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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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References

Barcilon, A. 1967 Vortex decay above a stationary boundary. J. Fluid Mech. 27, 155.Google Scholar
Benjamin, T. B. 1967 Some developments in the theory of vortex breakdown. J. Fluid Mech. 28, 65.Google Scholar
Burggraf, O. R. & Foster, M. R. 1975 Theoretical study of vortex breakdown in tornado-like vortices. Final Rep. U.S. Dept. Commerce, grant 04–3–022–37.
Burggraf, O. R., Stewartson, K. & Belcher, R. 1971 The boundary layer induced by a potential vortex. Phys. Fluids 14, 1921.Google Scholar
Hall, M. G. 1966 The structure of concentrated vortex cores. Prog. Aero. Sci., vol. 7. Pergamon.
Hall, M. G. 1967 A numerical method of solving the equations of the vortex core. Aero. Res. Counc. R. & M. no. 3467.Google Scholar
Hall, M. G. 1972 Vortex breakdown. Ann. Rev. Fluid Mech. 4, 195.Google Scholar
Harvey, J. K. 1962 Some observations of the vortex breakdown phenomenon. J. Fluid Mech. 14, 585.Google Scholar
Hoecker, W. H. 1960 Wind speed and air flow patterns in the Dallas tornado of April 2, 1957. Mon. Weather Rev. 88, 167.Google Scholar
Kirkpatrick, D. L. I. 1964 Experimental investigation of the breakdown of a vortex in a tube. R.A.E. Tech. Note Aero 2963, ARC 26227.
Lambourne, N. C. & Bryer, D. W. 1961 The bursting of leading-edge vortices — some observations and discussion of the phenomenon. Aero. Res. Counc. R. & M. no. 3282.Google Scholar
Long, R. R. 1962 A vortex in an infinite viscous fluid. J. Fluid Mech. 11, 611.Google Scholar
Mager, A. 1972 Dissipation and breakdown of a wing-tip vortex. J. Fluid Mech. 55, 609.Google Scholar
Morton, B. R. 1969 The strength of vortex and swirling core flows. J. Fluid Mech. 38, 315.Google Scholar
Nachtsheim, P. R. & Swigert, P. 1965 Satisfaction of asymptotic boundary conditions in numerical solution of systems of non-linear equations of boundary layer type. N.A.S.A. Tech. Note D-3004.
Randall, J. D. & Leibovich, S. 1973 The critical state: a trapped wave model of vortex breakdown. J. Fluid Mech. 58, 495.Google Scholar
Reber, C. M. 1954 The South Platte Valley tornadoes of June 7, 1953. Bull. Am. Met. Soc. 35, 191.Google Scholar
Sarpkaya, T. 1971 On stationary and travelling vortex breakdowns. J. Fluid Mech. 45, 545.Google Scholar
Squire, H. B. 1960 Analysis of the ‘vortex breakdown’ phenomenon. Part I. Imp. Coll. Aero. Dept. Rep. no. 102.Google Scholar
Ward, N. B. 1972 The explanation of certain features of tornado dynamics using a laboratory model. J. Atmos. Sci. 29, 1194.Google Scholar