Related papers: Edge waves along a sloping beach
In this paper we examine the flow generated by coupled surface and internal small-amplitude water waves in a two-fluid layer model, where we take the upper layer to be rotational (constant vorticity) and the lower layer to be irrotational.…
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…
The paper considers the application of two numerical models to simulate the evolution of steep breaking waves. The first one is a Lagrangian wave model based on equations of motion of an inviscid fluid in Lagrangian coordinates. A method…
In this paper, we numerically show and discuss the existence and characteristics of rogue heat and diffusion waves. More specifically, we use two different nonlinear heat (diffusion) models and show that modulation instability leads to the…
The description of complex wave processes, in addition to the shoaling problem, is often cumbersome even for the evolution of regular waves. For reflection under the regime of wave breaking, the surf similarity is generally accepted as the…
We study discrete rogue waves in an array of nonlinear waveguides. We show that very small degree of disorder due to experimental imperfection has a deep effect on the formation of discrete rogue waves. We predict long-living discrete rogue…
The Green-Naghdi equations are a nonlinear dispersive perturbation of the nonlinear shallow water equations, more precise by one order of approximation. These equations are commonly used for the simulation of coastal flows, and in…
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…
This paper presents a new numerical model based on the highly nonlinear potential flow theory for simulating the propagation of water waves in variable depth. A new set of equations for estimating the surface vertical velocity is derived…
In order to obtain quite precise information about the shape of the particle paths below small-amplitude gravity waves travelling on irrotational deep water, analytic solutions of the nonlinear differential equation system describing the…
The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous…
We experimentally investigate internal coastal Kelvin waves in a two-layer fluid system on a rotating table. Waves in our system propagate in the prograde direction and are exponentially localized near the boundary. Our experiments verify…
Ocean wind waves are a fundamental manifestation of complex dynamics in geophysical fluid systems, characterized by a rich interplay between dispersion and nonlinearity. While linear wave theory provides a first-order description of wave…
Numerical simulations of fully nonlinear equations of motion for long-crested waves at deep water demonstrate that in elongate wave groups the formation of extreme waves occurs most intensively if in an initial state the wave fronts are…
In this article, we introduce a moving-frame approach to the geophysical equation of two-dimensional uniformly stratified rotational fluid in oceans and find a family of exact solutions containing ten arbitrary parameter functions.
We predict the existence of linear discrete rogue waves governed by the discrete nonlinear Schrodinger equation. We discuss that Josephson effect is the underlying reason for the formation of such waves.
Propagation of gravitational and acoustic plane waves in a flat universe filled with a general relativistic, homogeneous and isotropic, spatially flat continuum is studied. The continuum is described by analogues of nonrelativistic…
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…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
Mathematical modeling of resonant waves propagating in 2D periodic infinite lattices is conducted. Rectangular-cell, triangular-cell and hexagonal-cell lattices are considered. Eigenvalues (here eigenfrequencies) of steady-state problems…