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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…
We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…
The existence of internal geophysical waves of extreme form is confirmed and an explicit solution presented. The flow is confined to a layer lying above an eastward current while the mean horizontal flow of the solutions is westward, thus…
We study the two-dimensional problem of propagation of linear water waves in deep water in the presence of a submerged body. Under some geometrical requirements, we derive an explicit bound for the solution depending on the domain and the…
We prove local exact controllability in arbitrary short time of the two-dimensional incompressible Euler equation with free surface, in the case with surface tension. This proves that one can generate arbitrary small amplitude periodic…
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…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on…
This paper is devoted to the computation of capillary-gravity solitary waves of the irrotational incompressible Euler equations with free surface. The numerical study is a continuation of a previous work in several points: an alternative…
The study of the Euler equations in flows with constant vorticity has piqued the curiosity of a considerable number of researchers over the years. Much research has been conducted on this subject under the assumption of steady flow. In this…
In this paper, we derive asymptotic models for the propagation of two and three-dimensional gravity waves at the free surface and the interface between two layers of immiscible fluids of different densities, over an uneven bottom. We assume…
We present a numerical study of essentially nonlinear dynamics of surface gravity waves on deep water with constant vorticity using governing equations in conformal coordinates. The dispersion relation of surface gravity waves on shear flow…
The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying…
A Hamiltonian model for the propagation of internal water waves interacting with surface waves, a current and an uneven bottom is examined. Using the so-called Dirichlet-Neumann operators, the water wave system is expressed in the…
Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation.…
In this paper we mainly investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed. We assume that the free surface is almost periodic in the horizontal direction. Using…
A unidirectional reduction of the deep-water surface gravity wave problem is derived in physical space using real variables. By employing a near-identity canonical transformation, cubic interactions are eliminated from the Hamiltonian, with…
In geophysical environments, wave motions that are shaped by the action of gravity and global rotation bear the name of gravito-inertial waves. We present a geometrical description of gravito-inertial surface waves, which are low-frequency…
We study the long-time evolution of gravity waves on deep water exited by the stochastic external force concentrated in moderately small wave numbers. We numerically implement the primitive Euler equations for the potential flow of an ideal…
We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…