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An unsteady two-cell vortex solution of the Navier—Stokes equations

Published online by Cambridge University Press:  29 March 2006

P. G. Bellamy-Knights
P. G. Bellamy-Knights
Affiliation:
Department of the Mechanics of Fluids, University of Manchester
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Abstract

The steady two-cell viscous vortex solution of Sullivan (1959) is extended to yield unsteady two-cell viscous vortex solutions which behave asymptotically as certain analogous unsteady one-cell solutions of Rott (1958). The radial flux is a parameter of the solution, and the effect of the radial flow on the circumferential velocity, is analyzed. The work suggests an explanation for the eventual dissipation of meteorological flow systems such as tornadoes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 41 , Issue 3 , 29 April 1970 , pp. 673 - 687
Copyright
© 1970 Cambridge University Press

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References

Burgers, J. M. 1940 Application of a model system to illustrate some points of the statistical theory of free turbulence. Proc. Acad. Sci. Amst. 43, 2.Google Scholar
Burgers, J. M. 1948 A mathematical model illustrating the theory of turbulence. Adv. appl. Mech. 1, 197.Google Scholar
Morton, B. R. 1966 Geophysical vortices. Progress in Aeronautical Sciences, 7, 145.Google Scholar
Oseen, C. W. 1911 Ark. Mat. Astr. Fys. 7.
Rott, N. 1958 On the viscous core of a line vortex. Z.A.M.P. 9 b, 543.Google Scholar
Rott, N. 1959 On the viscous core of a line vortex II. Z.A.M.P. 10, 73.Google Scholar
Sullivan, R. D. 1959 A two-cell solution of the Navier—Stokes equations. J. Aero/Space Sci. 26, 767.Google Scholar