Related papers: Spiral Wave Solutions in Water Waves
Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order…
Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as point-like objects moving along trajectories with a constant velocity. Interaction with medium boundaries alters this…
Since the early works[1-4] on the so-called nondiffracting waves (called also Localized Waves), a great deal of results has been published on this important subject, from both the theoretical and the experimental point of view. Initially,…
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 present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the…
We perform a detailed analytical and numerical study of the dynamics of perturbations (vortex/aperiodic mode, Rossby and spiral-density waves) in 2D compressible disks with a Keplerian law of rotation. We draw attention to the process of…
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…
In dispersive media, hydrodynamic singularities are resolved by coherent wavetrains known as dispersive shock waves (DSWs). Only dynamically expanding, temporal DSWs are possible in one-dimensional media. The additional degree of freedom…
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…
Trapping and un-trapping of spiral tips in a two-dimensional homogeneous excitable medium with local small-world connections is studied by numerical simulation. In a homogeneous medium which can be simulated with a lattice of regular…
Rotating spiral waves with a central core composed of phase-randomized oscillators can arise in reaction-diffusion systems if some of the chemical components involved are diffusion-free. This peculiar phenomenon is demonstrated for a…
In this work, we study the nonlinear traveling waves in density stratified fluids with depth varying shear currents. Beginning the formulation of the water-wave problem due to [1], we extend the work of [4] and [18] to examine the interface…
I present the numerical computation of speed and direction of the drift of a spiral wave in an excitable medium in the presence of an electric field. In contrast to earlier results, the drift speed presents a strong variation close to the…
A review of three-dimensional waves on deep-water is presented. Three forms of three dimensionality, namely oblique, forced and spontaneous type, are identified. An alternative formulation for these three-dimensional waves is given through…
Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a sub-critical…
The formulation of a canonical deep-water breaking wave problem is introduced, and the results of a set of three-dimensional numerical simulations for deep-water breaking waves are presented. In this paper fully nonlinear progressive waves…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
A system of two-dimensional nonlinear equations of hydrodynamics is considered. It is shown that for the this system in the general case a solution with weak discontinuity-type singularity behaves as a square root of S(x,y,t), where…
In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to…
N-body simulations of disc galaxies that display recurrent transient spiral patterns are comparatively easy to construct, but are harder to understand. In this paper, I summarise the evidence from such experiments that the spiral patterns…