Related papers: A Variational Characterization of Fluid Sloshing w…
We study the zero-viscosity limit of free boundary Navier-Stokes equations with surface tension in $\mathbb{R}^3$ thus extending the work of Masmoudi and Rousset [1] to take surface tension into account. Due to the presence of boundary…
Large scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory. At first order in both the random force amplitude and the angular velocity we find two types of…
In the paper we study the shape of the fundamental sloshing mode of a liquid in a container. Our approach is based on a mathematical model which is an appropriate Steklov eigenvalue problem. We present numerical results, a physical…
The paper addresses the question if there exists a finite stopping time for an unforced motion of a yield stress fluid with free surface. A variation inequality formulation is deduced for the problem of yield stress fluid dynamics with a…
We analyze the dynamics of concentrated polymer solutions modeled by a 2D Smoluchowski equation. We describe the long time behavior of the polymer suspensions in a fluid. When the flow influence is neglected the equation has a gradient…
We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a general rigid bottom in a three-dimensional horizontally periodic setting. We establish the…
Certain unresolved ambiguities surround pressure determinations for incompressible flows, both Navier-Stokes and magnetohydrodynamic. For uniform-density fluids with standard Newtonian viscous terms, taking the divergence of the equation of…
This paper studies the dynamics of an incompressible fluid driven by gravity and capillarity forces in a porous medium. The main interest is the stabilization of the fluid in Rayleigh-Taylor unstable situations where the fluid lays on top…
Here we have considered the effects of shallowness of the domain as well as the air-water free surface on the stratified shear instabilities of the fluid underneath. First, we numerically solve the non-Boussinesq Taylor-Goldstein equation…
We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…
We use spherical coordinates to devise a new exact solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible fluid with a general density distribution and subjected to forcing terms. The latter are…
This study examines the stability of a flexible material interface between two fluids of the same viscosity in interaction with a free surface. When the layers are motionless, we provide evidence for the onset of a novel instability by…
The linear transport equation allows to advect level-set functions to represent moving sharp interfaces in multiphase flows as zero level-sets. A recent development in computational fluid dynamics is to modify the linear transport equation…
Several methods for handling sloping fluid-solid interfaces with the elastic parabolic equation are tested. A single-scattering approach that is modified for the fluid-solid case is accurate for some problems but breaks down when the…
Motivated by a number of recent experimental and computational studies of the dynamics of fluids plunged in quenched-disordered external fields, we report on a theoretical investigation of this topic within the framework of the…
In order to describe behavior of various liquid-like materials at high pressures, incompressible fluid models with pressure dependent viscosity seem to be a suitable choice. In the context of implicit constitutive relations involving the…
Sloshing eigenvalues are studied for containers with porous baffles extending throughout the constant (possibly infinite) depth. The fluid transmission across the baffles is described by Darcy's law, and so the spectral problem is…
We study a free boundary problem which is motivated by a particular case of the flow of a non-Newtonian fluid, with a pressure depending yield stress given by a Drucker-Prager plasticity criterion. We focus on the steady case and…
Surface tension and wetting are dominating physical effects in micro and nanoscale flows. We present an efficient and reliable model of surface tension and equilibrium contact angles in Smoothed Particle Hydrodynamics for free-surface…
Sloshing eigenvalues and eigenfunctions are studied for vertical cylinders of constant, finite depth occupied by a two-layer fluid. Two families of eigenfrequencies are obtained in the form expressing them explicitly via the eigenvalues of…