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We present an exact solution for the time-dependent Stokes problem of aninfinite cylinder of radius r=a in a fluid with harmonic boundary conditions atinfinity. This is a 3-dimensional problem but, because of translationalinvariance along the axis of the cylinder it effectively reduces to a2-dimensional one. The Stokes problem being a linear reduction of the fullNavier-Stokes equations, we show how to satisfy the no-slip boundary conditionat the cylinder surface and the harmonic boundary condition at infinity,exhibit the full velocity field for radius r>a, and discuss the nature of thesolutions for the specific case of air at sea level.

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