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The surface gravity wave evolution, imitating tsunamis triggered by the ocean floor's arbitrary temporal motion over a generic seafloor topography, is investigated using the linearised water wave theory of a compressible ocean. The…
The standard analytical approach for studying gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its…
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…
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…
This paper deals with the dead-water phenomenon, which occurs when a ship sails in a stratified fluid, and experiences an important drag due to waves below the surface. More generally, we study the generation of internal waves by a…
We derived here in a systematic way, and for a large class of scaling regimes, asymptotic models for the propagation of internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid…
We investigate a hydrodynamic equation system which - with some approximation - is capable to describe the tsunami propagation in the open ocean with the time-dependent self-similar Ansatz. We found analytic solutions how the wave height…
We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist…
The reconstruction of water wave elevation from bottom pressure measurements is an important issue for coastal applications, but corresponds to a difficult mathematical problem. In this paper we present the derivation of a method which…
We derive a simple algebraic form of the nonlinear wavenumber correction of surface gravity waves in deep water, based on temporal measurements of the water surface and the spatial Zakharov equation. This allows us to formulate an…
We show that horizontally symmetric water waves are traveling waves. The result is valid for the Euler equations, and is based on a general principle that applies to a large class of nonlinear partial differential equations, including some…
We study numerically the generation of power laws in the framework of weak turbulence theory for surface gravity waves in deep water. Starting from a random wave field, we let the system evolve numerically according to the nonlinear Euler…
The evolution of random wave fields on the free surface is a complex process which is not completely understood nowadays. For the sake of simplicity in this study we will restrict our attention to the 2D physical problems only (i.e. 1D wave…
Special features of surface gravity waves in deep fluid flow with constant vertical shear of velocity is studied. It is found that the mean flow velocity shear leads to non-trivial modification of surface gravity wave modes dispersive…
While the propagation of tsunamis is well understood and well simulated by numerical models, there are still a number of unanswered questions related to the generation of tsunamis or the subsequent inundation. We review some of the basic…
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…
The generation of ocean surface waves by wind is a classic fluid mechanics problem whose theoretical study dates back to 1957, when the two seminal papers by Phillips and Miles were published in the incipient Journal of Fluid Mechanics.…
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 evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…