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A three-dimensional analogue of the Prandtl-Batchelor closed streamline theory

Published online by Cambridge University Press:  19 April 2006

P. J. Blennerhassett
P. J. Blennerhassett
Affiliation:
School of Mathematics, University of New South Wales, P.O. Box 1, Kensington, N.S.W. 2033, Australia
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Abstract

For steady laminar flow with closed streamlines Batchelor (1956) has shown how an integral condition arising from the effect of viscosity can be used with the inviscid flow equations to determine the vorticity distribution when the Reynolds number is large. Here a condition analogous to that used by Batchelor is derived for a class of flows with helical streamlines. An exact integral condition relating the constant axial pressure gradient and the viscous terms is obtained, which when combined with the inviscid flow equations leads to the result that the axial velocity is proportional to the stream function for the motion in the plane normal to the axial velocity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 93 , Issue 2 , 26 July 1979 , pp. 319 - 324
Copyright
© 1979 Cambridge University Press

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References

Batchelor, G. K. 1956 J. Fluid Mech. 1, 177.
Blennerhassett, P. J. 1976 Ph.D. thesis, University of London.
Burggraf, O. R. 1966 J. Fluid Mech. 24, 113.
Wood, W. W. 1957 J. Fluid Mech. 2, 77.