Rotational Dynamics of the Core

Treatise on Geophysics

Volumn 8, Issue , 2007, Pages 207-243

  Tilgner, A ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

Core; Dynamo theory; Precession; Tides

Indexed keywords

EID: 84882827569     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-044452748-6.00129-2     Document Type: Chapter

References (91)

1. Acheson D. Elementary Fluid Dynamics 1990, Clarendon Press, Oxford, UK.
2. Aldridge K. Inertial waves and the earths outer core. Geophysical Journal of the Royal Astronomical Society 1975, 42:337-345.
3. Aldridge K., Baker R. Paleomagnetic intensity data: A window on the dynamics of earths fluid core?. Physics of the Earth and Planetary Interiors 2003, 140:91-100.
4. Aldridge K., Lumb L. Inertial waves identified in the Earths fluid outer core. Nature 1975, 325:421-423.
5. Aldridge K., Seyed-Mahmoud B., Henderson G., van Wijngaarden W. Elliptical instability of the Earths fluid core. Physics of the Earth and Planetary Interiors 1997, 103:365-374.
6. Aldridge K., Toomre A. Axisymmetric inertial oscillations of a fluid in a rotating spherical container. Journal of Fluid Mechanics 1969, 37:307-323.
7. Beardsley R. An experimental study of inertial waves in a closed cone. Studies in Applied Mathematics 1970, 49:187-196.
8. Bondi H., Lyttleton R. On the dynamical theory of the rotation of the Earth: The effect of precession on the motion of the liquid core. Proceedings of the Cambridge Philosophical Society 1953, 49:498-515.
9. Buffett B. Inner core rotation: A test at the worldwide scale. Geophysical Research Letters 1996, 23:3803-3806.
10. Bullard E. The magnetic field within the Earth. Proceedings of the Royal Society of London A 1949, 197:433-453.
11. Busse F. Steady fluid flow in a precessing spheroidal shell. Journal of Fluid Mechanics 1968, 33:739-751.
12. Channell J., Hodell D., McNamus J., Lehman B. Orbital modulation of the Earths magnetic field intensity. Nature 1998, 394:464-468.
13. Consolini G., DeMichelis P. Stochastic resonance in geomagnetic polarity reversals. Physical Review Letters 2003, 90:058501.
14. Courant R., Hilbert D. Methoden der Mathematischen Physik 1968, Springer, Berlin, Germany.
15. Dintrans B., Rieutord M., Valdettaro L. Gravito-inertial waves in a rotating stratified sphere or spherical shell. Journal of Fluid Mechanics 1999, 398:271-297.
16. Eloy C., Le Gal P., Le Dizès S. Experimental study of the multipolar vortex instability. Physical Review Letters 2000, 85:3400-3403.
17. Gledzer E., Ponomarev V. Instability of bounded flows with elliptical streamlines. Journal of Fluid Mechanics 1992, 240:1-30.
18. Goldstein H. Classical Mechanics 1980, Addison-Wesley, Reading, MA.
19. Greenspan H. The Theory of Rotating Fluids 1968, Cambridge University Press, Cambridge, UK.
20. Greenspan H. On the non-linear interaction of inertial modes. Journal of Fluid Mechanics 1969, 36:257-264.
21. Hollerbach R. What can the observed rotation of the Earths inner core reveal about the state of the outer core?. Geophysical Journal International 1998, 135:564-572.
22. Hollerbach R., Kerswell R. Oscillatory internal shear layers in rotating and precessing flows. Journal of Fluid Mechanics 1995, 298:327-339.
23. Kerswell R. The instability of precessing flow. Geophyscial and Astrophysical Fluid Dynamcis 1993, 72:107-144.
24. Kerswell R. Tidal excitation of hydromagnetic waves and their damping in the Earth. Journal of Fluid Mechanics 1994, 274:219-241.
25. Kerswell R. Elliptical instability. Annual Review of Fluid Mechanics 2002, 34:83-113.
26. Knittle E., Jeanloz R. High-pressure metallization of FeO and implications for the Earths core. Geophysical Research Letters 1986, 13:1541-1544.
27. Kundu P., Cohen I. Fluid Mechanics 2002, Academic Press, San Diego, CA.
28. Lacaze L., Le Gal P., Le Dizès S. Elliptical instability in a rotating spheroid. Journal of Fluid Mechanics 2004, 505:1-22.
29. Lacaze L., Le Gal P., Le Dizès S. Elliptical instability of the flow in a rotating shell. Physics of the Earth and Planetary Interiors 2005, 151:194-205.
30. Lamb H. Hydrodynamics 1932, Cambridge University Press, Cambridge, UK.
31. Landau L., Lifshitz E. Fluid Mechanics 1987, Pergamon Press, Oxford, UK.
32. Laske G., Masters G. Limits on differential rotation of the inner core from an analysis of the Earths free oscillations. Nature 1999, 402:66-69.
33. Lilly D. On the instability of Ekman boundary flow. Journal of the Atmospheric Sciences 1966, 23:481-494.
34. Loper D. Torque balance and energy budget for the precessionally driven dynamo. Physics of the Earth and Planetary Interiors 1975, 11:43-60.
35. Lorenzani S., Tilgner A. Fluid instabilities in precessing spheroidal cavities. Journal of Fluid Mechanics 2001, 447:111-128.
36. Lorenzani S., Tilgner A. Inertial instabilities of fluid flow in precessing spheroidal shells. Journal of Fluid Mechanics 2003, 492:363-379.
37. Maas L., Benielli D., Sommeria J., Lam F.-P. Observation of an internal wave attractor in a confined, stably stratified fluid. Nature 1997, 388:557-561.
38. Maas L., Lam F.-P. Geometric focusing of internal waves. Journal of Fluid Mechanics 1995, 300:1-41.
39. Malkus V. Precession of the Earth as the cause of geomagnetism. Science 1968, 160:259-264.
40. Malkus V. Do precessional torques cause geomagnetism?. Mathematical Problems in the Geophysical Sciences, Lectures in Applied Mathematics 1971, vol. 14:207-228. American Mathematical Society, Providence, RI. P.H. Roberts, K. Stewartson (Eds.).
41. Malkus V. An experimental study of global instabilities due to the tidal (elliptical) distortion of a rotating elastic cylinder. Geophysical and Astrophysical Fluid Dynamics 1989, 48:123-134.
42. Manasseh R. Breakdown regimes of inertia waves in a precessing cylinder. Journal of Fluid Mechanics 1992, 243:261-296.
43. Matthews P., Buffet B., Herring T., Shapiro I. Forced nutations of the Earth: Influence of inner core dynamics. 1: Theory. Journal of Geophysical Research 1991, 96:8219-8242.
44. Matthews P., Buffet B., Herring T., Shapiro I. Forced nutations of the Earth: Influence of inner core dynamics. 2: Numerical results and comparisons. Journal of Geophysical Research 1991, 96:8243-8257.
45. McEwan A. Inertial oscillations in a rotating fluid cylinder. Journal of Fluid Mechanics 1970, 40:603-640.
46. Melchior P., Ducarme B. Detection of inertial gravity oscillations in the Earths core with a superconducting gravimeter at Brussels. Physics of the Earth and Planetary Interiors 1986, 42:129-134.
47. Néron de Surgy O., Laskar J. On the long term evolution of the spin of the Earth. Astronomy and Astrophysics 1997, 318:975-989.
48. Noir J., Brito D., Aldridge K., Cardin P. Experimental evidence of inertial waves in a precessing spheroidal cavity. Geophysical Research Letters 2001, 28:3785-3788.
49. Noir J., Cardin P., Jault D., Masson J.-P. Experimental evidence of non-linear resonance effects between retrograde precession and the tilt-over mode within a spheroid. Geophysical Journal International 2003, 154:407-416.
50. Noir J., Jault D., Cardin P. Numerical study of the motions within a slowly precessing sphere at low Ekman number. Journal of Fluid Mechanics 2001, 437:283-299.
51. Oser H. Experimentelle Untersuchung über harmonische Schwingungen in rotierenden Flüssigkeiten. Zeitschrift Fur Angewandte Mathematik Und Mechanik 1958, 38:386-391.
52. Pais M., LeMouël J. Precession-induced flows in liquid-filled containers and in the Earths core. Geophysical Journal International 2001, 144:539-554.
53. Phillips O. Energy transfer in rotating fluids by reflection of inertial waves. Physics of Fluids 1963, 6:513-520.
54. Poincaré H. Sur la précession des corps déformables. Bulletin Astronomique 1910, 27:321-356.
55. Poirier J. Transport properties of liquid metals and viscosity of the Earths core. Geophysical Journal 1988, 92:99-105.
56. Ray R., Eanes R., Chao B. Detection of tidal dissipation in the solid Earth by satellite tracking and altimetry. Nature 1996, 381:595-597.
57. Ray R., Eanes R., Lemoine F. Constraints on energy dissipation in the Earths body tide from satellite tracking and altimetry. Geophysical Journal International 2001, 144:471-480.
58. Reynolds A. Forced oscillations in a rotating liquid (I). Zeitschrift Fur Angewandte Mathematik Und Physik 1962, 13:460-468.
59. Reynolds A. Forced oscillations in a rotating liquid (II). Zeitschrift Fur Angewandte Mathematik Und Physik 1962, 13:561-572.
60. Rieutord M., Georgeot B., Valdettaro L. Inertial waves in a rotating spherical shell: Attractors and asymptotic spectrum. Journal of Fluid Mechanics 2001, 435:103-144.
61. Roberts P., Stewartson K. On the stability of a MacLaurin spheroid of small viscosity. Astrophysical Journal 1963, 137:777-790.
62. Roberts P., Stewartson K. On the motion of a liquid in a spheroidal cavity of a precessing rigid body. II. Proceedings of the Cambridge Philosophical Society 1965, 61:279-288.
63. Rochester M., Jacobs J., Smylie D., Chong K. Can precession power the geomagnetic dynamo?. Geophysical Journal of the Royal Astronomical Society 1975, 43:661-678.
64. Seyed-Mahmoud B., Aldridge K., Henderson G. Elliptical instability in rotating spherical fluid shells: Application to earths fluid core. Physics of the Earth and Planetary Interiors 2004, 142:257-282.
65. Sloudsky T. De la rotation de la terre supposée fluide á son intérieur. Bulletin de la Société Impériale des Naturalistes 1895, 9:285-318.
66. Souriau A., Poupinet G. Inner core rotation: A test at the worldwide scale. Physics of the Earth and Planetary Interiors 2000, 118:13-27.
67. Stewartson K., Rickard J. Pathological oscillations of a rotating fluid. Journal of Fluid Mechanics 1969, 35:759-773.
68. Stewartson K., Roberts P. On the motion of a liquid in a spheroidal cavity of a precessing rigid body. Journal of Fluid Mechanics 1963, 17:1-20.
69. Suess S. Viscous flow in a deformable rotating container. Journal of Fluid Mechanics 1971, 45:189-201.
70. Tatro P., Mollo-Christensen E. Experiments on Ekman layer instability. Journal of Fluid Mechanics 1967, 28:531-543.
71. Tilgner A. Driven inertial oscillations in spherical shells. Physical Review E 1999, 59:1789-1794.
72. Tilgner A. Magnetohydrodynamic flow in precessing spherical shells. Journal of Fluid Mechanics 1999, 379:303-318.
73. Tilgner A. Non-axisymmetric shear layers in precessing fluid ellipsoidal shells. Geophysical Journal International 1999, 136:629-636.
74. Tilgner A. Spectral methods for the simulation of incompressible flows in spherical shells. International Journal for Numerical Methods in Fluids 1999, 30:713-724.
75. Tilgner A. Oscillatory shear layers in source driven flows in an unbounded rotating fluid. Physics of Fluids 2000, 12:1101-1111.
76. Tilgner A. Precession driven dynamos. Physics of Fluids 2005, 17:034104.
77. Tilgner A., Busse F. Fluid flows in precessing spherical shells. Journal of Fluid Mechanics 2001, 426:387-396.
78. Valet J.-P. Time variations in geomagnetic intensity. Reviews of Geophysics 2003, 41:4.
79. Vanyo J. A geodynamo powered by luni-solar precession. Geophysical and Astrophysical Fluid Dynamics 1991, 59:209-234.
80. Vanyo J. Core-mantle relative motion and coupling. Geophysical Journal International 2004, 158:470-478.
81. Vanyo J., Likins P. Measurement of energy dissipation in a liquid-filled, precessing, spherical cavity. Transactions of the ASME Journal of Applied Mechanics 1971, 38:674-682.
82. Vanyo J., Likins P. Rigid-body approximations to turbulent motion in a liquid-filled, precessing, spherical cavity. Transactions of the ASME Journal of Applied Mechanics 1972, 39:18-24.
83. Vanyo J., Lods D., Wilde P. Precessing mantle, liquid core and solid core interactions. The 4th SEDI Symposium, Abstract Book 1994, SEDI, Whistler, BC, pp. 62-64.
84. Vanyo J., Wilde P., Cardin P., Olson P. Experiments on precessing flows in the earths liquid core. Geophysical Journal International 1995, 121:136-142.
85. Williams G. History of the Earths obliquity. Earth-Science Reviews 1993, 34:1-45.
86. Yamazaki T., Hirokuni O. Orbital influence on earths magnetic field: 100,000 year periodicity in inclination. Science 2002, 295:2435-2438.
87. Zhang K. On coupling between the Poincaré equation and the heat equation. Journal of Fluid Mechanics 1993, 268:211-229.
88. Zhang K. On coupling between the Poincaré equation and the heat equation: Non-slip boundary condition. Journal of Fluid Mechanics 1995, 284:239-256.
89. Zhang K., Liao X., Earnshaw P. On inertial waves and oscillations in a rapidly rotating spheroid. Journal of Fluid Mechanics 2004, 504:1-40.
90. Zharkov V., Molodensky S., Brzezinsky A., Groten E., Varga P. The Earth and Its Rotation 1996, Wichmann, Heidelberg, Germany.
91. Zürn W., Richter B., Rydelek P., Neuberg J. Comment: Detection of inertial gravity oscillations in the Earths core with a superconducting gravimeter at Brussels. Physics of the Earth and Planetary Interiors 1987, 49:176-178.