Related papers: Overhanging solitary water waves
This paper establishes the conditional orbital stability of fully localized solitary waves for the three-dimensional capillary-gravity water wave problem in finite depth under strong surface tension. The waves, constructed via a…
We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…
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…
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…
While some works have investigated the particle trajectories and stagnation points beneath solitary waves with constant vorticity, little is known about the pressure beneath such waves. To address this gap, we investigate numerically the…
We investigate theoretically the onset of capillary-gravity waves created by a small object moving at the water-air interface. It is well established that, for straight uniform motion, no steady waves appear at velocities below the minimum…
The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of…
Fully localised solitary waves are travelling-wave solutions of the three-dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence for water of finite depth has recently…
In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal…
This paper studies the classical water wave problem with vorticity described by the Euler equations with a free surface under the influence of gravity over a flat bottom. Based on fundamental work \cite{ConstantinStrauss}, we first obtain…
This paper is concerned with two-dimensional, steady, periodic water waves propagating at the free surface of water in a flow of constant vorticity over an impermeable flat bed. The motion of these waves is assumed to be governed both by…
We prove a long-term regularity result for three-dimensional gravity water waves with small initial data but nonzero initial vorticity. We consider solutions whose vorticity vanishes on the free boundary and use this to derive a system for…
This paper is a study of the water wave problem in a two-dimensional domain of infinite depth in the presence of nonzero constant vorticity. A goal is to describe the effects of uniform shear flow on the modulation of weakly nonlinear…
A fundamental question in the study of water waves is the existence and stability of solitary waves. Solitary waves have been proved to exist and have been studied in many interesting situations, and often arise from the balance of…
The motion of an interface separating two fluids under the effect of electric fields is a subject that has picked the attention of researchers from different areas. While there is an abundance of studies investigating the free surface wave…
This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and…
Hydrodynamic bores are front-type traveling wave solutions to the two-layer free boundary Euler equations in two dimensions. The velocity field in each layer is assumed to be incompressible and irrotational, and it limits to distinct…
This paper studies the structural implications of constant vorticity for steady three-dimensional internal water waves. It is known that in many physical regimes, water waves beneath vacuum that have constant vorticity are necessarily two…
We prove the existence of small amplitude time quasi-periodic solutions of the pure gravity water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space periodic free interface. Using a…
This paper considers two-dimensional stratified water waves propagating under the force of gravity over an impermeable flat bed and with a free surface. We prove the existence of a global continuum of classical solutions that are periodic…