Related papers: Near-linear Dynamics for Shallow Water Waves
Low-frequency simulations of a one-layer model with lateral buoyancy variations (i.e., thermodynamically active) have revealed circulatory motions resembling quite closely submesoscale observations in the surface ocean rather than…
We present a theory for experimentally observed phenomenon of one dimensional asynchronous waves. The general principle of coexistence of linear and nonlinear solutions of a dynamical system is underlying the present theoretical work. The…
It is demonstrated that a standard coupled-mode theory can successfully describe weakly-nonlinear gravity water waves in Bragg resonance with a periodic one-dimensional topography. Analytical solutions for gap solitons provided by this…
Whereas electromagnetic surface waves are confined to a planar interface between two media, line waves exist at the one-dimensional interface between three materials. Here we derive a non-local integral equation for computing the properties…
Nonlinear initial-boundary value problem on deep-water gravity waves of finite amplitude is solved approximately (up to small terms of higher order) assuming that the waves are generated by an initial disturbance to the water and the…
We theoretically show that a superposition of plane waves causes small (compared to the wavelength) particles dispersed in a fluid to assemble in quasiperiodic two or three dimensional patterns. We experimentally demonstrate this theory by…
The data of simultaneous measurements of the surface displacement produced by propagating planar waves in experimental flume and of the dynamic pressure beneath the waves are compared with the theoretical predictions based on different…
Consideration is given to three different full dispersion Boussinesq systems arising as asymptotic models in the bi-directional propagation of weakly nonlinear surface waves in shallow water. We prove that, under a non-cavitation condition…
We prove the local well-posedness for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime.
We report the experimental observation of intermittency in a regime dominated by random shock waves on the surface of a fluid. We achieved such a nondispersive surface-wave field using a magnetic fluid subjected to a high external magnetic…
An experimental validation of theoretical models of transmission of regular water waves by large arrays of floating disks is presented. The experiments are conducted in a wave basin. The models are based on combined potential-flow and…
We prove an extended lifespan result for the full gravity-capillary water waves system with a $2$ dimensional periodic interface: for initial data of sufficiently small size $\varepsilon$, smooth solutions exist up to times of the order of…
The standing surface waves in a rectangular vertically oscillating vessel filled with water (Faraday waves) in the presence of a floating elastic sheet are studied experimentally and theoretically. The threshold amplitude of the instability…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
In the approximation of linear dissipative magnetohydrodynamics (MHD) it can be shown that driven MHD waves in magnetic plasmas with high Reynolds number exhibit a near resonant behaviour if the frequency of the wave becomes equal to the…
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…
A semilinear wave equation with slowly varying wave speed is considered in one to three space dimensions on a bounded interval, a rectangle or a box, respectively. It is shown that the action, which is the harmonic energy divided by the…
A low loss propagating electromagnetic wave is shown to exist at a gradual interface between two lossy conductive media. The electromagnetic frequency range of this phenomenon may span from UV optics to RF range. In particular, it is…
In this paper we study the propagation of weakly nonlinear surface waves on a plasma-vacuum interface. In the plasma region we consider the equations of incompressible magnetohydrodynamics, while in vacuum the magnetic and electric fields…
Ocean motions at frequencies of the internal wave band are generally associated with freely propagating waves that are supported by stable vertical stratification in density. Previous analyses of yearlong current observations from the Bay…