Secondary instabilities in rapidly rotating fluids: Inertial wave breakdown

Journal of Fluid Mechanics

Volumn 382, Issue , 1999, Pages 283-306

  Kerswell, R R ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); FLOW INTERACTIONS; RESONANCE; STABILITY; THREE DIMENSIONAL;

EKMAN NUMBERS; GASTROPHIC FLOWS; INERTIAL WAVE BREAKDOWN; ROTATING FLUIDS;

ROTATIONAL FLOW;

EID: 0032649207     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112098003954     Document Type: Article

References (49)

1. ALDRIDGE, K. D. & LUMB, L. I. 1987 Inertial waves identified in the Earth's fluid outer core. Nature 325, 421-423.
2. ALDRIDGE, K. D., LUMB, L. I. & HENDERSON, G. A. 1989 A Poincaré model for the Earth's fluid core. Geophys. Astrophys. Fluid Dyn. 48, 5-23.
3. ALDRIDGE, K., SEYED-MAHMOUD, B., HENDERSON, G. & WIJNGAARDEN, W. VAN 1997 Elliptical instability of the Earth's fluid core. Phys. Earth Planet. Inter. 103, 365-374.
4. ALDRIDGE, K. D. & TOOMRE, A. 1969 Inertial oscillations of a rotating fluid sphere. J. Fluid Mech. 37, 307-323.
5. BAINES, P. G. 1967 Forced oscillations of an enclosed rotating fluid. J. Fluid Mech. 30, 533-546.
6. BJERKNES, V., BJERKNES, J., SOLBERG, H. & BERGERON, T. 1933 Physikalische Hydrodynamik, pp. 465-471. Springer.
7. BUSSE, FH. 1968 Steady fluid flow in a precessing spheroidal shell. J. Fluid Mech. 33, 739-752.
8. CARTAN, E. 1922 Sur les petites oscillations d'une masse fluid. Bull. Sci. Math. 46, 317-352, 356-369.
9. FABIJONAS, B., HOLM, D. D. & LIFSCHITZ, A. 1997 Secondary instabilities of flows with elliptic streamlines. Phys. Rev. Lett. 78, 1900-1903.
10. FULTZ, D. 1959 A note on overstability, and the elastoid-inertia oscillations of Kelvin, Solberg and Bjerknes. J. Met. 16, 199-208.
11. GANS, R. F. 1970 On the precession of a resonant cylinder. J. Fluid Mech. 41, 865-872.
12. GLEDZER, YE. B., NOVIBOV, YU. V, OBUKHOV, A. M. & CHUSOV, M. A. 1974 An investigation of the stability of liquid flows in a three-axis ellipsoid. Isv. Atmos. Ocean. Phys. 10, 69-71.
13. GLEDZER, E. B. & PONOMAREV, V. M. 1977 Finite-dimensional approximation of the motions of an incompressible fluid in an ellipsoidal cavity. Isv. Atmos. Ocean. Phys. 13, 565-569.
14. GLEDZER, E. B. & PONOMAREV, V. M. 1992 Instability of bounded flows with elliptical streamlines. J. Fluid Mech. 240, 1-30.
15. GREENSPAN, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press (reprinted Breukelen Press 1990).
16. GREENSPAN, H. P. 1969 On the non-linear interaction of inertial modes. J. Fluid Mech. 36, 257-264.
17. HOLLERBACH, R. & KERSWELL, R. R. 1995 Oscillatory internal shear layers in rotating and precessing flows. J. Fluid Mech. 298, 327-339.
18. JOHNSON, L. E. 1967 The precessing cylinder. In Notes on the 1967 Summer Study Program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Inst. Ref. 67-54, pp. 85-108.
19. KELVIN, LORD 1880 Vibrations of a columnar vortex. Phil. Mag. 10, 155-168.
20. KERSWELL, R. R. 1993 The instability of precessing flow. Geophys. Astrophys. Fluid Dyn. 72, 107-144.
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. 1995 On the internal shear layers spawned by the critical regions in oscillatory Ekman boundary layers. J. Fluid Mech. 298, 311-325.
23. KERSWELL, R. R. & BARENGHI, C. F. 1995 On the viscous decay rates of inertial waves in a rotating circular cylinder. J. Fluid Mech. 285, 203-214.
24. KERSWELL, R. R. & DAVEY, A. 1996 On the linear instability of elliptic pipe flow. J. Fluid Mech. 316, 307-324.
25. KERSWELL, R. R. & MALKUS, W. V. R. 1998 Tidal instability as the source for Io's magnetic signature. Geophys. Res. Lett. 25, 603-606.
26. KOBINE, J. J. 1995 Inertial wave dynamics in a rotating and precessing cylinder. J. Fluid Mech. 303, 233-252.
27. KOBINE, J. J. 1996 Azimuthal flow associated with inertial wave resonance in a precessing cylinder. J. Fluid Mech. 319, 387-406.
28. LIFSCHITZ, A. & FABIJONAS, B. 1996 A new class of instabilities of rotating fluids. Phys. Fluids 8, 2239-2241.
29. MALKUS, W. V. R. 1968 Precession of the Earth as the cause of geomagnetism. Science 160, 259-264.
30. MALKUS, W. V. R. 1989 An experimental study of the global instabilities due to the tidal (elliptical) distortion of a rotating elastic cylinder. Geophys. Astrophys. Fluid Dyn. 48, 123-134.
31. MALKUS, W. V. R. 1994 Energy sources for planetary dynamos. In Theory of Solar and Planetary Dynamos. NATO ASI Conference Series, Cambridge University Press.
32. MALKUS, W. V. R. & WALEFFE, F. A. 1991 Transition from order to disorder in elliptical flow: a direct path to shear flow turbulence. In Advances in Turbulence 3 (ed. A. V. Johansson & P. H. Alfredsson), pp. 197-203.
33. MANASSEH, R. 1992 Breakdown regimes of inertia waves in a precessing cylinder. J. Fluid Mech. 243, 261-296.
34. MANASSEH, R. 1994 Distortions of inertia waves in a rotating fluid cylinder forced near its fundamental mode resonance. J. Fluid Mech. 265, 345-370.
35. MANASSEH, R. 1996 Nonlinear behaviour of contained inertia waves. J. Fluid Mech. 315, 151-173.
36. MASON, D. M. & KERSWELL, R. R. 1998 Nonlinear evolution of the elliptical instability. (In preparation).
37. MCEWAN, A. D. 1970 Inertial oscillations in a rotating fluid cylinder. J. Fluid Mech. 40, 603-640.
38. m, m ≥ 3. Commun. Math. Phys. 64, 35-40.
39. O'SULLIVAN, P. L. & BREUER, K. S. 1994 Transient growth in circular pipe flow. I. Linear disturbances. Phys. Fluids 6, 3643-3651.
40. POINCARÉ, H. 1910 Sur la précession des corps déformables. Bull. Astronomique 27, 321-356.
41. RIEUTORD, M. 1991 Linear theory of rotating fluids using spherical harmonics part II, time-periodic flows. Geophys. Astrophys. Fluid Dyn. 59, 185-208.
42. RUELLE, D. & TAKENS, F. 1971 On the nature of turbulence. Commun. Math. Phys. 20, 167-192.
43. STERGIOPOULOS, S. & ALDRIDGE, K. D. 1982 Inertial waves in a fluid partially filling a cylindrical cavity during spin-up from rest. Geophys. Astrophys. Fluid Dyn. 21, 89-112.
44. STERGIOPOULOS, S. & ALDRIDGE, K. D. 1987 Ringdown of inertial waves during spin-up from rest of a fluid contained in a rotating cylindrical cavity. Phys. Fluids 30, 302-311.
45. TILGNER, A. 1998 Driven inertial oscillations in spherical shells. Preprint.
46. VLADIMIROV, V. A. & TARASOV, V. 1985 Resonance instability of the flows with closed streamlines. In Laminar-Turbulent Transition; IUTAM Symp., Novosibirsk, 1984 (ed. V. V. Kozlov), pp. 717-722. Springer.
47. VLADIMIROV, V. A. & VOSTRETSOV, D. 1986 Instability of steady flows with constant vorticity in vessels of elliptic cross-section. Prikl. Matem. Mekhan. 50(3), 367-377. (Transl. J. Appl. Math. Mech. 50(3), 369-377.)
48. VLADIMIROV, V. A. & VOSTRETSOV, D. 1986 Instability of steady flows with constant vorticity in vessels of elliptic cross-section. Prikl. Matem. Mekhan. 50(3), 367-377. (Transl. J. Appl. Math. Mech. 50(3), 369-377.)
49. WALEFFE, F. A. 1989 The 3D instability of a strained vortex and its relation to turbulence. PhD thesis, MIT.