The magnetoelliptic instability of rotating systems

Journal of Fluid Mechanics

Volumn 632, Issue , 2009, Pages 401-430

  Mizerski, Krzystof A ^a,b   Bajer, K ^b  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ASTROPHYSICS; DEFORMATION; GRAVITATION;

ACCRETION DISCS; ANALYTICAL PREDICTIONS; ASTROPHYSICAL OBJECTS; EXTERNAL MAGNETIC FIELD; GRAVITATIONAL INTERACTION; NUMERICAL CALCULATION; PRINCIPAL RESONANCE; ROTATING SYSTEMS;

MAGNETIC FIELDS;

CORIOLIS FORCE; EULER FLOW; FLOW STABILITY; MAGNETIC FIELD; NUMERICAL MODEL; ROSSBY NUMBER; VORTEX FLOW; VORTICITY;

EID: 69749123352     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112009007307     Document Type: Article

References (56)

1. ALDRIDGE, K. D. & LUMB, L. I. 1987 Inertial waves identified in the Earth's fluid outer core. Nature 325, 421-423.
2. BAJER, K. & MIZERSKI, K. A. 2009 Elliptical flow instability triggered by a magnetic field. Phys. Rev. Lett. Submitted.
3. BALBUS, S. A. & HAWLEY, J. F. 1991 A powerful local shear instability in weakly magnetized disks. Part 1. Linear analysis. Astrophys. J. 376, 214-222.
4. BAYLY, B. J. 1986 Three-Dimensional instability of elliptical flow. Phys. Rev. Lett. 57 (17), 2160-2163.
5. BRAGINSKY, S. I. 1991 Towards a realistic theory of the geodynamo. Geophys. Astrophys. Fluid Dyn. 60, 89-134.
6. BRAGINSKY, S. I. 1999 Dynamics of the stably stratified ocean at the top of the core. Phys. Earth Planet. Inter. 111, 21-34.
7. CADOT, O., DOUADY, S. & COUDER, Y. 1995 Characterization of the low pressure filaments in three-dimensional turbulent shear flow. Phys. Fluids 7, 630.
8. CHANDRASEKHAR, S. 1969 Ellipsoidal Figures of Equilibrium, Yale University Press.
9. CRAIK, A. D. D. 1986 Exact solutions of non-conservative equations for three-wave and second-harmonic resonance. Proc. R. Soc. Lond. A 406, 1-12.
10. CRAIK, A. D. D. 1988 A class of exact solutions in viscous incompressible magnetohydrodynamics. Proc. R. Soc. Lond. A 417 235-244.
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. CRAIK, A. D. D. & CRIMINALE, W. O. 1986 Evolution of wave-like disturbances in shear flows. A class of exact-solutions of the Navier-Stokes equations. Proc. R. Soc. Lond. A 406, 13-26.
13. CROSSLEY, D. J., HINDERER, J. & LEGROS, H. 1991 On the excitation, detection and damping of core modes. Phys. Earth Plant. Inter. 68, 97-116.
14. ELOY, C H., LE GAL, P. & LE DIZÈS, S. 2000 Experimental study of the multipolar vortex instability. Phys. Rev. Lett. 85, 3400-3403.
15. FABRE, D. & JACQUIN, L. 2004 Short-wave cooperative instabilities in representative aircraft vortices. Phys. Fluids 16, 1366.
16. GOODMAN, J. 1993 The local instability of tidally distorted accretion disks. Astrophys. J. 406, 596-613.
17. HASEGAWA, H. 2005 Structure of the magnetopause boundary layers discovered by Cluster multipoint observations. In Proceedings of the Cluster and Double Star Symposium: Fifth Anniversary of Cluster in Space Noordwijk, Denmark.
18. HILLE, E. 1962 Analytic Function Theory, vol. 2. Ginn.
19. JI, H., BURIN, M., SCHARTMAN, E. & GOODMAN, J. 2006 Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks. Nature 444, 343-346. Doi:10.1038/ nature05323.
20. KELVIN, LORD W. THOMSON 1887 Stability of fluid motion: rectilinear motion of viscous fluid between two parallel plates. Philos. Mag. 24, 188-196.
21. KERSWELL, R. R. 1994 Tidal excitation of hydromagnetic waves and their damping in the Earth. J. Fluid Mech. 274, 219-241.
22. KERSWELL, R. R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83-113.
23. KERSWELL, R. R. & MALKUS, W. V. R. 1998 Tidal instability as the source for Io's magnetic signature. Geophys. Res. Lett. 25 (5), 603-606.
24. LACAZE, L., HERREMAN, W., LE BARS, M., LE DIZÈS, S. & LE GAL, P. 2006 Magnetic field induced by elliptical instability in a rotating spheroid. Geophys. Astrophys. Fluid Dyn. 100 (4-5), 299-317.
25. LANDMAN, M. J. & SAFFMAN, P. G. 1987 The three dimensional instability of strained vortices in a viscous fluid. Phys. Fluids 30 (8), 2339-2342.
26. LE BARS, M. & LE DIZÈS, S. 2006 Thermo-elliptical instability in a rotating cylindrical shell. J. Fluid. Mech. 563, 189-198.
27. LEBOVITZ, N. R. & LIFSCHITZ, A. 1996 Short wavelength instabilities of Riemann ellipsoids. Phil. Trans. R. Soc. Lond. A 354, 927-950.
28. LEBOVITZ, N. R. & SALDANHA, K. I. 1999 On the weakly nonlinear development of the elliptic instability. Phys. Fluids 11, 3374-3379.
29. LEBOVITZ, N. R. & ZWEIBEL, E. 2004 Magnetoelliptic instabilities. Astrophys. J. 609, 301-312.
30. LE DIZÈS, S. 2003 Modal growth and non-modal growth in a stretched shear layer. Eur. J. Mech. B 22, 411-430.
31. LE DIZÈS, S. & LACAZE, L. 2005 An asymptotic description of vortex Kelvin modes. J. Fluid Mech. 542, 69-96.
32. LE DIZÈS, S. & LAPORTE, F. 2002 Theoretical predictions for the elliptic instability in a two-vortex flow. J. Fluid Mech. 471 169.
33. LE GAL, P., LACAZE, L. & LE DIZÈS, S. 2005 Magnetic field induced by elliptical instability in a rotating tidally-distorted sphere. J. Phys. Conf. Ser. 14, 30-34.
34. LEWEKE, T. & WILLIAMSON, C. H. K. 1998 Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85.
35. MELCHOIR, P. W., CROSSLEY, D. J., DEHANT, V. P. & DUCARME, B. 1988 Have inertial waves been identified from the Earth's core?. In Structure and Dynamics of the Earth's Deep Interior (ed. D. E. Smylie & R. Hide), pp. 1-12. American Geophysical Union.
36. MELCHOIR, P. W. & DUCARME, B. 1986 Detection of inertial gravity oscillations in the Earth's core with a superconducting gravimeter at Brussels. Phys. Earth Planet. Inter. 42, 129.
37. MEUNIER, P., LE DIZÈS, S. & LEWEKE, T. 2005 Physics of vortex merging. C. R. Phys. 6, 431-450.
38. MEUNIER, P. & LEWEKE, T. 2001 Three-dimensional instability during vortex merging. Phys. Fluids 13, 2747.
39. MIYAZAKI, T. 1993 Elliptical instability in a stably stratified rotating fluid. Phys. Fluids A 5 (11), 2702-2709.
40. MIYAZAKI, T. & FUKUMOTO, Y. 1992 Three-dimensional instability of strained vortices in a stably stratified fluid. Phys. Fluids A 4 (11), 2515-2522.
41. Mizerski, K. , Bajer, K., The magnetoelliptic instability in the presence of inertial forces,Advances in Turbulence XI - Proceedings of the 11th EUROMECH European Turbulence Conference(2007),Pages 121-123.
42. MIZERSKI, K. A., BAJER, K. & MOFFATT, H. K. 2009 The α-effect generated by elliptical instability. J. Fluid Mech. Submitted.
43. MOZER, F. S., PHAN, T. D. & BALE, S. D. 2003 The complex structure of the reconnecting magnetopause. Phys. Plasmas 10 (6), 2480-2485.
44. NOIR, J., BRITO, D., ALDRIDGE, K. & CARDIN, P. 2001 Experimental evidence of inertial waves in a precessing spheroidal cavity. Geophys. Res. Lett. 19, 3785-3788.
45. ORSZAG, S. A. & PATERA, A. T. 1983 Secondary instability of wall-bounded shear flows. J. Fluid Mech. 128, 347-385.
46. PIERREHUMBERT, R. T. 1986 Universal short-wave instability of two-dimensional eddies in an inviscid fluid. Phys. Rev. Lett. 57 (17), 2157-2159.
47. ROBERTS, P. H. & SOWARD, A. M. 1992 Dynamo theory. Annu. Rev. Fluid Mech. 24, 459-512.
48. ROTH, M., DE KEYSER, J., DARROUZET, F. & ČADEŽ. V. 2001 Structure and dynamics of the Earth's magnetopause. In Space Scientific Research in Belgium vol. 2, part 2, pp. 81, Federal Office for Scientific, Technical and Cultural Affairs (Brussels).
49. SIPP, D. & JACQUIN, L. 2003 Widnall instabilities in vortex pairs. Phys. Fluids 15, 1861.
50. SOWARD, A. M. 1991 The Earth's dynamo. Geophys. Astrophys. Fluid Dyn. 62, 191-209.
51. SUESS, S. T. 1970 Some effects of gravitational tides on a model Earth's core. J. Geophys. Res. 75, 6650-6661.
52. THESS, A. & ZIKANOV, O. 2007 Transition from two-dimensional to three-dimensional magneto-hydrodynamic turbulence. J. Fluid Mech. 579, 383-412.
53. Tilgner, A. 2005 Precession driven dynamos. Phys. Fluids 17, 034104.
54. VANYO, J., WILDE, P., CARDIN, P. & OLSON, P. 1995 Experiments on precessing flows in the Earth's liquid core. Geophys. J. Intl 121, 136-142.
55. WALEFFE, F. 1990 On the three-dimensional instability of strained vortices. Phys. Fluids A 2 (1), 76-80.
56. WIENBRUCH, U. & SPOHN, T. 1995 A self-sustained magnetic field on Io?. Planet. Space. Sci. 43, 1045-1057.