Related papers: Water wave problem with inclined walls

We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…

We study the two dimensional water waves problem with surface tension in the case when there is a non-zero contact angle between the free surface and the bottom. In the presence of surface tension, dissipations take place at the contact…

We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a…

The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…

The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete…

Shallow water waves are a striking example of nonlinear hydrodynamics, giving rise to phenomena such as tsunamis and undular waves. These dynamics are typically studied in hundreds-of-meter-long wave flumes. Here, we demonstrate a…

Spiral wave solutions are found in linear and weakly nonlinear irrotational water wave equations. These unsteady spiral waves evolve from suitable initial conditions; they are not induced by external forcing. In the linear case, a long-time…

We will consider the resolution of the 3D non linear wave equation under the assumption of spherical symmetry on the euclidian space. For this purpose, we will build a non trivial measure on distributions such that there exists a set of…

We report experiments on the full space and time resolved statistics of capillary wave turbulence at the air-water interface. The three-dimensional shape of the free interface is measured as a function of time by using the optical method of…

There has been significant recent interest in the study of water waves coupled with non-zero vorticity. We derive analytical approximations for the exponentially-small free-surface waves generated in two-dimensions by one or several…

In this paper we study the propagation of weakly nonlinear surface waves on a plasma-vacuum interface. In the plasma region we consider the equations of incompressible magnetohydrodynamics, while in vacuum the magnetic and electric fields…

Weakly nonlinear internal wave-wave interaction is a key mechanism that cascades energy from large to small scales, leading to ocean turbulence and mixing. Oceans typically have a non-uniform density stratification profile; moreover,…

We derived here in a systematic way, and for a large class of scaling regimes, asymptotic models for the propagation of internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid…

We consider the linear water-wave problem in a periodic channel which consists of infinitely many identical containers connected with apertures of width $\epsilon$. Motivated by applications to surface wave propagation phenomena, we study…

In this paper we examine triad resonances in a rotating shallow water system when there are two free interfaces. This allows for an examination in a relatively simple model of the interplay between baroclinic and barotropic dynamics in a…

In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…

We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…

This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary…

The formulation of a canonical deep-water breaking wave problem is introduced, and the results of a set of three-dimensional numerical simulations for deep-water breaking waves are presented. In this paper fully nonlinear progressive waves…

We consider two-layers of immiscible liquids confined between an upper and a lower rigid plate. The dynamics of the free liquid-liquid interface is described for arbitrary amplitudes by a single evolution equation derived from the basic…