Related papers: Efficient computation of capillary-gravity general…
The dynamic conformal transformation method has been generalized for the first time to numerically simulate the capillary wave turbulence of a liquid surface in the plane symmetric anisotropic geometry. The model is strongly nonlinear and…
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…
We prove variational instability for small-amplitude solutions to the periodic irrotational gravity water wave problem in finite depth. Our results are based on a reformation of the water wave problem as a pseudo-differential Euler-Lagrange…
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians…
We consider the gravity-capillary waves in any dimension and in fluid domains with general bottoms. Using the paradiferential reduction established in the companion paper, we prove Strichartz estimates for solutions to this problem, at a…
We prove the existence of small steady periodic capillary-gravity water waves for general stratified flows, where we allow for stagnation points in the flow. We establish the existence of both laminar and non-laminar flow solutions for the…
Gravitational waves (GWs) provide an excellent opportunity to test the gravity in the strong gravitational fields. In this article, we calculate the waveform of GWs, produced by the coalescence of compact binaries, in an extension of the…
We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.
In this paper, we present port-Hamiltonian formulations of the incompressible Euler equations with a free surface governed by surface tension and gravity forces, modelling e.g. capillary and gravity waves and the evolution of droplets in…
We obtain a new family of exact vacuum solutions to quadratic gravity that describe pp-waves with two-dimensional wave surfaces that can have any prescribed constant curvature. When the wave surfaces are flat we recover the Peres waves…
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…
The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer…
A gauge-invariant formulation for the gravitational wave equations is presented. Using this approach, weak, plane wave solutions in a vacuum are derived in various theories. These include general relativity with two modes of polarization…
We report the observation of capillary wave turbulence on the surface of a fluid layer in a low-gravity environment. In such conditions, the fluid covers all the internal surface of the spherical container which is submitted to random…
We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable…
In this work, we solve the Euler's equations for periodic waves travelling under a sheet of ice using a reformulation introduced in Ablowitz et al. (2006). These waves are referred to as flexural-gravity waves. We compare and contrast two…
We present a semi-Lagrangian characteristic mapping method for the incompressible Euler equations on a rotating sphere. The numerical method uses a spatio-temporal discretization of the inverse flow map generated by the Eulerian velocity as…
We consider the stability of periodic gravity-capillary waves of finite amplitude for small values of the surface tension. Linear stability with respect to both superharmonic and subharmonic perturbations is calculated for each solution,…
In this paper, we study the existence and concentration of solitary waves for a class of generalized Kadomtsev-Petviashvili equations with the potential in $\mathbb{R}^2$ via the variational methods.
Using the FLUIDICS (Fluid Dynamics in Space) experiment in the International Space Station, turbulence of capillary waves at the air-water interface is experimentally investigated in weightlessness. Capillary waves are excited in a…