Related papers: Many Models for Water Waves
We present a rigorous mathematical analysis of the modeling of inviscid water waves. The free-surface is described as a parametrized curve. We introduce a numerically stable algorithm which accounts for its evolution with time. The method…
In this work we study and contrast implicit solvation models against explicit atomistic, quantum mechanical models in the description of the band alignment of semiconductors in aqueous environment, using simulations based on density…
A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids in two-dimensional domains. Beginning with the general Hamiltonian formalism of…
This article describes the fluid dynamics video, "A Numerical Simulation of a Plunging Breaking Wave", which was submitted to the gallery of fluid motion at the 2009 APS/DFD conference. The simulation was of a deep-water plunging breaking…
In the paper a new nonlinear equation describing shallow water waves with the topography of the bottom directly taken into account is derived. This equation is valid in the weakly nonlinear, dispersive and long wavelength limit. Some…
The problem of reconstructing non-harmonic internal gravity wave packets generated by a source moving in a stratified ocean is considered. The uniform asymptotic form of the internal gravity waves field generated by a source moving above…
Waves play an essential role in many aspects of plasma science, such as plasma manipulation and diagnostics. Due to the complexity of the governing equations, approximate models are often necessary to describe wave dynamics. In this…
Many complex systems exhibit hydrodynamic (or macroscopic) behavior at large scales characterized by few variables such as the particle number density, temperature and pressure obeying a set of hydrodynamic (or macroscopic) equations. Does…
The motion of the free surface of an incompressible fluid is a very active research area. Most of these works examine the case of an inviscid fluid. However, in several practical applications, there are instances where the viscous damping…
We present an explicit scheme for a two-dimensional multilayer shallow water model with density stratification, for general meshes and collocated variables. The proposed strategy is based on a regularized model where the transport velocity…
The paper takles a procedure which allow to extend some linear, wave type equations to the study of nonlinear models. More concretely, we present a practical way to generate the largest class of a given form of second order differential…
We prove the local well-posedness for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime.
The floating structure problem describes the interaction between surface water waves and a floating body, generally a boat or a wave energy converter. As shown by Lannes in [18] the equations for the fluid motion can be reduced to a set of…
In the present Letter we use the Direct Numerical Simulation (DNS) of the Navier-Stokes equation for a two-phase flow (water and air) to study the dynamics of the modulational instability of free surface waves and its contribution to the…
In this work we study the generation of water waves by an underwater sliding mass. The wave dynamics are assumed to fell into the shallow water regime. However, the characteristic wavelength of the free surface motion is generally smaller…
In the study of ocean wave impact on structures, one often uses Froude scaling since the dominant force is gravity. However the presence of trapped or entrained air in the water can significantly modify wave impacts. When air is entrained…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
We derive a new approach to analyze the coupling of linear Boussinesq and Saint-Venant shallow water wave equations in the case where the interface remains at a constant position in space. We propose a one-way coupling model as a reference,…
In this paper, we give the first rigorous justification of the Benjamin-Ono equation as an internal water wave model on the physical time scale. Let $\varepsilon$ be the small parameter measuring the weak nonlinearity of the waves, $\mu$ be…
In this contribution we describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of…