Theoretical analysis of the zigzag instability of a vertical co-rotating vortex pair in a strongly stratified fluid

Journal of Fluid Mechanics

Volumn 584, Issue , 2007, Pages 103-123

  Otheguy, Pantxika ^a,b   Billant, Paul ^a   Chomaz, Jean Marc ^a  

^a ECOLE POLYTECHNIQUE   (France)

^b Lyonnaise des Eaux   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FROUDE NUMBER; NUMERICAL ANALYSIS; ROTATIONAL FLOW; STRAIN;

NUMERICAL STABILITY ANALYSIS; STRATIFIED FLUID; VERTICAL CO-ROTATING VORTEX;

VORTEX FLOW;

CONVERGENCE OF NUMERICAL METHODS; FROUDE NUMBER; NUMERICAL ANALYSIS; ROTATIONAL FLOW; STRAIN; VORTEX FLOW;

BUOYANCY; GAUSSIAN METHOD; GROWTH RATE; PERTURBATION; STABILITY ANALYSIS; STRATIFIED FLUID; THEORETICAL STUDY; VORTEX FLOW; WAVELENGTH;

EID: 34547702500     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112007006295     Document Type: Article

References (28)

1. BATCHELOR, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
2. 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.
3. Billant, P. & Chomaz, J.-M. 2000b Theoretical analysis of the zigzag instability of a vertical columnar vortex pair in a strongly stratified fluid. J. Fluid Mech. 419, 29-63.
4. 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.
5. BILLANT, P. & CHOMAZ, J.-M. 2001 Self-similarity of strongly stratified inviscid flows. Phys. Fluids 13, 1645-1651.
6. BONNIER, M., EIFF, O. & BONNETON, P. 2000 On the density structure of far-wake vortices in a stratified fluid. Dyn. Atmos. Oceans 31, 117-137.
7. ELOY, C. & LE DIZÈS, S. 1999 Three-dimensional instability of Burgers and Lamb-Oseen vortices in a strain field. J. Fluid Mech. 378, 145-166.
8. FINCHAM, A. M., MAXWORTHY, T. & SPEDDING, G. R. 1996 Energy dissipation and vortex structure in freely decaying, stratified grid turbulence. Dyn. Atmos. Oceans 23, 155-169.
9. GODEFERD, F. S. & STAQUET, C. 2003 Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 2. Large-scale and small-scale anisotropy. J. Fluid Mech. 486, 115-159.
10. GODOY-DIANA, R., CHOMAZ, J. M. & BILLANT, P. 2004 Vertical length scale selection for pancake vortices in strongly stratified viscous fluids. J. Fluid Mech. 504, 229-238.
11. HERRING, J. R. & MÉTAIS, O. 1989 Numerical experiments in forced stably stratified turbulence. J. Fluid Mech. 202, 97-115.
12. HOLFORD, J. M. & LINDEN, P. F. 1999 Turbulent mixing in a stratified fluid. Dyn. Atmos. Oceans 30, 173-198.
13. JIMENEZ, J. 1975 Stability of a pair of co-rotating vortices. Phys. Fluids 18, 1580-1582.
14. LAMB, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
15. LE DIZÈS, S. & LAPORTE, F. 2002 Theoretical predictions for the elliptical instability in a two-vortex flow. J. Fluid Mech. 471 169-201.
16. LEIBOVICH, S., BROWN, S. N. & PATEL, Y. 1986 Bending waves on inviscid columnar vortices. J. Fluid Mech. 173, 595-624.
17. LILLY, D. K. 1983 Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci. 40, 749-761.
18. LINDBORG, E. 2006 The energy cascade in a strongly stratified fluid. J. Fluid Mech. 550, 207-242.
19. MOFFATT, H. K., KIDA, S. & OHKITANI, K. 1994 Stretched vortices-the sinews of turbulence-large reynolds number asymptotics. J. Fluid Mech. 259, 241-264.
20. MOORE, D. W. & SAFFMAN, P. G. 1975 The instability of a straight vortex filament in a strain field. Proc. R. Soc. Lond. 346, 413-425.
21. OTHEGUY, P., CHOMAZ, J.-M. & BILLANT, P. 2006 Elliptic and zigzag instabilities on co-rotating vertical vortices in a stratified fluid. J. Fluid Mech. 553, 253-272.
22. PARK, Y.-G., WHITEHEAD, J. A. & GNANADESKIAN, A. 1994 Turbulent mixing in stratified fluids: Layer formation and energetics. J. Fluid Mech. 279, 279-311.
23. PRAUD, O., FINCHAM, A. M. & SOMMERIA, J. 2005 Decaying grid turbulence in a strongly stratified fluid. J. Fluid Mech. 522 1-33.
24. RILEY, J. J. & LELONG, M.-P. 2000 Fluid motions in the presence of strong stable stratification. Annu. Rev. Fluid Mech. 32, 617-657.
25. RILEY, J. J., METCALFE, W. & WEISSMAN, M. A. 1981 Direct numerical simulations of homogeneous turbulence in density-stratified fluids. Proc. AIP Conf. Nonlinear Properties of Internal Waves (ed. B. J. West), pp. 79-112.
26. SAFFMAN, P. G. 1992 Vortex Dynamics. Cambridge University Press.
27. SPEDDING, G. R., BROWAND, F. K. & FINCHAM, A. M. 1996 Turbulence, similarity scaling and vortex geometry in the wake of a sphere in a stably-stratified fluid. J. Fluid Mech. 314, 53-103.
28. WAITE, M. L. & BARTELLO, P. 2004 Stratified turbulence dominated by vortical motion. J. Fluid Mech. 517, 281-308.