Abstract
The stability is considered of the flow with velocity components
\[
\{0,\Omega r[1+O(\epsilon^2)],\;2\epsilon\Omega r_0f(r/r_0)\}
\]
(where f(x) is a function of order one) in cylindrical polar co-ordinates (r, ϕ, z), bounded by the rigid cylinders r/r0 = x1 and r/r0 = 1 (0 [les ] x1 < 1). When ε [Lt ] 1, the flow is shown to be unstable to non-axisymmetric inviscid disturbances of sufficiently large axial wavelength. The case of Poiseuille flow in a rotating pipe is considered in more detail, and the growth rate of the most rapidly growing disturbance is found to be 2εΩ.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference3 articles.
1. Watson, G. N. 1944 Theory of Bessel Functions ,2nd ed. Cambridge University Press.
2. Ludwieg, H. 1961 Z. Flugwiss. 9,359.
3. Howard, L. N. & Gupta, A. S. 1962 J. Fluid Mech. 14,463.
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