Related papers: Capillary-gravity waves: a "fixed-depth" analysis
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…
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…
This article is devoted to the study of local well-posedness for deep water waves with constant vorticity in two space dimensions on the real line. The water waves can be paralinearized and written as a quasilinear dispersive system of…
The Plateau-Rayleigh theory essentially explains the breakup of liquid jets as due to growing perturbations along the length of the jet. The essential idea is supported by several experiments carried out in the past. Recently, the existence…
We report on the observation of gravity-capillary wave turbulence on the surface of a fluid in a high-gravity environment. By using a large-diameter centrifuge, the effective gravity acceleration is tuned up to 20 times the Earth gravity.…
The classical irrotational capillary-gravity water wave problem described by the Euler equations with a nonlinear free surface boundary condition over a flat bed is considered. A modified flow force has been defined and a new formulation of…
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…
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…
In this paper we construct small amplitude periodic internal waves traveling at the boundary region between two rotational and homogeneous fluids with different densities. Within a period, the waves we obtain have the property that the…
Intuitively, crest speeds of water waves are assumed to match their phase velocities. However, this is generally not the case for natural waves within unsteady wave groups. This motivates our study, which presents new insights into the…
We describe the effect of vibration on a confined volume of fluid which is density stratified due to its compressibility. We show that internal gravity-acoustic waves can be parametrically destabilized by the vibration. The resulting…
We develop a time-dependent conformal method to study the effect of viscosity on steep surface waves. When the effect of surface tension is included, numerical solutions are found that contain highly oscillatory parasitic capillary ripples.…
We consider the gravity-capillary water waves problem in a domain $\Omega_t \subset \mathbb{T} \times \mathbb{R}$ with substantial geometric features. Namely, we consider a variable bottom, smooth obstacles in the flow and a constant…
The aim of this work is to investigate the interaction of gravity-capillary waves resonantly excited by two moving disturbances along the free surface. The problem is formulated using the full Euler equations and numerical computations are…
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…
We present an existence and stability theory for gravity-capillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove…
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…
Breakup of water jets under gravity is a common-place phenomenon. The role of surface tension in the instability of water jets was recognized by Rayleigh and the theory propounded goes by the name of Plateau-Rayleigh theory. The necks and…
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…
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…