Related papers: Many Models for Water Waves
In the present manuscript, we consider the practical problem of wave interaction with a vertical wall. However, the novelty here consists in the fact that the wall can move horizontally due to a system of springs. The water wave evolution…
This paper describes a method for deriving approximate equations for irrotational water waves. The method is based on a 'relaxed' variational principle, i.e., on a Lagrangian involving as many variables as possible. This formulation is…
We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model, and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic…
A new theory of edge waves over a slowly varying depth.
Wave shape (i.e. skewness or asymmetry) plays an important role in beach morphology evolution, remote sensing, and ship safety. Wind's influence on ocean waves has been extensively studied theoretically in the context of growth, but most…
In this study we investigate shallow turbidity density currents and underflows from mechanical point of view. We propose a simple hyperbolic model for such flows. On one hand, our model is based on very basic conservation principles. On the…
This study deals with asymptotic models for the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with a flat bottom. We present…
Many equations that arise in a physical context can be posed in the form of a Hamiltonian system, meaning that there is a symplectic structure on an appropriate phase space, and a Hamiltonian functional with respect to which time evolution…
Shallow water equations are extensively considered in the domains of oceans, atmospheric modelling, and engineering research (Franca et al., 2022), which play significant roles in floods and tsunami governance. Nonetheless, the accurate…
We derive and analyze in the framework of the mild-slope approximation a new double-layer Boussinesq-type model which is linearly and nonlinearly accurate up to deep water. Assuming the flow to be irrotational, we formulate the problem in…
We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated and motion of the…
We present a model of mesoparticles, very much in the Dissipative Particle Dynamics spirit, in which a molecule is replaced by a particle with an internal thermodynamic degree of freedom (temperature or energy). The model is shown to give…
In order to describe the dynamics of monochromatic surface waves in deep water, we derive a nonlinear and dispersive system of equations for the free surface elevation and the free surface velocity from the Euler equations in infinite…
A new analytical approach to description of electromagnetic waves in nonmagnetic anisotropic media is presented. Amplitudes of their reflection and refraction at interfaces and also reflection and transmission of plane parallel plates are…
This paper is a continuation of research started in [7] devoted to explicit asymptotic formulas for standing coastal-trapped waves. Our main goal is to construct formal asymptotic eigenfunctions of the wave operator $\langle \nabla,…
An experimental validation of theoretical models of transmission of regular water waves by large arrays of floating disks is presented. The experiments are conducted in a wave basin. The models are based on combined potential-flow and…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
We establish a shallow water model for flows of electrically conducting fluids in homogeneous static magnetic fields that are confined between two parallel planes where turbulent Hartmann layers are present. This is achieved by modelling…
We propose a generic, phenomenological approach to modifying the dispersion of gravitational waves, independent of corrections to the generation mechanism. This model-independent approach encapsulates all previously proposed…
The paper continues the analysis, started in [1] (Part I,arXiv:2302.04353), of the model open wave-guide problem defined by 2 semi-infinite, rectangular wave-guides meeting along a common perpendicular line. In Part I we reduce the solution…