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Similarity solutions for viscous vortex cores

Published online by Cambridge University Press:  26 April 2006

Ernst W. Mayer  and
Kenneth G. Powell
Ernst W. Mayer
Affiliation:
Department of Aerospace Engineering, The University of Michigan. Ann Arbor, MI 48109, USA
Kenneth G. Powell
Affiliation:
Department of Aerospace Engineering, The University of Michigan. Ann Arbor, MI 48109, USA
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Abstract

Results are presented for a class of self-similar solutions of the steady, axisymmetric Navier–Stokes equations, representing the flows in slender (quasi-cylindrical) vortices. Effects of vortex strength, axial gradients and compressibility are studied. The presence of viscosity is shown to couple the parameters describing the core growth rate and the external flow field, and numerical solutions show that the presence of an axial pressure gradient has a strong effect on the axial flow in the core. For the viscous compressible vortex, near-zero densities and pressures and low temperatures are seen on the vortex axis as the strength of the vortex increases. Compressibility is also shown to have a significant influence upon the distribution of vorticity in the vortex core.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 238 , May 1992 , pp. 487 - 507
Copyright
© 1992 Cambridge University Press

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