Hydromagnetic oscillations of the Earth's core

The dispersion relationship for hydromagnetic waves in a rotating system indicates that, under plausible assumptions concerning the strength of the toroidal magnetic field in the earth's liquid core, the periods associated with slow planetary-scale waves in the core would be comparable with the characteristic time scales found in the geomagnetic secular variation, decades to centuries, and it now seems likely that such waves could also play a key role in the production of the geomagnetic field by the ‘dynamo’ process. Attempts to interpret specific features of the field in terms of hydromagnetic oscillations of the core (or of any other type of fluid motion, for that matter) have not yet proved entirely successful, for they encounter serious and in some cases fundamental mathematical difficulties. The present paper reviews theoretical work on free hydromagnetic oscillations of a bounded rotating fluid in the context of the geomagnetic problem.

[1]  F. D. Stacey,et al.  Electrical resistivity of the core , 1971 .

[2]  J. A. Jacobs,et al.  Boundaries of the Earth's Core , 1971 .

[3]  K. Stewartson.  On the motion of a non-conducting body through a perfectly conducting fluid , 1960, Journal of Fluid Mechanics.

[4]  P. Stone.  The dynamics of the atmospheres of the major planets , 1973 .

[5]  D. Loper,et al.  On the spin-up of an electrically conducting fluid Part 1. The unsteady hydromagnetic Ekman-Hartmann boundary-layer problem , 1969, Journal of Fluid Mechanics.

[6]  Roger F. Gans,et al.  Viscosity of the earth's core. , 1972 .

[7]  S. Chandrasekhar.  Hydrodynamic and Hydromagnetic Stability , 1961 .

[8]  S. Runcorn.  The Magnetism of the Earth’s Body , 1956 .

[9]  F. Lowes,et al.  Earth currents of deep internal origin , 1961 .

[10]  P. H. Roberts,et al.  On the motion of liquid in a spheroidal cavity of a precessing rigid body , 1963, Journal of Fluid Mechanics.

[11]  F. Busse.  Shear flow instabilities in rotating systems , 1968, Journal of Fluid Mechanics.

[12]  N. Phillips,et al.  Some laboratory experiments on Rossby waves in a rotating annulus , 1967 .

[13]  S. Malin,et al.  Correlations between the Earth's Gravitational and Magnetic Fields: Effect of Rotation in Latitude , 1971 .

[14]  R. Doell,et al.  Pacific Geomagnetic Secular Variation , 1971, Science.

[15]  D. Tozer.  The electrical properties of the earth's interior , 1959 .

[16]  D. Loper.  STEADY HYDROMAGNETIC BOUNDARY LAYER NEAR A ROTATING, ELECTRICALLY CONDUCTING PLATE. , 1970 .

[17]  M. Steenbeck,et al.  Berechnung der mittleren Lorentz-Feldstärke für ein elektrisch leitendes Medium in turbulenter, durch Coriolis-Kräfte beeinflußter Bewegung , 1966 .

[18]  M. McElhinny,et al.  An investigation of the strength of the geomagnetic field in the early precambrian , 1968 .

[19]  D. W. Allan,et al.  Distortion of a Toroidal Field by Convection , 1958 .

[20]  W. Elsasser.  Hydromagnetic Dynamo Theory , 1956 .

[21]  R. Hide,et al.  Interaction between the Earth's Liquid Core and Solid Mantle , 1969, Nature.

[22]  W. Malkus,et al.  Precessional torques as the cause of geomagnetism , 1963 .

[23]  R. Hide.  On hydromagnetic waves in a stratified rotating incompressible fluid , 1969, Journal of Fluid Mechanics.

[24]  Raymond Hide,et al.  Free hydromagnetic oscillations of the earth's core and the theory of the geomagnetic secular variation , 1966, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[25]  R. Hide.  Motions of the Earth's Core and Mantle, and Variations of the Main Geomagnetic Field , 1967, Science.

[26]  Paul H. Roberts,et al.  On Analysis of the Secular Variation , 1965 .

[27]  M. McElhinny.  Geomagnetic Reversals during the Phanerozoic , 1971, Science.

[28]  K. Stewartson.  On the stability of a spinning top containing liquid , 1959, Journal of Fluid Mechanics.

[29]  F. Busse.  The Dynamical Coupling Between Inner Core and Mantle of the Earth and the 24-Year Libration of the Pole , 1970 .

[30]  H. Greenspan.  On the transient motion of a contained rotating fluid , 1964, Journal of Fluid Mechanics.

[31]  M. Camac,et al.  Thermal conductivity of argon at high temperatures , 1965, Journal of Fluid Mechanics.

[32]  D. Gubbins,et al.  Geomagnetic Dynamos in a Stable Core , 1971, Nature.

[33]  Slow oscillations of fluid in a rotating cavity in the presence of a toroidal magnetic field , 1967, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[34]  M. Longuet-Higgins,et al.  The free oscillations of fluid on a hemisphere bounded by meridians of longitude , 1970, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[35]  G. L. Kalra.  Propagation of gravity waves in a non-isentropic rotating,hydromagnetic medium , 1969 .

[36]  S. Malin,et al.  Novel Correlations between Global Features of the Earth's Gravitational and Magnetic Fields , 1970, Nature.

[37]  P. Gilman,et al.  Influence of an Axial Magnetic Field on the Steady Linear Ekman Boundary Layer , 1968 .

[38]  B. Lehnert,et al.  Magnetohydrodynamic Waves Under the Action of the Coriolis Force. II. , 1954 .

[39]  G. N. Petrova,et al.  SOME ARCHAEOMAGNETIC DATA INDICATIVE OF THE WESTWARD DRIFT OF THE GEOMAGNETIC FIELD , 1969 .

[40]  R. Hide.  On the earth's core - mantle interface , 1970 .

[41]  A. Toomre,et al.  Axisymmetric inertial oscillations of a fluid in a rotating spherical container , 1969, Journal of Fluid Mechanics.

[42]  Edward Crisp Bullard,et al.  Homogeneous dynamos and terrestrial magnetism , 1954, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[43]  H. K. Moffatt.  Dynamo action associated with random inertial waves in a rotating conducting fluid , 1970, Journal of Fluid Mechanics.

[44]  J. Booker,et al.  Geomagnetic data and core motions , 1969, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[45]  S. I. Braginskii.  KINEMATIC MODELS OF THE EARTH'S HYDROMAGNETIC DYNAMO , 1964 .

[46]  P. Roberts,et al.  The origin of the main geomagnetic field , 1961 .

[47]  B. Gutenberg,et al.  Internal constitution of the earth , 1939 .

[48]  A. Kahle,et al.  Correction to paper by Anne B. Kahle, R. H. Ball, and E. H. Vestine, ‘Comparison of estimates of surface fluid motions of the Earth's core for various epochs’ , 1967 .

[49]  S. I. Braginskii.  Torsional Magnetohydrodynamic Vibrations in the Earth's Core and Variations in Day Length , 1970 .

[50]  R. Hide.  Dynamics of the Atmospheres of the Major Planets with an Appendix on the Viscous Boundary Layer at the Rigid Bounding Surface of an Electrically-Conducting Rotating Fluid in the Presence of a Magnetic Field , 1969 .

[51]  Paul H. Roberts,et al.  Magnetohydrodynamics of the Earth's Core , 1972 .

[52]  T. Rikitake.  Non-dipole Field and Fluid Motion in the Earth's Core , 1967 .

[53]  JOHN S. Lewis.  Consequences of the presence of sulfur in the core of the earth , 1971 .

[54]  S. I. Braginskiy.  Magnetic Waves in the Earth's Core , 1967 .

[55]  S. Malin,et al.  Novel Correlations between Global Features of the Earth's Gravitational and Magnetic Fields: Further Statistical Considerations , 1971 .

[56]  K. Stewartson.  Toroidal oscillations of a spherical mass of viscous conducting fluid in a uniform magnetic field , 1957 .

[57]  D. Acheson.  On the hydromagnetic stability of a rotating fluid annulus , 1972, Journal of Fluid Mechanics.

[58]  G. Kennedy,et al.  The adiabatic gradient and the melting point gradient in the core of the Earth , 1971 .

[59]  H. C. Longuet-Higgins.  Planetary waves on a rotating sphere , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[60]  D. W. Allan,et al.  The secular variation of the earth's magnetic field , 1966, Mathematical Proceedings of the Cambridge Philosophical Society.

[61]  W. Malkus.  Hydromagnetic planetary waves , 1967, Journal of Fluid Mechanics.

[62]  T. Rikitake.  Magneto-hydrodynamic Oscillations of a Conducting Fluid Sphere under the Influence of the Coriolis Force. , 1956 .

[63]  Edward Crisp Bullard,et al.  Kinematics of geomagnetic secular variation in a perfectly conducting core , 1968, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[64]  P. Roberts,et al.  HYDROMAGNETIC FLOW DUE TO AN OSCILLATING PLANE , 1960 .

[65]  M. Longuet-Higgins.  On group velocity and energy flux in planetary wave motions , 1964 .

[66]  E. A. Flinn,et al.  Seismic Waves reflected from the Earth's Inner Core , 1970, Nature.

[67]  C. Plumpton,et al.  On Toroidal Magnetic Fields in the Sun and Stars. , 1955 .

[68]  K. Stewartson,et al.  On trapped oscillations of a rotating fluid in a thin spherical shell II , 1971 .

[69]  Harvey P. Greenspan,et al.  The Theory of Rotating Fluids. By H. P. GREENSPAN. Cambridge University Press, 1968. 327 pp. £5.50. , 1972, Journal of Fluid Mechanics.

[70]  K. Stewartson,et al.  Pathological oscillations of a rotating fluid , 1969, Journal of Fluid Mechanics.

[71]  R. Hide.  The hydrodynamics of the earth's core , 1956 .