Undular bores, also termed dispersive shock waves, generated by an initial discontinuity in height as governed two forms of the Boussinesq system weakly nonlinear shallow water wave theory, standard formulation and a Hamiltonian formulation, related Whitham–Boussinesq equations, full equations for gravity surface waves are studied compared. It is found that systems give solutions excellent agre...

The propagation of linear water waves over a three-dimensional ocean is modelled using the mildslope equation. Various parabolic wave models are described that approximate the governing elliptic partial differential equation, and so are very convenient for computing wave propagation over large distances. Several aspects are discussed: computation of the reflected wavefield, the construction of ...

We are interested in the modeling of wave-current interactions around surf zones at beaches. Any model that aims to predict the onset of wave breaking at the breaker line needs to capture both the nonlinearity of the wave and its dispersion. We have therefore formulated the Hamilto5 nian dynamics of a new water wave model, incorporating both the shallow water and pure potential flow water wave ...

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the const...

In this paper, using the tanh-function method, we introduce a new approach to solitary wave solutions for solving nonlinear PDEs. The proposed method is based on adding integration constants to the resulting nonlinear ODEs from the nonlinear PDEs using the wave transformation. Also, we use a transformation related to those integration constants. Some examples are considered to find their exact ...

A one-dimensional hybrid numerical model is presented of a shallow-water flume with an incorporated piston paddle. The hybrid model is based on the improved Boussinesq equations by Madsen and Sørensen (1992) and the nonlinear shallow water equations. It is suitable for breaking and non-breaking waves and requires only two adjustable parameters: a friction coefficient and a wave breaking paramet...

the development of the dynamical core of a potential-vorticity-based atmospheric general circulation model is explored. there are some advantages of using potential vorticity (pv) as a prognostic variable in that the resulting model can give more accurate simulation of the evolution of pv, as arguably the most fundamental dynamical quantity. further, there is possibility of explicit representat...

We study the scattering of a long longitudinal radiating bulk strain solitary wave in the delaminated area of a two-layered elastic structure with soft ("imperfect") bonding between the layers within the scope of the coupled Boussinesq equations. The direct numerical modelling of this and similar problems is challenging and has natural limitations. We develop a semi-analytical approach, based o...