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The dynamics of stretched vortices

Published online by Cambridge University Press:  20 April 2006

John C. Neu
John C. Neu
Affiliation:
Mathematical Sciences Research Institute, 2223 Fulton Street, Room 603, Berkeley, CA94720
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Abstract

The dynamics of vortices subject to stretching by a uniform plane straining flow is studied asymptotically and by means of a new class of exact solutions. The asymptotic analysis treats the stretched Burger's vortex sheet for strain rates much greater than the gradient of the sheet strength. It is found that portions of the sheet where the strength density is sufficiently large compared to (viscosity x strain rate)½ will collapse to form concentrated vortices. The exact solutions describe uniform vortices of elliptical cross-section in inviscid fluid subject to stretching parallel to their axes. These solutions complement the description of vortex collapse found by asymptotic methods. The relevance of these results stems from the prevalence of vortex structures subject to strain in turbulent flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 143 , June 1984 , pp. 253 - 276
Copyright
© 1984 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Mechanics, pp. 272–273. Cambridge University Press.
Benjamin, T. B. 1967 Internal waves of permanent form in fluids of great depth. J. Fluid Mech. 29, 559–592.Google Scholar
Browand, F. K. & Weidman, P. D. 1976 Large scales in the developing mixing layer. J. Fluid Mech. 76, 127–144.Google Scholar
Browand, F. K. & Winant, C. D. 1974 Vortex pairing: a mechanism of turbulent mixing layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237–255.Google Scholar
Brown, G. & Roshko, A. 1974 On the density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.Google Scholar
Corcos, G. & Lin, S. 1984 The mixing layer: deterministic models of a turbulent flow. Part 2. The origin of the three-dimensional motion. J. Fluid Mech. 139, 67–95.Google Scholar
Corcos, G. & Sherman, F. 1984 The mixing layer: deterministic models of a turbulent flow. Part 1. Introduction and the two-dimensional flow. J. Fluid Mech. 139, 29–65.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn, pp. 232–233. Cambridge University Press.
Lin, S. J. & Corcos, G. 1984 The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plain strain on the dynamics of streamwise vortices. J. Fluid Mech. 141, 139–178.Google Scholar
Roshko, A. 1976 Structure of turbulent shear flows: a new look. AIAA J. 14, 1349–1357.Google Scholar
Saffman, P. & Baker, G. 1979 Vortex interactions. Ann. Rev. Fluid Mech. 11, 95–122.Google Scholar