Related papers: Edge waves along a sloping beach
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 free surface water waves in a 2-D symmetric triangular channel with sides that have a 45o slope. We develop models for small amplitude nonlinear waves, extending earlier studies that have considered the linearized problem. We see…
Lagrangian averaging has been shown to be more effective than Eulerian mean in separating waves from slow dynamics in two-timescale flows. It also appears in many reduced models that capture the wave feedback on the slow flow. Its…
We describe a simple mechanical system, a ball rolling along a specially-designed landscape, that mimics the dynamics of a well known phenomenon, the two-bounce resonance of solitary wave collisions, that has been seen in countless…
We determine the phase portrait of a Hamiltonian system of equations describing the motion of the particles in linear deep-water waves. The particles experience in each period a forward drift which decreases with greater depth.
The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom…
We numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and the breaking of solitary waves. The numerical method utilizes…
For any kind of wave phenomenon one can find ways to derive the respective dispersion relation from experimental observations and measurements. This dispersion relation determines the structure of the wave equation and thus characterizes…
The majority of coastal flows are characterized by turbulence, rendering the application of shallow water equations an inadequate approach for their accurate description. This paper presents a theory for characterizing accelerated coastal…
Exact plane gravitational radiation fields are presented within the framework of general relativity and their properties are described. The physics of nonlinear elliptically polarized plane gravitational waves is developed in close analogy…
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves,…
Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…
Direct phase-resolved simulations are performed to investigate the propagation and scattering of nonlinear ocean waves in fragmented sea ice. The numerical model solves the full time-dependent equations for nonlinear potential flow coupled…
We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and…
The propagation of wave disturbances over a vertically oscillating liquid may form standing waves, known as Faraday waves. Here we present an alternative description of the generation and evolution of Faraday waves by nonlinear resonant…
In the linear approximation, we study a one-dimensional problem of the reflectionless wave propagation on a surface of a shallow duct with the spatially varying water depth, duct width, and current. We show that both global and bounded…
We compute electromagnetic wave propagation through the magnetosphere of a magnetar. The magnetosphere is modeled as the QED vacuum and a cold, strongly magnetized plasma. The background field and electromagnetic waves are treated…
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…
We investigate the propagation of transverse elastic waves in crumpled media. We set up the wave equation for transverse waves on a generic curved, strained surface via a Langrangian formalism and use this to study the scaling behaviour of…
Coastal erosion is a major and growing environmental problem describing the movement of sand caused by tides, waves or currents. Several phenomena contribute to the significant advance of the sea. These include climate change, with rising…