On the stability of Poiseuille pipe flow

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1969

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Abstract

The problem of the stability of Poiseuille pipe flow was studied numerically. The finite-difference equations which were solved are approximations to the nonlinear, axisymmetric, Navier-Stokes equations in cylindrical coordinates subject to a stream function perturbation. The disturbance to the stream function which was used is axisymmetric, oscillatory and fixed in space. The resulting solutions show the experimentally observed instability of the stream function and vorticity at Reynolds numbers of 10,000 and 100,000. The experimentally observed stability at a Reynolds number of 1,000 is also found.

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