Exact Solution for the Stokes Problem of an Infinite Cylinder in a Fluid with Harmonic Boundary Conditions at Infinity
Mathematical Physics
2008-04-14 v2 math.MP
Abstract
We present an exact solution for the time-dependent Stokes problem of an infinite cylinder of radius r=a in a fluid with harmonic boundary conditions at infinity. This is a 3-dimensional problem but, because of translational invariance along the axis of the cylinder it effectively reduces to a 2-dimensional one. The Stokes problem being a linear reduction of the full Navier-Stokes equations, we show how to satisfy the no-slip boundary condition at the cylinder surface and the harmonic boundary condition at infinity, exhibit the full velocity field for radius r>a, and discuss the nature of the solutions for the specific case of air at sea level.
Keywords
Cite
@article{arxiv.0804.0023,
title = {Exact Solution for the Stokes Problem of an Infinite Cylinder in a Fluid with Harmonic Boundary Conditions at Infinity},
author = {Andreas N. Vollmayr and Jan-Moritz P. Franosch and J. Leo van Hemmen},
journal= {arXiv preprint arXiv:0804.0023},
year = {2008}
}
Comments
Minor corrections with respect to typos and readability