Related papers: Dispersive and non-dispersive nonlinear long wave …
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…
Motivated by the discrepancy between satellite observations of coherent westward propagating surface features and Rossby wave theory, this paper revisits the planetary wave propagation problem, taking into account the effects of lateral…
The dispersing equation was derived from system of the hydrodynamic equations that take into account the gravity, and from boundary conditions of shock front. The dispersing equation made it possible to study unstable stability of front not…
We present a phenomenological approach to dispersion in nonlinear elasticity. A simple, thermomechanically sound, constitutive model is proposed to describe the (non-dissipative) properties of a hyperelastic dispersive solid, without…
This paper describes the results from a numerical estimation of the force exerted by long surface waves on a fixed and partially immersed rectangular structure. The topic is connected with the need of making decisions on the design,…
Wave impact and run-up onto vertical obstacles are among the most important phenomena which must be taken into account in the design of coastal structures. From linear wave theory, we know that the wave amplitude on a vertical wall is twice…
Nonlinear wave propagation in large extra spatial dimensions (on and above $d=2$) is investigated in the context of nonlinear electrodynamics theories that depend exclusively on the invariant…
Processes of propagation and interaction of nonlinear gravity-capillary waves on the free surface of a deep non-conducting liquid with high dielectric constant under the action of a tangential electric field are numerically simulated. The…
The propagation of weak gravitational waves on the background of dark energy is studied. The consideration is carried out within the framework of an approximate approach where the cosmological scale factor is expanded as a power series for…
To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the…
This article introduces a physically realistic model for explaining how electromagnetic waves can be internally generated, propagate and interact in strongly magnetized plasmas or in nuclear magnetic resonance experiments. It studies high…
This paper is concerned with the processes of spatial propagation and penetration of turbulence from the regions where it is locally excited into initially laminar regions. The phenomenon has come to be known as "turbulence spreading" and…
In this work, we investigate mathematical models for electromagnetic wave propagation in dispersive isotropic media. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is…
We perform full-scale numerical simulation of instability of weakly nonlinear waves on the surface of deep fluid. We show that the instability development leads to chaotization and formation of wave turbulence. We study instability both of…
Wave breaking is a critical process in the upper ocean: an energy sink for the surface wave field and a source for turbulence in the ocean surface boundary layer. We apply a novel multi-layer numerical solver resolving upper-ocean dynamics…
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…
Numerical simulations of the unidirectional random waves are performed within the Korteweg -de Vries equation to investigate the statistical properties of surface gravity waves in shallow water. Nonlinear evolution shows the relaxation of…
Wave shoaling of water waves over mild bottom slopes is well described by linearized theories. However, the analytical treatment of nonlinear wave shoaling subject to rapidly varying bottoms has proven to be elusive in the past decades. As…
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…
The study of the process of catastrophic tsunami-type waves on the coast makes it possible to determine the destructive force of waves on the coast. In hydrodynamics, the one-dimensional theory of the run-up of non-linear waves on a flat…