The instability of a vortex tube in a weak external shear and strain

Physics of Fluids

Volumn 10, Issue 2, 1998, Pages 530-532

  Arendt, Steve ^a   Fritts, David C ^a  

^a Colorado Research Associates/NWRA ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 11744347153     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869576     Document Type: Article

References (15)

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2. A. Vincent and M. Meneguzzi, "The dynamics of vorticity tubes in homogeneous turbulence," J. Fluid Mech. 258, 245 (1994).
3. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1967).
4. M. Lessen, P. J. Singh, and F. Paillet, "The stability of a trailing line vortex. Part 1. Inviscid theory," J. Fluid Mech. 63, 753 (1974).
5. E. W. Mayer and K. G. Powell, "Viscous and inviscid instabilities of a trailing vortex," J. Fluid Mech. 245, 91 (1992).
6. D. W. Moore and P. G. Saffman, "The instability of a straight vortex filament in a strain field," Proc. R. Soc. London, Ser. A 346, 413 (1975).
7. C.-Y. Tsai and S. E. Widnall, "The stability of short waves on a straight vortex filament in a weak externally imposed strain field," J. Fluid Mech. 73, 721 (1976).
8. S. E. Widnall, D. B. Bliss, and C.-Y. Tsai, "The instability of short waves on a vortex ring," J. Fluid Mech. 66, 35 (1974).
9. S. E. Widnall and C.-Y. Tsai, "The instability of the thin vortex ring of constant vorticity," Philos. Trans. R. Soc. London, Ser. A 287, 273 (1977).
10. P. G. Saffman, "The number of waves on unstable vortex rings," J. Fluid Mech. 84, 625 (1978).
11. S. C. Crow, "Stability theory for a pair of trailing vortices," AIAA J. 8, 2172 (1971); J. S. Marshall and H. Chen, "Stability of a counter-rotating vortex pair immersed in cross-stream shear flow," ibid. 35, 295 (1997).
12. S. C. Crow, "Stability theory for a pair of trailing vortices," AIAA J. 8, 2172 (1971); J. S. Marshall and H. Chen, "Stability of a counter-rotating vortex pair immersed in cross-stream shear flow," ibid. 35, 295 (1997).
13. D. W. Moore and P. G. Saffman, "Structure of a line vortex in an imposed strain," in Aircraft Wake Turbulence and its Detection, edited by J. H. Olsen, A. Goldburg, and M. Rogers (Plenum. New York, 1971).
14. Lord Kelvin, "Vibrations of a columnar vortex," Philos. Mag. 10, 155 (1880).
15. This factor of ∈ for the unsheared case is not present explicitly in TW's equation for the maximum growth rate (the bottom of p. 729 of TW), as it has been removed by their normalization.