Related papers: Deep water gravity wave triad resonances on unifor…
We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L^2 related norms, with dispersive estimates, which give decay…
We investigate the effect of wave-eddy interaction and dissipation of internal gravity waves propagating in a coherent meso-scale eddy simulated using a novel numerical model called the Internal Wave Energy Model based on the…
Motivated by problems arising in geophysical fluid dynamics, we investigate resonant and near resonant wave interactions in nonlinear wave equations with quadratic nonlinearity, We place a special focus on interactions between slow wave…
We perform full-scale numerical simulation of instability of weakly nonlinear waves on the surface of deep fluid. We show that the instability development leads to chaotization and formation of wave turbulence. We study instability both of…
We present the derivation of generic equations describing the long gravity waves in incompressible fluid with decaying effect. We show that in this theory the only restriction to the surface deviation is connected with the stability…
Capillary waves are a classical free-surface phenomenon in fluid mechanics, yet their behavior in chiral fluids remains largely unexplored. We show that odd viscosity breaks the reciprocity of capillary waves. Using linear theory together…
We investigate exact and near resonant triad interactions (RTI) in a two-dimensional stably stratified uniform shear flow confined between two infinite parallel walls in the absence of viscous and diffusive effects. RTI occur when three…
Nonlinear interaction of three acoustic waves in a sandy sediment is studied in the frequency range where there is a considerable wave velocity dispersion. The possibility of an experimental observation of the generation of a sound wave by…
Real world water waves often propagate on current. And, the measurement of waves and current is an important task for coastal and marine engineers. Modern marine measurement technologies (i.e. unmanned autonomous vehicles, drones) often…
Using standard signal processing tools, we experimentally report that intermittency of wave turbulence on the surface of a fluid occurs even when two typical large-scale coherent structures (gravity wave breakings and bursts of capillary…
We consider steady three-dimensional gravity-capillary water waves with vorticity propagating on water of finite depth. We prove a variational principle for doubly periodic waves with relative velocities given by Beltrami vector fields,…
The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…
We investigate the existence of solitary gravity waves traversing a two-dimensional body of water that is bounded below by a flat impenetrable ocean bed and above by a free surface of constant pressure. Our main interest is constructing…
We investigate experimentally turbulence of surface gravity waves in the Coriolis facility in Grenoble by using both high sensitivity local probes and a time and space resolved stereoscopic reconstruction of the water surface. We show that…
The scattering of inertia-gravity waves by large-scale geostrophic turbulence in a rapidly rotating, strongly stratified fluid leads to the diffusion of wave energy on the constant-frequency cone in wavenumber space. We derive the…
We study dispersion properties of linear surface gravity waves propagating in an arbitrary direction atop a current profile of depth-varying magnitude using a piecewise linear approximation, and develop a robust numerical framework for…
The standard resonance conditions for Bragg scattering as well as weakly nonlinear wave triads have been traditionally derived in the absence of any background velocity. In this paper, we have studied how these resonance conditions get…
In the weak field approximation the gravitational wave is approximated as a linear wave, which ignores the nonlinear effect. In this paper, we present an exact general solution of the cylindrical gravitational wave. The exact solution of…
In this paper we discuss a theoretical model for the interfacial profiles of progressive non-linear waves which result from introducing a triangular obstacle, of finite height, attached to the bottom below the flow of a stratified, ideal,…
Finite-dimensional wave turbulence refers to the chaotic dynamics of interacting wave `clusters' consisting of finite number of connected wave triads with exact three-wave resonances. We examine this phenomenon using the example of…