Related papers: Fractional Fourier approximations for potential gr…
The gravity water waves equations describe the evolution of the surface of an incompressible, irrotational fluid in the presence of gravity. The classical regularity threshold for the well-posedness of this system requires initial velocity…
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…
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…
We construct small-amplitude steady periodic gravity water waves arising as the free surface of water flows that contain stagnation points and possess a discontinuous distribution of vorticity in the sense that the flows consist of two…
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…
We consider a full set of harmonics for the Stokes wave in deep water in the absence of viscosity, and examine the role that higher harmonics play in modifying the classical Benjamin-Feir instability. Using a representation of the 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…
We revisit the classical but as yet unresolved problem of predicting the breaking onset of 2D and 3D irrotational gravity water waves. This study focuses on domains with flat bottom topography and conditions ranging from deep to…
We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, quasi-periodic in time, traveling waves. This provides the…
We propose a Stokes expansion ansatz for finite-depth standing water waves in two dimensions and devise a recursive algorithm to compute the expansion coefficients. We implement the algorithm on a supercomputer using arbitrary-precision…
The Weak Turbulence Theory is a statistical framework to describe a large ensemble of nonlinearly interacting waves. The archetypal example of such system is the ocean surface that is made of interacting surface gravity waves. Here we…
This paper is concerned with two-dimensional, steady, periodic water waves propagating at the free surface of water either in a flow of finite depth and constant vorticity over an impermeable flat bed or in an irrotational flow of great…
We describe the theory and present numerical evidence for a new type of nonlinear resonant interaction between gravity waves on the surface of deep water. The resonance constitutes a generalisation of the usual 'exact' resonance as we show…
The dynamics of solitary gravity-capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential…
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of…
We generalize the periodic Evans function approach recently used to study the spectral stability of Stokes wave and gravity-capillary (including Wilton ripples) in water of finite depth to study spectral stability of Stokes waves in water…
It is suggested that gravity waves could, in several cases, be detected by means of already (or shortly to be) available technology, independently of current efforts of detection. The present is a follow-up on a recently suggested detection…
After giving a brief introduction and presenting a complete classification of gravitational waves (GWs) according to their frequencies, we review and summarize the detection methods, the sensitivities, and the sources. We notice that…
Third-order approximate solutions for surface gravity waves in the finite water depth are studied in the context of potential flow theory. This solution provides explicit expressions for the surface elevation, free-surface velocity…
We prove Strichartz estimates for gravity water waves, in arbitrary dimension and in fluid domains with general bottoms. We consider rough solutions such that, initially, the first order derivatives of the velocity field are not controlled…