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Continuation or breakdown in tornado-like vortices

Published online by Cambridge University Press:  11 April 2006

Odus R. Burggraf  and
M. R. Foster
Odus R. Burggraf
Affiliation:
Department of Aeronautical and Astronautical Engineering, The Ohio State University, Columbus
M. R. Foster
Affiliation:
Department of Aeronautical and Astronautical Engineering, The Ohio State University, Columbus
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Abstract

Laboratory experiments on swirling flows through tubes often exhibit a phenomenon called vortex breakdown, in which a bubble of reversed flow forms on the axis of swirl. Mager has identified breakdown with a discontinuity in solutions of the quasicylindrical flow equations. In this study we define a tornado-like vortex as one for which the axial velocity falls to zero for sufficiently large radius, and seek to clarify the conditions under which the solution of the quasi-cylindrical flow equations can be continued indefinitely or breaks down at a finite height. Vortex breakdown occurs as a dynamical process. Hence latent-heat effects, though doubtless important to the overall structure and maintenance of the tornado, are neglected here on the scale of the breakdown process. The results show that breakdown occurs when the effective axial momentum flux (flow force) is less than a critical value; for higher values of the flow force, the solution continues indefinitely, with Long's (1962) similarity solution as the terminal state. When applied to the conditions of the 1957 Dallas tornado, the computed breakdown location is in agreement with Hoecker's analysis of the observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 80 , Issue 4 , 23 May 1977 , pp. 685 - 703
Copyright
© 1977 Cambridge University Press

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