Exact Solution for the Stokes Problem of an Infinite Cylinder in a Fluid with Harmonic Boundary Conditions at Infinity

Details Exact Solution for the Stokes Problem of an Infinite Cylinder in a Fluid with Harmonic Boundary Conditions at Infinity Exact Solution for the Stokes Problem of an Infinite Cylinder in a Fluid with Harmonic Boundary Conditions at Infinity

2008-03-31

arxiv.org/abs/0804.0023v2

Physics

Mathematical Physics

Minor corrections with respect to typos and readability

Scientific paper

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.

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