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The critical state: a trapped wave model of vortex breakdown

Published online by Cambridge University Press:  29 March 2006

J. D. Randall  and
S. Leibovich
J. D. Randall
Affiliation:
Upson Hall, Corn011 University, Ithaca, N.Y. 14850
S. Leibovich
Affiliation:
Upson Hall, Corn011 University, Ithaca, N.Y. 14850
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Abstract

A model of vortex breakdown is presented and its predictions compared with the experiments of Sarpkaya (1971). The model is cntred about a theory of long, weakly nonlinear waves propagating on critical flows in tubes of variable cross-section. Although the weakly nonlinear theory must be extended beyond its domain of formal validity, many of the experimentally observed features of vortex breakdown are reproduced by the model. The description of the time evolution of the flow field that is presented requires numerical calculations that are not simple, but some important conclusions may be determined by easy computations. In particular, the axial position of a breakdown may be found from a very simple equation (10).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 3 , 8 May 1973 , pp. 495 - 515
Copyright
© 1973 Cambridge University Press

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References

Batchelor, G. K. 1964 Axial flow in trailing line vortices. J. Fluid Mech. 20, 645.Google Scholar
Benjamix, T. B. 1962 Theory of the vortex breakdown phenomenon. J. Fluid Mech. 14, 593.Google Scholar
Benjamin, T. B. 1967 Some developments in the theory of vortex breakdown. J. Fluid Mech. 28, 65Google Scholar
Bossel, H. H. 1967 Inviscid and viscous models of the vortex breakdown phenomenon. Ph.D. Thesis, University of California, Berkeley.
Bossm, H. H. 1969 Vortcx breakdown flowfiold, Phys. Fluids, 12, 498.Google Scholar
Hall, M. G. 1965 A numerical method for solving the equations for a vortex core. Aero. Res. Counc. R. &. M. no. 3467.
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
Howard, L. N. & Gupta, A. S. 1962 On the hydrodynamic and hydromagnetic stability of swirling flows. J. Fluid Mech. 14, 463.Google Scholar
Kirkpatrice, D. L. I. 1965 Experimental investigations of the breakdown of a vortex in a tube. Aero. Res. Counc. Current Paper, no. 821.
Korteweg, D. J. & De Vries, G. 1895 On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Phil. Mag. 39 (5), 422.Google Scholar
Leibovich, S. 1968 Axially-symmetric eddies embedded in a rotational stream. J. Fluid Mech. 32, 629.Google Scholar
Leibovich, S. 1969 Wave motion and vortex breakdown. A.I.A.A. Paper, no. 69–645.
Leibovich, S. 1970 Weakly non-linear waves in rotating fluids. J. Fluid Mech. 42, 803.Google Scholar
Leibovich, S. & Randall, J. D. 1971 Dissipative effects on non-linear waves in rotating fluids. Phys. Fluids, 14, 2559.Google Scholar
Leibovich, S. & Randall, J. D. 1973 A amplification and decay of long nonlinear waves. J. Fluid Mech. 58, 481.Google Scholar
Pritchard, W. G. 1969 The motion generated by a body moving along the axis of a uniformly rotating fluid. J. Fluid Mech. 39, 443.Google Scholar
Randall, J. D. 1972 Two studies of solitary wave propagation in rotating fluids. Ph.D. Thesis, Cornell University.
Sarpraya, T. 1970 An experimental investigation of the vortex breakdown phenomenon. U.S. Naval Postgrad. School. Rep. NPS-59L007lA.
Sarpkaya, T. 1971 On stationary and travelling vortex breakdowns. J. Fluid Mech. 45, 545.Google Scholar
Squire, H. B. 1962 Analysis of the ‘vortex breakdown’ phenomenon. In Mizellaneen du Angewandten Mechanik. Berlin: Akademie.
Zabusky, N. J. 1968 Solitons and bound states of the time-independent Schrodinger equation. Phys. Rev. 168, 124.Google Scholar