相关论文: Water waves over a strongly undulating bottom

Analysing two-dimensional shallow water equations with idealised bottom topographies have many applications in the atmospheric and oceanic sciences; however, restrictive flow pattern assumptions have been made to achieve explicit solutions.…

The runup of tsunami waves on the coasts of the barrow bays, channels and straits is studied in the framework of the nonlinear shallow water theory. Using the narrowness of the water channel, the one-dimensional equations are applied; they…

The computation of long wave propagation through the ocean obviously depends on the initial condition. When the waves are generated by a moving bottom, a traditional approach consists in translating the ``frozen'' sea bed deformation to the…

Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this paper, we study long linear and weakly-nonlinear ring waves in a stratified fluid in the presence of a…

The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of…

We provide high-order approximations to periodic travelling wave profiles and to the velocity field and the pressure beneath the waves, in flows with constant vorticity over a flat bed.

The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…

A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…

An iterative numerical method to compute the conformal mapping in the context of propagating water waves over uneven topographies is investigated. The map flattens the fluid domain onto a canonical strip in which computations are performed.…

We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear flow. The far-field modal and amplitude equations for the ring waves are presented in dimensional form. We re-derive them from the…

Nonlinear dynamics of the free surface of finite depth non-conducting fluid with high dielectric constant subjected to a strong horizontal electric field is considered. Using the conformal transformation of the region occupied by the fluid…

In the paper a new nonlinear equation describing shallow water waves with the topography of the bottom directly taken into account is derived. This equation is valid in the weakly nonlinear, dispersive and long wavelength limit. Some…

We investigate exact nonlinear waves on surfaces locally approximating the rotating sphere for two-dimensional inviscid incompressible flow. Our first system corresponds to a beta-plane approximation at the equator and the second to a gamma…

In this work we present a further analytical development and a numerical implementation of the recently suggested theoretical model for highly nonlinear potential long-crested water waves, where weak three-dimensional effects are included…

The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…

In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to…

We study the two-dimensional problem of propagation of linear water waves in deep water in the presence of a submerged body. Under some geometrical requirements, we derive an explicit bound for the solution depending on the domain and the…

The evolution of random wave fields on the free surface is a complex process which is not completely understood nowadays. For the sake of simplicity in this study we will restrict our attention to the 2D physical problems only (i.e. 1D wave…

In this paper we examine the flow generated by coupled surface and internal small-amplitude water waves in a two-fluid layer model, where we take the upper layer to be rotational (constant vorticity) and the lower layer to be irrotational.…

We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom…