Inviscid waves on a Lamb-Oseen vortex in a rotating stratified fluid: Consequences for the elliptic instability

Journal of Fluid Mechanics

Volumn 597, Issue , 2008, Pages 283-303

  Le Dizès, Stéphane ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC ANALYSIS; COMPUTATIONAL FLUID DYNAMICS; CORIOLIS FORCE; GRAVITY WAVES;

GLOBAL KELVIN MODE; INVISCID WAVE; WAVENUMBER;

VORTEX FLOW;

ASYMPTOTIC ANALYSIS; COMPUTATIONAL FLUID DYNAMICS; CORIOLIS FORCE; GRAVITY WAVES; VORTEX FLOW;

CORIOLIS FORCE; GRAVITY WAVE; GROWTH RATE; LAGRANGIAN ANALYSIS; ROTATING FLUID; STRATIFIED FLUID; VORTEX; WAVE PROPAGATION;

EID: 39049131648     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112007009780     Document Type: Article

References (43)

1. AFANASYEV, Y. D. 2002 Experiments on instability of columnar vortex pairs in rotating fluid. Geophys. Astrophys. Fluid Dyn. 96, 31-48.
2. AFANASYEV, Y. D. & PELTIER, W. R. 1998 Three-dimensional instability of anticyclonic swirling flow in rotating fluid: Laboratory experiments and related theoretical predictions. Phys. Fluids 10, 3194-3202.
3. BAYLY, B. J. 1986 Three-dimensional instability of elliptical flow. Phys. Rev. Lett. 57, 2160-2163.
4. BILLANT, P. & CHOMAZ, J.-M. 2000a Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid. J. Fluid Mech. 418, 167-188.
5. BILLANT, P. & CHOMAZ, J.-M. 2000b Theoretical analysis of the zigzag instability of a columnar vortex pair in a strongly stratified fluid. J. Fluid Mech. 419, 29-63.
6. BILLANT, P. & CHOMAZ, J.-M. 2000c Three-dimensional stability of a vertical columnar vortex pair in a stratified fluid. J. Fluid Mech. 419, 65-91.
7. BILLANT, P. & GALLAIRE, F. 2005 Generalized Rayleigh criterion for non-axisymmetric centrifugal instabilities. J. Fluid Mech. 542 365-379.
8. BILLANT, P., CHOMAZ, J.-M. & OTHEGUY, P. 2005 A general theory for the zigzag instability in stratified fluids. In Intl Conf. on High Reynolds Number Vortex Interactions, Toulouse, France, pp. 39-40.
9. BOUBNOV, B., GLEDZER, E. & HOPFINGER, E. 1995 Stratified circular Couette flow: Instability and flow regimes. J. Fluid Mech. 292 333-358.
10. CAIRNS, R. A. 1979 The role of negative energy waves in some instabilities of parallel flows. J. Fluid Mech. 92, 1-14.
11. CRAIK, A. D. D. 1989 The stability of unbounded two- and three-dimensional flows subject to body forces: Some exact solutions. J. Fluid Mech. 198, 275-292.
12. CROW, S. C. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 2172-2179.
13. DRAZIN, P. G. & REID, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
14. FABRE, D., SIPP, D. & JACQUIN, L. 2006 The Kelvin waves and the singular modes of the Lamb-Oseen vortex. J. Fluid Mech. 551, 235-274.
15. FRIEDLANDER, S. & LIPTON-LIFSCHITZ, A. 2003 Localized instabilities in fluids. In Handbook of Mathematical Fluid Dynamics (ed. S. Fiendlander & D. Serre), vol. 2, pp. 289-354. North-Holland.
16. FUKUMOTO, Y. 2003 The three-dimensional instability of a strained vortex tube revisited. J. Fluid Mech. 493, 287-318.
17. KERSWELL, R. R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83-113.
18. KLOOSTERZIEL, R. C. & VAN HEIJST, G. J. F. 1991 An experimental study of unstable barotropic vortices in a rotating fluid. J. Fluid Mech. 223, 1-24.
19. LACAZE, L., RYAN, K. & LE DIZÈS, S. 2007 Elliptic instability in a strained Batchelor vortex. J. Fluid Mech. 577, 341-361.
20. LANDAU, L. & LIFCHITZ, E. 1967 Mécanique Quantique, Théorie non relativiste. Éditions MIR, Moscow.
21. LE BARS, M., LE DIZÈS, S. & LE GAL, P. 2007 Coriolis effects on the elliptical instability in cylindrical and spherical rotating containers. J. Fluid Mech. 585, 323-342.
22. LE DIZÈS, S. 2000 Three-dimensional instability of a multipolar vortex in a rotating flow. Phys. Fluids 12 (11), 2762-2774.
23. LE DIZÈS, S. 2004 Viscous critical-layer analysis of vortex normal modes. Stud. Appl. Maths 112, 315-332.
24. LE DIZÈS, S. & BILLANT, P. 2006 Instability of an axisymmetric vortex in a stably stratified fluid. In 6th European Fluid Mechanics Conference, Stockholm, Sweden, p. 143.
25. LE DIZÈS, S. & BILLANT, P. 2007 Radiative instability in stratified vortices. Phys. Rev. Lett. (submitted).
26. LE DIZÈS, S. & LACAZE, L. 2005 An asymptotic description of vortex Kelvin modes. J. Fluid Mech. 542, 69-96.
27. LE DIZÈS, S. & LAPORTE, F. 2002 Theoretical predictions for the elliptic instability in a two-vortex flow. J. Fluid Mech. 471 169-201.
28. LEBLANC, S. 2003 Internal wave resonances in strain flows. J. Fluid Mech. 477, 259-283.
29. LEWEKE, T. & WILLIAMSON, C. H. K. 1998 Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85-119.
30. LIFSCHITZ, A. & HAMEIRI, E. 1991 Local stability conditions in fluid dynamics. Phys. Fluids A 3 (11), 2644-2651.
31. MEUNIER, P. & LEWEKE, T. 2005 Elliptic instability of a co-rotating vortex pair. J. Fluid Mech. 533, 125-159.
32. MIYAZAKI, T. 1993 Elliptical instability in a stably stratified rotating fluid. Phys. Fluids A 5 (11), 2702-2709.
33. MIYAZAKI, T. & FUKUMOTO, Y. 1991 Axisymmetric waves on a vertical vortex in a stratified fluid. Phys. Fluids A 3, 606-616.
34. MIYAZAKI, T. & FUKUMOTO, Y. 1992 Three-dimensional instability of strained vortices in stably stratified fluid. Phys. Fluids A 4 2515-2522.
35. OTHEGUY, P., BILLANT, P. & CHOMAZ, J.-M. 2006a The effect of planetary rotation on the zigzg instability of co-rotating vortices in a stratified fluid. J. Fluid Mech. 553, 273-281.
36. OTHEGUY, P., CHOMAZ, J.-M. & BILLANT, P. 2006b Elliptic and zigzag instabilities on co-rotating vertical vortices in a stratified fluid. J. Fluid Mech. 553, 253-272.
37. SAFFMAN, P. G. 1992 Vortex Dynamics. Cambridge University Press.
38. SCHECTER, D. A. & MONTGOMERY, M. T. 2004 Damping and pumping of a vortex Rossby wave in a monotonic cyclone: Critical layer stirring versus inertia-buoyancy wave emission. Phys. Fluids 16, 1334-48.
39. SIPP, D. & JACQUIN, L. 2003 Widnall instabilities in vortex pairs. Phys. Fluids 15, 1861-1874.
40. STAQUET, C. & SOMMERIA, J. 2002 Internal gravity waves: From instabilities to turbulence. Annu. Rev. Fluid Mech. 34, 559-593.
41. STEGNER, A., PICHON, T. & BEUNIER, M. 2005 Elliptical-inertial instability of rotating Kármán streets. Phys. Fluids 17 066602.
42. WALEFFE, F. 1990 On the three-dimensional instability of strained vortices. Phys. Fluids A 2 (1), 76-80.
43. WITHJACK, E. & CHEN, C. 1974 An experimental study of Couette instability of stratified fluids. J. Fluid Mech. 66, 725-737.