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On conical swirling flows in an infinite fluid

Published online by Cambridge University Press:  26 April 2006

C. Sozou ,
L. C. Wilkinson  and
V. N. Shtern
C. Sozou
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, UK
L. C. Wilkinson
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, UK
V. N. Shtern
Affiliation:
Mechanical Engineering Department, University of Houston, 4800 Calhoun Road, Houston, Texas 77204–4792, USA
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Abstract

The steady axisymmetric flow generated in an unbounded incompressible viscous fluid, of density ρ and kinematic viscosity v, by torque-producing singularities with constant line density c along the semi-infinite line θ = 0 of a spherical polar coordinate system (r, θ, ϕ) that was investigated by Paull & Pillow (1985b), is reconsidered. The numerical solution constructed revealed the following features. (i) For values of c up to about 46.9 there is only one solution where the axial component of the meridional flow is directed from θ = 0 to θ = π. This solution can be continued to all values of c. (ii) For c > 46.9 the system of equations allows bifurcation and two more solutions with a single separatrix are possible. (iii) For c = ∞ one of the two branches of the separatrix asymptotes to θ = ½π and the other to θ = π. The asymptotic solution for large c constructed by Paull & Pillow (1985b), where the meridional flow consists of two colliding flows, relates to the bifurcation solution where the separatrix asymptotes to ½π as c → ∞.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 276 , 10 October 1994 , pp. 261 - 271
Copyright
© 1994 Cambridge University Press

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References

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