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A laminar jet in a rotating fluid

Published online by Cambridge University Press:  28 March 2006

D. M. Herbert
D. M. Herbert
Affiliation:
Department of Mathematics, the University of manchester
Now at Imperial College, London.
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Abstract

A solution is presented of the asymptotic flow due to a point source of momentum in a uniformly rotating unbounded environment. Under the condition that the relative swirl velocity of the jet is small compared with the ambient swirl velocity, the equations of motion reduce to a set of linear equations. These equations are expressed in terms of similarity variables and a single ordinary differential equation is derived in terms of the similarity stream function. The profiles of the flow are calculated numerically.

The jet is shown to have a narrow viscous core whose thickness increases with distance z from the virtual source of momentum as ($(vz|\Omega)^{\frac {1}{3}}$, where v is the kinematic viscosity and Ω the ambient angular velocity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 23 , Issue 1 , September 1965 , pp. 65 - 75
Copyright
© 1965 Cambridge University Press

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References

Long, R. R. 1958 Vortex motion in a viscous fluid. J. Meteor. 15, 108.Google Scholar
Long, R. R. 1961 A vortex in an infinite viscous fluid. J. Fluid Mech. 11, 611.Google Scholar
Wright, E. M. 1935 The asymptotic expansion of the generalized hypergeometric function. J. London Math. Soc. 10, 286.Google Scholar