相关论文: Normal mode decomposition and dispersive and nonli…

A one-dimensional long-wave model of an unsteady three-layer flow of a stratified fluid under a lid is proposed, taking into account turbulent mixing in the intermediate layer. In the Boussinesq approximation, the equations of motion are…

We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…

In the study of oceanic flows at the geophysical scale, the phenomenon of density stratification plays a central role in the dynamics of the system. Two categories of mathematical models are commonly used to describe the role played by the…

Mixing effect in a stratified fluid is considered and examined. Euler equations for incompressible fluid stratified by a gravity field are applied to state a mathematical problem and describe the effect. It is found out that a system of…

We investigate the hydrostatic approximation for inviscid stratified fluids, described by the two-dimensional Euler-Boussinesq equations in a periodic channel. Through a perturbative analysis of the hydrostatic homogeneous setting, we…

In this paper we study the well-posedness in Sobolev spaces of the incompressible Euler equations in an infinite strip delimited from below by a non-flat bottom and from above by a free-surface. We allow the presence of vorticity and…

In this article we consider the multi-layer shallow water system for the propagation of gravity waves in density-stratified flows, with additional terms introduced by the oceanographers Gent and McWilliams in order to take into account…

We regard the Cauchy problem for a particular Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. We are interested in well-posedness at a very low level of regularity. We derive dispersive and…

Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this paper, we study long linear and weakly-nonlinear ring waves in a stratified fluid in the presence of a…

The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite 2D channel.…

This article is concerned with the well-posedness of the incompressible Euler equations describing a stably stratified ocean, reformulated in isopycnal coordinates. Our motivation for using this reformulation is twofold: first, its quasi-2D…

We present a perturbation-based framework that captures buoyancy effects on modal instabilities in stratified boundary-layer flows within the fully compressible, non-Oberbeck-Boussinesq formulation. Treating the Richardson number as a small…

The time evolution emanating from "internal dam-break" initial conditions is studied for a class of models of stratified Euler fluids in configurations close to two-homogeneous layers separated by a thin diffused interface. Direct numerical…

Mathematical modeling of fluid flow in a porous medium is usually described by a continuity equation and a chosen constitutive law. The latter, depending on the problem at hand, may be a nonlinear relation between the fluid's pressure…

We claim that changes of scales and fine-structure could increase from multisoliton behavior of internal waves dynamics and, further, in the so-called "wave mixing". We consider initial-boundary problems for Euler equations with a…

Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The…

In this paper, we study the stability of various difference approximations of the Euler-Korteweg equations. This system of evolution PDEs is a classical isentropic Euler system perturbed by a dispersive (third order) term. The Euler…

In this paper we present an experimental study of the long surface wave instability that can develop when a granular material flows down a rough inclined plane. The threshold and the dispersion relation of the instability are precisely…

The rigid-lid approximation is a commonly used simplification in the study of density-stratified fluids in oceanography. Roughly speaking, one assumes that the displacements of the surface are negligible compared with interface…

Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in…