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Weak thermal vortex rings

Published online by Cambridge University Press:  28 March 2006

B. R. Morton
B. R. Morton
Affiliation:
Department of Mathematics, University of Manchester
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Abstract

A similarity solution is obtained up to the first order in an effective Rayleigh number for the behaviour of very weak thermal vortex rings produced by the rapid release of heat at one point of a large region of fluid.

The laminar pattern of flow is similar to that in ordinary vortex rings, but the temperature decreases outwards from the centre in all directions with some asymmetry about the horizontal plane through the centre, and there is no accumulation of heat into the vortex ring. The vortex propagates slowly in relation to its rate of growth, and the process is dominated by viscous and thermal diffusion.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 9 , Issue 1 , September 1960 , pp. 107 - 118
Copyright
© 1960 Cambridge University Press

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References

Carslaw, H. S. & Jaeger, J. C. 1947 The conduction of heat in solids. Oxford University Press.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Taylor, G. I. 1950 Proc. Roy. Soc. A, 201, 192.
Turner, J. S. 1957 Proc. Roy. Soc. A, 239, 61.