On the stability of incompressible viscous fluid motions past objects

On the Stability of the Motion of a Viscous Fluid.

A criterion for the stability of the steady motion of a viscous fluid between two parallel planes was established by Reynolds' as 2pbUr1nu < 517, where p = density, 2b = distance between the parallel planes, Un. mean velocity, and , = coefficient of viscosity. A much lower figure 167 was found by Sharpe2 and later Orr3 obtained the figure 117. In this paper by expressing the small motion which ...

Concerning the Effect of a Viscoelastic Foundation on the Dynamic Stability of a Pipeline System Conveying an Incompressible Fluid

In this paper, we present an analytical method for solving a well-posed boundary value problem of mathematical physics governing the vibration characteristics of an internal flow propelled fluid-structure interaction where the pipeline segment is idealized as an elastic hollow beam conveying an incompressible fluid on a viscoelastic foundation. The effect of Coriolis and damping forces on the o...

Asymptotic stability of Oseen vortices for a density-dependent incompressible viscous fluid

In the analysis of the long-time behaviour of two-dimensional incompressible viscous fluids, Oseen vortices play a major role as attractors of any homogeneous solution with integrable initial vorticity [8]. As a first step in the study of the density-dependent case, the present paper establishes the asymptotic stability of Oseen vortices for slighty inhomogeneous fluids with respect to localize...

Mathematical models of turbulent motion of an incompressible viscous fluid

Motion of an Elastic Solid inside an Incompressible Viscous Fluid

The motion of an elastic solid inside an incompressible viscous fluid is ubiquitous in nature. Mathematically, such motion is described by a PDE system that couples the parabolic and hyperbolic phases, the latter inducing a loss of regularity which has left the basic question of existence open until now. In this paper, we prove the existence and uniqueness of such motions (locally in time), whe...