On the evolution and saturation of instabilities of two-dimensional isolated circular vortices

Journal of Fluid Mechanics

Volumn 388, Issue , 1999, Pages 217-257

  Kloosterziel, R C ^a   Carnevale, G F ^b  

^a UNIVERSITY OF HAWAII   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; FLOW INTERACTIONS; GALERKIN METHODS; MATHEMATICAL MODELS;

DYNAMICAL SYSTEM TRUNCATION;

VORTEX FLOW;

EID: 0032665355     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112099004760     Document Type: Article

References (33)

1. BATCHELOR, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
2. BECKERS, M. & HEIJST, G. J. F. VAN 1998 The observation of a triangular vortex in a rotating fluid. Fluid Dyn. Res. 22, 265-279.
3. BENZI, R., PATARNELLO, S. & SANTANGELO, P. 1988 Self-similar coherent structures in two-dimensional decaying turbulence. J. Phys. A: Math. Gen. 21, 1221-1237.
4. CARNEVALE, G. F. & KLOOSTERZIEL, R. C. 1994 Emergence and evolution of triangular vortices. J. Fluid Mech. 259, 305-331.
5. CARNEVALE, G. F. & SHEPHERD, T. G. 1990 On the interpretation of Andrew's theorem. Geophys. Astrophys. Fluid Dyn. 51, 1-17.
6. CARTON, X., FLIERL, G. R. & POLVANI, L. 1989 The generation of tripoles from unstable axisymmetric isolated vortex structures. Europhys. Lett. 9, 339-344.
7. CARTON, X. & LEGRAS, B. 1994 The life-cycle of tripoles in two-dimensional incompressible flows. J. Fluid Mech. 267, 53-82.
8. CARTON, X. & MCWILLIAMS, J. C. 1989 Barotropic and baroclinic instabilities of axisymmetric vortices in a quasi-geostrophic model. In Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence (ed. J. C. J. Nihoul & B. M. Jamart), pp. 225-244. Elsevier.
9. DAVIDSON, P. A. 1998 On the application of the Kelvin-Arnol'd energy principle to the stability of forced two-dimensional inviscid flows. J. Fluid Mech. 356, 221-257.
10. DRAZIN, P. G. & REID, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
11. DRITSCHEL, D. G. 1988 Nonlinear stability bounds for inviscid, two-dimensional, parallel or circular flows with monotonic vorticity, and the analogous three-dimensional quasi-geostrophic flows. J. Fluid Mech. 191, 575-581.
12. FLOR, J. B. & HEIJST, G. J. F. VAN 1996 Stable and unstable monopolar vortices in a stratified fluid. J. Fluid Mech. 311, 257-287.
13. GENT, P. R. & MCWILLIAMS, J. C. 1986 The instability of circular vortices. Geophys. Astrophys. Fluid Dyn. 35, 209-233.
14. HEIJST, G. J. F. VAN & KLOOSTERZIEL, R. C. 1989 Tripolar vortices in a rotating fluid. Nature, 338, 569-571.
15. HEIJST, G. J. F. VAN, KLOOSTERZIEL, R. C. & WILLIAMS, C. W. M. 1991 Laboratory experiments on the tripolar vortex in a rotating fluid. J. Fluid Mech. 225, 301-331.
16. HIGGINS, J. R. 1977 Completeness and Basic Properties of Sets of Special Functions. Cambridge University Press.
17. KLOOSTERZIEL, R. C. & CARNEVALE, G. F. 1992 Formal stability of circular vortices. J. Fluid Mech. 242, 249-278.
18. KLOOSTERZIEL, R. C. & HEIJST, G. J. F. VAN 1991 An experimental study of unstable barotropic vortices in a rotating fluid. J. Fluid Mech. 223, 1-24.
19. KRAICHNAN, R. H. 1958 Irreversible statistical mechanics of incompressible hydromagnetic turbulence. Phys. Rev. 109, 1407-1422.
20. LEGRAS, B., SANTANGELO, P. & BENZI, R. 1988 High-resolution numerical experiments for forced two-dimensional turbulence. Europhys. Lett. 5, 37-42.
21. LORENZ, E. N. 1960 Maximum simplification of the dynamic equations. Tellus 12, 243-254.
22. LORENZ, E. N. 1963 Deterministic non-periodic flow. J. Atmos. Sci. 20, 130-141.
23. MCCALPIN, J. D. 1987 On the adjustment of azimuthally perturbed vortices. J. Geophys. Res. 92, 8213-8255.
24. MCWILLIAMS, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21-43.
25. MOREL, Y. & CARTON, X. 1994 Multipolar vortices in two-dimensional incompressible flow. J. Fluid Mech. 267, 23-51.
26. ORLANDI, P. & HEIJST, G. J. F. VAN 1992 Numerical simulations of tripolar vortices in 2D flow. Fluid Dyn. Res. 9, 170-206.
27. PATTERSON, G. S. & ORSZAG, S. A. 1971 Spectral calculations of isotropic turbulence: Efficient removal of aliasing errors. Phys. Fluids 14, 2438-2541.
28. PINGREE, R. D. & LE CANN, B. 1992 Anticyclonic eddy X91 in the Southern Bay of Biscay, May 1991 to February 1992. J. Geophys. Res. 97, 14353-14367.
29. PLATZMAN, G. W. 1960 The spectral form of the vorticity equation. J. Metl. 17, 635-644.
30. PRESS, W. H., FLANNERY, B. P., TEUKOLSKY, S. A. & VETTERLING, W. T. 1989 Numerical Recipes: the Art of Scientific Computing. Cambridge University Press.
31. SADOURNY, S. 1985 Quasi-geostrophic turbulence: an introduction. In Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics (ed. M. Ghil), pp. 133-158.
32. SILBERMAN, I. S. 1954 Planetary waves in the atmosphere. J. Metl. 11, 27-34.
33. THOMPSON, P. D. 1972 Some exact statistics of two-dimensional viscous flow with random forcing. J. Fluid Mech. 55, 711-717.