A new form of the Boussinesq equations with improved linear dispersion characteristics

Numerical simulation of extreme wave runup during storm events in Tramandaí Beach, Rio Grande do Sul, Brazil

“…The Boussinesq models are well established (e.g. Madsen et al, 1991;Nwogu, 1994;Wei et al, 1995) and have been very successful in applications for near-shore regions. However, numerical implementation of large models required for high accuracy is rather complicated.…”

Inner harbour wave agitation using boussinesq wave model

“…In 1991 Madsen P.A (Madsen et al, 1991) introduced a new form of the Boussinesq equations, which improved the dispersion characteristics. It is demonstrated that the depth-limitation of the new equations is much less restrictive than for the classical forms of the Boussinesq equations, and it became possible to simulate the propagation of irregular wave trains travelling from deep water to shallow water.…”

A new form of Boussinesq equations for long waves in water of non-uniform depth

“…Since that work of Peregine, the depth averaging procedure, applied to the continuity and momentum equations, has become a standard in the derivation of Boussinesq-like equations (Nwogu [3]). Another, classical approach to the derivation of these equations is to follow the Laplace equation for the velocity potential, combined with boundary conditions at the bottom and the free surface of a fluid domain (Volcinger et al [4], Madsen et al [5]). In such a formulation the potential function is expressed in the form of a power series expansion with respect to the water depth (Wei et al [1]).…”

“…That method however, cannot be easily extended to a more general two-dimensional case of the variable water depth. Madsen et al [5] improved the dispersion characteristic of Boussinesq-type equations by adding a third order term to the momentum equation written for a fluid with a horizontal bottom. This term, derived from the long wave equations, was chosen to give the best possible linear dispersion relation.…”