Related papers: Hamiltonian structure for two-dimensional extended…
In this paper, we derive a new shallow asymptotic model for the free boundary plasma-vacuum problem governed by the magnetohydrodynamic equation, vital in describing large-scale processes in flows of astrophysical plasma. More precisely, we…
Considered in this paper is a bi-directional model for the propagation of interfacial capillary-gravity waves in a two-layer system of fluids with rigid lid condition for the upper layer and lower layer with a much larger or infinite depth.…
In this short communication we present the multi-symplectic structure for the two-layer Serre-Green-Naghdi equations describing the evolution of large amplitude internal gravity long waves. We consider only a two-layer stratification with…
Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of…
The fully nonlinear and weakly dispersive Green-Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume…
Many equations that arise in a physical context can be posed in the form of a Hamiltonian system, meaning that there is a symplectic structure on an appropriate phase space, and a Hamiltonian functional with respect to which time evolution…
Two methods to treat wave breaking in the framework of the Hamiltonian formulation of free-surface potential flow are presented, tested, and validated. The first is an extension of Kennedy et al (2000)'s eddy-viscosity approach originally…
We consider the Isobe-Kakinuma model for water waves, which is obtained as the system of Euler-Lagrange equations for a Lagrangian approximating Luke's Lagrangian for water waves. We show that the Isobe-Kakinuma model also enjoys a…
A Hamiltonian model for the propagation of internal water waves interacting with surface waves, a current and an uneven bottom is examined. Using the so-called Dirichlet-Neumann operators, the water wave system is expressed in the…
The paper deals with the 2D gravity-capillary water waves equations in their Hamiltonian formulation, addressing the question of the nonlinear interaction of a plane wave with its reflection off a vertical wall. The main result is the…
We consider the linear problem for water-waves created by sources on the bottom and the free surface in a 3-D basin having slowly varying profile $z=-D(x)$. The fluid verifies Euler-Poisson equations. These (non-linear) equations have been…
Using the KAM method, we exhibit some solutions of a finite-dimensional approximation of the Zakharov Hamiltonian formulation of gravity water waves, which are spatially periodic, quasi-periodic in time, and not permanent form travelling…
We propose a locally adaptive non-hydrostatic model and apply it to wave propagation generated by a moving bottom. This model is based on the non-hydrostatic extension of the shallow water equations (SWE) with a quadratic pressure relation,…
The Serre-Green-Naghdi equations of water wave theory have been widely employed to study undular bores. In this study, we introduce a modified Serre-Green-Naghdi system incorporating the effect of an artificial term that results in…
The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV…
We consider an asymptotic 1D (in space) rotation-Camassa-Holm (R-CH) model, which could be used to describe the propagation of long-crested shallow-water waves in the equatorial ocean regions with allowance for the weak Coriolis effect due…
We consider two `Classical' Boussinesq type systems modelling two-way propagation of long surface waves in a finite channel with variable bottom topography. Both systems are derived from the 1-d Serre-Green-Naghdi (SGN) system; one of them…
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of…
The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface…
We derive a hyperbolic system of equations approximating the two-layer dispersive shallow water model for shear flows recently proposed by Gavrilyuk, Liapidevskii \& Chesnokov (J. Fluid Mech., vol. 808, 2016, pp. 441--468). The use of this…