相关论文: Steady water-waves with arbitrary surface-pressure…

We derive equations relating the pressure at a flat seabed and the free-surface profile for steady gravity waves with constant vorticity. The resulting set of nonlinear equations enables the recovery of the free surface from pressure…

A new method is proposed to recover the water-wave surface elevation from pressure data obtained at the bottom of the fluid. The new method requires the numerical solution of a nonlocal nonlinear equation relating the pressure and the…

In the general context of rotational water waves with a smooth vorticity it is shown that the wave profile can be recovered from the horizontal component of the velocity field on a line of symmetry. The method, which applies to waves of…

Steady two-dimensional surface capillary-gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions…

We consider the problem of recovering the surface wave profile from noisy bottom pressure measurements with (\textit{a priori} unknown) arbitrary pressure at the surface. Without noise, the direct approach developed in…

In this short note, we derive a system of two nonlocal equations for the water-wave problem following the work of [AFM06]. Specifically, we consider a fluid with a one-dimensional free surface for an irrotational fluid both with, and…

This paper considers two-dimensional steady continuous stratified periodic water waves. Firstly, we prove that each streamline must be symmetric about the crest line when it is strictly monotonous between troughs and crests by exploiting…

The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying…

This paper is devoted to the stabilization of the water-wave equations with surface tension through of an external pressure acting on a small part of the free surface. It is proved that the energy decays to zero exponentially in time,…

We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…

Two-dimensional potential flows of an ideal fluid with a free surface are considered in situations when shape of the bottom depends on time due to external reasons. Exact nonlinear equations describing surface waves in terms of the so…

Consider a two-dimensional stratified solitary wave propagating through a body of water that is bounded below by an impermeable ocean bed. In this work, we study how such a wave can be reconstructed from data consisting of the wave speed,…

Regularizing effects of surface tension are studied for interfacial waves between a two-dimensional, infinitely-deep and irrotational flow of water and vacuum. The water wave problem under the influence of surface tension is formulated as a…

Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitude waves, we find the exact solutions of the…

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…

We consider the problem of reconstructing the seabed topography from observations of surface gravity waves. We formulate the problem as a classical inverse scattering problem using the mild-slope equation, and analyze the topographic…

Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…

A novel boundary integral approach for the recovery of overhanging (or not) rotational (or not) water waves from pressure measurements at the bottom is presented. The method is based on the Cauchy integral formula and on an…

The reconstruction of water wave elevation from bottom pressure measurements is an important issue for coastal applications, but corresponds to a difficult mathematical problem. In this paper we present the derivation of a method which…

The present study describes, first, an efficient algorithm for computing capillary-gravity solitary waves solutions of the irrotational Euler equations with a free surface and, second, provides numerical evidences of the existence of an…