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A note on a source in a rotating liquid

Published online by Cambridge University Press:  24 October 2008

K. Stewartson
K. Stewartson
Affiliation:
University College London
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Extract

Consider an inviscid incompressible fluid confined within an infinite tube of radius b and assume that its motion initially consists of a uniform translation with velocity U and a uniform rotation, with angular velocity ω, about the tube axis. Suppose now that at time t = 0 a unit source of fluid situated at a point O of the axis begins to emit fluid at a uniform rate and that ultimately the flow pattern so modified becomes steady (at a fixed point as t → ∞). Under the further assumption that far upstream flow conditions are undisturbed by the source the stream function ψ of the disturbance satisfies

where z denotes distance along the axis from O, r distance from the axis and k = 2ω/U.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 2 , April 1968 , pp. 507 - 511
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Fraenkel, L. E.Proc. Boy. Soc. Ser. A 233 (1956), 506.Google Scholar
(2)Stewartson, K.Quart. J. Mech. Appl. Math. 11 (1958), 39.CrossRefGoogle Scholar
(3)Stewartson, K.Quart. J. Mech. Appl. Math. 21 (1968) (accepted for publication).Google Scholar