Related papers: Dispersion relation for water waves with non-const…
We describe the physical hypotheses underlying the derivation of an approximate model of water waves. For unidirectional surface shallow water waves moving over an irrotational flow as well as over a non-zero vorticity flow, we derive the…
We study modulational stability and instability in the Whitham equation, combining the dispersion relation of water waves and a nonlinearity of the shallow water equations, and modified to permit the effects of surface tension and constant…
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…
In the linear approximation we study long wave scattering on an axially symmetric flow in a shallow water basin with a drain in the center. This classical problem can be considered as a model of wave scattering on a rotating black hole. For…
We study here the propagation of long waves in the presence of vorticity. In the irrotational framework, the Green-Naghdi equations (also called Serre or fully nonlinear Boussinesq equations) are the standard model for the propagation of…
We describe the Hamiltonian structures, including the Poisson brackets and Hamiltonians, for free boundary problems for incompressible fluid flows with vorticity. The Hamiltonian structure is used to obtain variational principles for…
The formalism of the exact six polarization modes of gravitational waves is constructed in terms of both the small metric perturbations and the Newman-Penrose scalars. The obtained formulae are applicable to any metric-compatible gravity…
We demonstrate that mechanical waves traveling in a torsional, mechanical wave machine exhibit dispersion due to gravity and the discreteness of the medium. We also show that although the dispersion due to discreteness is negligible, the…
Vortices in electron fluids are a key indicator of electron hydrodynamics. However, a comprehensive framework linking macroscopic vorticity measurements with microscopic interactions and scattering mechanisms has been lacking. We employ…
The dispersion equation of MGD plasma waves measured in a reference frame with a relative speed from that where they are generated is derived. The analysis leads further from what is known for waves produced in stationary plasmas in the…
The Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler's equations is taken (to a certain order of smallness of the scale parameters), relations to…
In this paper we consider the steady water wave problem for waves that possess a merely $L_r-$integrable vorticity, with $r\in(1,\infty)$ being arbitrary. We first establish the equivalence of the three formulations--the velocity…
Properties of modified plasma waves in non-linear electrodynamics are investigated. We consider a cold, uniform, collisionless, and magnetized plasma model. Initially, we also assume small amplitude waves and the non-relativistic…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
The purpose of this note is to prove dispersive estimates for the wave equation outside a ball in R^d. If d = 3, we show that the linear flow satisfies the dispersive estimates as in R^3. In higher dimensions d $\ge$ 4 we show that losses…
A new description of the dynamics of warped accretion discs is presented. A theory of fully nonlinear, slowly varying bending waves is developed, involving a proper treatment of viscous fluid dynamics but neglecting self-gravitation. 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…
A class of water wave problems concerns the dynamics of the free interface separating an inviscid, incompressible and irrotational fluid, under the influence of gravity, from a zero-density region. In this note, we present some recent…
The discontinuity of the vorticity is written as a function of the vector T grad s, (where T is the temperature and s the specific entropy). The expression is obtained thanks to potential equations and independently of the mass conservation…
We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed…