Related papers: Capillary-Gravity Water Waves: Modified Flow Force…
In this note, we study the existence of traveling waves of a surface model in a non-newtonian fluid with odd viscosity. The proof relies on nonlinear bifurcation techniques.
We report on the experimental study of axisymmetric gravity-capillary standing waves generated by a vertically vibrating ring partially immersed into a fluid. Different regimes of standing waves are highlighted at the basin center depending…
A nonlinear Schr\"odinger equation for the envelope of two-dimensional gravity-capillary waves propagating at the free surface of a vertically sheared current of constant vorticity is derived. In this paper we extend to gravity-capillary…
For partially wetting, ellipsoidal colloids trapped at a fluid interface, their effective, interface--mediated interactions of capillary and fluctuation--induced type are analyzed. For contact angles different from 90$^o$, static interface…
This paper is devoted to the 2D gravity-capillary water waves equations in their Hamiltonian formulation, addressing the general question of proving Morawetz inequalities. We continue the analysis initiated in our previous work, where we…
We find a new class of solutions that are traveling waves on the boundary of two--dimensional droplet of ideal fluid. We assume that the free surface is subject only to the force of surface tension, and the fluid flow is potential. We use…
Models that describe two-fluid flow in porous media suffer from a widely-recognized problem that the constitutive relationships used to predict capillary pressure as a function of the fluid saturation are non-unique, thus requiring a…
The aim of this paper is to prove the existence of gravity-capillary Crapper waves with the presence of vorticity. In particular, we consider a concentrated vorticity: point vortex and vortex patch. We show that for small gravity and small…
We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. Explicit solutions to such a water wave problem are static configurations where the surface is an unduloid, that is, a…
In this paper, we investigate the spectral stability of periodic traveling waves in the two dimensional gravity-capillary water wave problem. We derive a stability criterion based on an index function, whose sign determines the spectral…
A rigid object moving in a viscous fluid and in close proximity with an elastic wall experiences self-generated elastohydrodynamic interactions. This has been the subject of an intense research activity, with a recent and growing attention…
We show that capillary waves can exist at the the boundary between miscible co-flowing fluids. We unveil that the interplay between transient interfacial stresses and confinement drives the progressive transition from the well-known…
The unsteady response of a water free surface to a localized pressure source moving at constant speed $U$ in the range $0.95c_\mathrm{min} \lesssim U \leq 1.02 c_\mathrm{min}$, where $c_\mathrm{min}$ is the minimum phase speed of linear…
This article is devoted to the Cauchy problem for the 2D gravity-capillary water waves in fluid domains with general bottoms. We prove that the Cauchy problem in Sobolev spaces is uniquely solvable for data $\frac{1}{4}$ derivatives less…
In this study we consider the problem of the interface motion under the capillary-gravity and an external electric forces. The infinitely deep fluid layer is assumed to be viscous, perfectly conducting and the flow to be incompressible. The…
Starting form the Zakharov/Craig-Sulem formulation of the water-waves equations, we prove that one can define a pressure term and hence obtain a solution of the classical Euler equations. It is proved that these results hold in rough…
This paper focuses on the analysis of stratified steady periodic water waves that contain stagnation points. The initial step involves transforming the free-boundary problem into a quasilinear pseudodifferential equation through a conformal…
We prove the existence of three-dimensional steady gravity-capillary waves with vorticity on water of finite depth. The waves are periodic with respect to a given two-dimensional lattice and the relative velocity field is a Beltrami field,…
This paper is devoted to the study of water waves under the influence of the gravity and the Coriolis force. It is quite common in the physical literature that the rotating shallow water equations are used to study such water waves. We…
We experimentally study gravity-capillary wave turbulence on the interface between two immiscible fluids of close density with free upper surface. We locally measure the wave height at the interface between both fluids by means of a highly…