org/paper/d7a50cb6f3ad1ab8e9b58898e36c685e3414a421

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Citations in the corpus

A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry (2006, methodology): “…0.5h, in which case the vertical distribu- tion of the velocity field in fully nonlinear waves is accurate for wave numbers in the interval 0 kh 12 while the dispersion relation and non-linear wave–wave interaction properties are accurate in the interval of 0 kh 25 (see Madsen et al., 2002, 2003).”
Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: derivation and analysis (2003, methodology): “A more complete description of the numerical implementation, along with a number of illustrative calculations, can be found in Madsen et al. (2002). The solution is obtained over a grid of N equally spaced points and at equally spaced time-steps (only one horizontal dimension is discussed here).”
A two-layer approach to wave modelling (2004, neutral): “Madsen et al .”
A new level set numerical wave tank with improved density interpolation for complex wave hydrodynamics (2016, background): “Extended versions of the Boussinesq equations make it possible to predict wave propagation and transformation from deep to shallow water with the help of improved dispersive terms [29].”
Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation (2009, background): “This is the case because the expansion (29) keeps the nonlocal eects of the Dirichlet-Neumann operator Gµ[",b ] . In [41, 42, 43 ], the authors make a dierential approximation of shallow water type based on Pad´e approximants; they show that the dispersive properties remain good far beyond the shal”
On the solitary wave paradigm for tsunamis (2008, methodology): “A detailed description of the scheme can be found in Madsen et al. [2002] for one horizontal dimension, and in Fuhrman and Bingham [2004] for two horizontal dimensions.”