A 2DH nonlinear Boussinesq-type wave model of improved dispersion, shoaling, and wave generation characteristics

Discussion of “A 2DH nonlinear Boussinesq-type wave model of improved dispersion, shoaling, and wave generation characteristics” by Chondros and Memos

“…Finally they conducted numerical experiments to validate the modified model using both analytical solution and laboratory data. We disagree on many issues involved in the work by Chondros and Memos (2014), as listed below.…”

“…Madsen and Schäffer (1998) comprehensively derived a series of Boussinesq models and great efforts have been made to improve these equations. Recently, Chondros and Memos (2014) (referred to as CM2014 hereafter) proposed an approach to modify Madsen and Schäffer's fourth-order Boussinesq equations and claimed that the resulting model satisfies exactly the dispersion relation in terms of both first-and second-order analyses matching in parallel the associated shoaling gradient. This was achieved by directly matching the first-order and second-order solutions and shoaling gradient of the Boussinesq model (Madsen and Schäffer, 1998) with the analytical solutions.…”

“…As an outcome, the free coefficients (α 1 , β 1 ) (which can be used to improve dispersion and second order harmonics) and α 2 (which can be used to improve shoaling) in the Boussinesq equations are time-and space-varying while they are fixed as constants by Madsen and Schäffer (1998) (refer to CM2014 for details). Chondros and Memos (2014) also proposed a way to calculate wave number in a computational domain at each time step and grid cell. Finally they conducted numerical experiments to validate the modified model using both analytical solution and laboratory data.…”

“…The most critical step of the procedure proposed by Chondros and Memos (2014) is allowing the coefficients (α 1 , β 1 and α 2 ) to be related to relative water depth. This means that the values of (α 1 , β 1 and α 2 ) depend on local wave conditions and will be different in the entire wave field.…”

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The procedure proposed by Chondros and Memos [Chondros and Memos, 2014, A 2DH nonlinear Boussinesqtype wave model of improved dispersion, shoaling, and wave generation characteristics, Coast. Eng., 91: 99-122] for improving dispersion, shoaling and wave generation characteristics of a 2DH Boussinesq-type wave model is discussed.

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