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 ...

The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the group of diffeomorphisms of the ambient space. A key advantage is that one obtains in a natural way all the needed balance laws on both the macro and micro levels along with two Doyle-Erickson formulas....

The Serre–Green–Naghdi (SGN) equations, also known as the fully-nonlinear Boussinesq wave equations, accurately describe the behaviour of dispersive shoaling water waves. This article presents and validates a novel combination of methods for the numerical approximation of solutions to the SGN equations. The approach preserves the robustness of the original finite-volume Saint-Venant solver, in ...

We derive an asymptotic formula for the amplitude distribution in a fully nonlinear shallow-water solitary wave train which is formed as the long-time outcome of the initial-value problem for the Su-Gardner (or one-dimensional Green-Naghdi) system. Our analysis is based on the properties of the characteristics of the associated Whitham modulation system which describes an intermediate “undular ...

We shall briefly present here the main idea of partial selective reduced integration as developed in [1], [2]. As we shall see the idea is quite general and can be applied to a number of different situations. For the sake of simplicity, however, we shall concentrate on the particular case of Naghdi shell models. Once the idea is understood, its generalisation to other cases should be straightfo...

We show that although no actual mathematical shell model is explicitly used in ‘general shell element’ formulations, we can identify an implicit shell model underlying these nite element procedures. This ‘underlying model’ compares well with classical shell models since it displays the same asymptotic behaviours—when the thickness of the shell becomes very small—as, for example, the Naghdi mode...