Instability and breakdown of a vertical vortex pair in a strongly stratified fluid

Journal of Fluid Mechanics

Volumn 606, Issue , 2008, Pages 239-273

  Waite, Michael L ^a,b   Smolarkiewicz, Piotr K ^a  

^a NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

^b UNIVERSITY OF VICTORIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

REYNOLDS NUMBER; STABILITY; TURBULENCE;

DENSITY PERTURBATION; GRAVITATIONAL INSTABILITY; HORIZONTAL DISPLACEMENTS; HORIZONTAL VELOCITY; INITIAL PERTURBATION; LABORATORY EXPERIMENTS; MODERATE REYNOLDS NUMBERS; TRANSITION TO TURBULENCE;

VORTEX FLOW;

COMPUTER SIMULATION; FROUDE NUMBER; INSTABILITY; REYNOLDS NUMBER; STRATIFIED FLOW; TURBULENCE; VISCOSITY; VORTEX FLOW;

EID: 45749144366     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112008001912     Document Type: Article

References (58)

1. BASAK, S. & SARKAR, S. 2006 Dynamics of a stratified shear layer with horizontal shear. J. Fluid Mech. 568, 19-54.
2. BATCHELOR, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
3. BAYLY, B. J. 1986 Three-dimensional instability of elliptical flows. Phys. Rev. Lett. 57, 2160-2163.
4. BILLANT, P. BRANCHER, P. & CHOMAZ, J.-M. 1999 Three-dimensional stability of a vortex pair. Phys. Fluids 11, 2069-2077.
5. 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.
6. BILLANT, P. & CHOMAZ, J.-M. 2000b Theoretical analysis of the zigzag instability of a vertical columnar vortex pair in a strongly stralified fluid. J. Fluid Mech. 419, 29-63.
7. 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.
8. BILLANT, P. & CHOMAZ, J.-M. 2001 Self-similarity of strongly stratified inviscid flows. Phys. Fluids 13, 1645-1651.
9. CHAPLYGIN, S. A. 1903 One case of vortex motion in a fluid. Trans. Phys. Sect. Imperial Moscow Soc. Friends of Natural Sciences 11 (2), 11-14.
10. CLYNE, J. & RAST, M. 2005 A prototype discovery environment for analyzing and visualizing terascale turbulent fluid fluid flow simulations. In Visualization and Data Analysis 2005 (ed. R. F. Erbacher, J. C. Roberts, M. T. Gordon & K. Borner), pp. 284-294. SPIE.
11. CROW, S. C. 1970 Stability theory for a pair of trailing voctices. AIAA J 8, 2172-2179.
12. DELONCLE, A., BILLAN, P. & CHOMAZ, J.-M. 2008 Nonlinear evolution of the zigzag instability in stratified fluids: A shortcut on the route to dissipation. J. Fluid Mech. 599, 229-239.
13. DOMARADZKI, J. A., XIAO, Z. & SMOLARKIEWICZ, P. K. 2003 Effective eddy viscosities in implicit. large eddy simulations of turbulent flows. Phys. J. Fluids 15, 3890-3893.
14. DRAZIN, P. G. 1961 On the steady flow of a fluid of variable density past an obstacle. Tellus 13, 239-251.
15. GRINSTEIN, F. F., MARGOLIN, L. G. & RIDER, W. J. (Ed.) 2007 Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics. Cambridge University Press.
16. HERRING, J. R. & MÉTAIS, O. 1989 Numerical experiments in forced stablv stratified turbulence. J. Fluid Mech. 202, 97-115.
17. KELVIN, LORD 1880 Vibrations of a columnar vortex. Phil. Mag. 10 (5), 155-168.
18. KERSWELL, R. R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83-113.
19. LAMB, H. 1895 Hydrodynamics, 2nd edn. Cambridge University Press.
20. LAPORTE, F. & CORJON, A. 2000 Direct numerical simulation of the ellintir instability of a vortex pair. Phys. Fluids 12, 1016-1031.
21. LE DIZÈS, S. & LAPORTE, F. 2002 Theoretical predictions for the elliptical instability in a two-vortex flow. J. Fluid Mech. 471 169-201.
22. LEWEKE, T. & WILLIIAMSON, C. H. K. 1998 Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85-119.
23. LILLY, D. K. 1983 Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci. 40, 749-761.
24. LINDBORG, E. 2006 The energy cascade in a strongly stratified fluid, J. Fluid Mech. 550, 207-242.
25. MARGOLIN, L. G., RIDER, W. J. & GRINSTEIN, F. F. 2006a Modeling turbulent flows with implicit LES. J. Turbul. 7 (15), 1-27.
26. MARGOLIN, L. G., SMOLARKIEWICZ, P. K. & WYSZOGRADZKI, A. A. 2006b Dissipation in implicit turbulence models: A computational study. Trans. ASME: J. Appl. Mech. 73, 469-473.
27. MARGOLIN, L. G., SMOLARKIEWICZ, P. K. & WYZOGRODZKI, A. A. 2002 Implicit turbulence modeling for high Reynolds number flows. Trans. ASME: J. Fluids Engng 124, 862-867.
28. MELESHKO, V. V. & VAN HEIJST, G. L. V. 1994 On Chaplygin's investigations of two-dimensional vortex structures in an inviscid fluid. J. Fluid Mech. 272, 157-182.
29. MIYAZAKI, T. & FUKUMOTO, Y. 1992 Three-dimensional instability of strained vortices in a stably stratified fluid. Phys. Fluids, A 4, 2515-2522.
30. MOIN, P. & MAHESH, K. 1998 Direct numerical simulation: A tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539-578.
31. MOORE, D. W. & SAFFMAN, P. G. 1975 The instability of a straight vortex filament in a strain field. Proc. R. Soc. Lond. A 346 413-425.
32. NGAN, K., STRAUB, D. N. & BARTELLO, P. 2005 Aspect ratio effects in quasi-two-dimensional turbulence. Phys. Fluids 17, 125102.
33. OTHEGUY, P., BILLANT, P. & CHOMAZ, J.-M. 2006a The effect of planetary rotation on the zigzag instability of co-rotating vortices in a stratified fluid. J. Fluid Mech. 553, 273-281.
34. OTHEGUY, P., CHOMAZ, J.-M. & BILLANT, P. 2006b Elliptic and zigzag instabilities on co-rotating vertical vortices in a statified fluid. J. Fluid Mech. 553, 253-272.
35. PIERREHUMBERT, R. T. 1986 Universal short-wave instability of two-dimensional eddies in an inviscid fluid. Phys. Rev. Lett. 57, 2157-2159.
36. PRUSA, J. M. & SMOLARKIEWICZ, P. K. 2003 An all-scale anelastic model for geophysical flows: Dynamic grid formation. J. Comput. Phys. 190, 601-622.
37. RILEY, J. J. & DEBRUYNKOPS, S. M. Dynamics of turbulence strongly influenced by buoyancy. Phys. Fluids 15, 2047-2059.
38. RILEY, J. J., METCALFE, R. W. & WEISSMAN, M. A. 1981 Direct numerical simulations of homogeneous turbulence in density-stratified fluids. In Nonlinear Properties of Internal Waves (ed. B. J. West), pp. 79-112, APS.
39. ROBINSON, A. C. & SAFFMAN, P. G. 1984 Three-dimensional stability of an elliptical vortex in a straining field. J. Fluid Mech. 142, 451-466.
40. SCHUMANN, U. 1991 Subgrid length-scales for large-eddy simulation of stratified turbulence. Theor. Comput. Fluid Dyn. 2, 279-290.
41. SIPP, D. & JACQUIN, L. 2003 Widnall instabilities in vortex pairs. Phys. Fluids 15, 1861-1874.
42. SMOLARKIEWICZ, P. K. 2006 Multidimensional positive definite advection transport algorithm: An overview. Intl J. Numer. Meth. Fluids 50, 1123-1144.
43. SMOLARKIEWICZ, P. K. & GRABOWSKI, W. W. 1990 The multidimensional positive definite advection transport algorithm: Nonoscillatory option. J. Comput. Phys. 86, 355-375.
44. SMOLARKIEWICZ, P. K. & MARGOLIN, L. G. 1993 On forward-in-time differencing for fluids: Extension to a curvilinear framework. Mon. Wea. Rev. 121, 1847-1859.
45. SMOLARKIEWICZ, P. K. & MARGOLIN, L. G. 1998 MPDATA: A positive definite solver for geophysical flows. J. Comput. Phys. 140, 459-480.
46. SMOLARKIEWICZ, P. K. & MARGOLIN, L. G. 2000 Variational methods for elliptic problems in fluid models. In Proc. ECMWF Workshop on Developments in Numerical Methods for Very High Resolution Global Models pp. 137-159. Reading, UK: ECMWF.
47. SMOLARKIEWICZ, P. K. & MARGOLIN, L. G. 2007 Studies in geophysics. In Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics (ed. F. F. Grinstein, L. Margolin & W. Rider). Cambridge University Press.
48. SMOLARKIEWICZ, P. K. & MARGOLIN, L. G. & WYSZOGRODZKI, A. A. 2001 A class of nonhydrostatic global models. J. Atmos. Sci. 58, 349-364.
49. SMOLARKIEWICZ, P. K. & PRUSA, J. M. 2002 Forward-in-time differencing for fluids: Simulations of geophysical turbulence. In Turbulent Flow Computation (ed. D. Drikakis & B. J. Guertz), pp. 279-312. Kluwer.
50. SMOLARKIEWICZ, P. K. & PRUSA, J. M. 2005 Towards mesh adaptivity for geophysical turbulence: Continuous mapping approach. Intl J. Numer. Meth. Fluids 47, 789-801.
51. SMOLARKIEWICZ, P. K. SHARMAN, R., WEIL, J., PERRY, S. G., HEIST, D. & BOWKER, G. 2007 Building resolving large-eddy simulations and comparison with wind tunnel experiments. J. Comput. Phys. 227 633-653.
52. THOMAS, P. J. & AUERBACH, D. 1994 The observation of the simultaneous development of a long-and a short-wave instability mode on a vortex pair. J. Fluid Mech. 265, 289-302.
53. TSAI, C.-Y. & WIDNALL, S. E. 1976 The stability of short waves on a straight vortex filament in a weak externally imposed strain field. J. Fluid Mech. 73, 721-733.
54. VLADIMIROV, V. A. & IL'IN, K. I. 1988 Three-dimensional instability of an elliptic Kirchhoff vortex. Fluid Dyns. 23, 356-360.
55. WAITE, M. L. & BARTELLO, P. 2004 Stratified turbulence dominated by vortical motion. J. Fluid Mech. 517, 281-308.
56. WALEFFE, F. 1990 On the three-dimensional instability of strained vortices. Phys. Fluids A 2, 76-80.
57. WARN-VARNAS, A., HAWKINS, J., SMOLARKIEWICZ, P. K., CHIN-BING, S. A., KING, D. & HALLOCK, Z. 2007 Solitary wave effects north of Strait of Messina. Ocean Modell. 18, 97-121.
58. WEDI, N. P. & SMOLARKIEWICZ, P. K. 2006 Direct numerical simulation of the Plumb-McEwan laboratory analog of the QBO. J. Atmos. Sci. 63, 3226-3252.