Geodynamo Simulations—How Realistic Are They?

▪ Abstract The past seven years have seen significant advances in computational simulations of convection and magnetic field generation in the Earth's core. Although dynamically self-consistent models of the geodynamo have simulated magnetic fields that appear in some ways quite similar to the geomagnetic field, none are able to run in an Earth-like parameter regime because of the considerable spatial resolution that is required. Here we discuss some of the subtle compromises that have been made in current models and propose a grand challenge for the future, requiring significant improvements in numerical methods and spatial resolution.

[1]  G. Glatzmaier,et al.  The geodynamo, past, present and future , 2001 .

[2]  A. Kageyama,et al.  Flip-Flop Transitions of the Magnetic Intensity and Polarity Reversals in the Magnetohydrodynamic Dynamo , 1999 .

[3]  Thomas C. Clune,et al.  Computational aspects of geodynamo simulations , 2000, Comput. Sci. Eng..

[4]  P. Roberts,et al.  An anelastic evolutionary geodynamo simulation driven by compositional and thermal convection , 1996 .

[5]  Jeremy Bloxham,et al.  Numerical Modeling of Magnetohydrodynamic Convection in a Rapidly Rotating Spherical Shell , 1999 .

[6]  Paul H. Roberts,et al.  Rotation and Magnetism of Earth's Inner Core , 1996, Science.

[7]  W. Kuang.  Force balances and convective state in the earth's core , 1999 .

[8]  Paul H. Roberts,et al.  Equations governing convection in earth's core and the geodynamo , 1995 .

[9]  Keke Zhang,et al.  The effect of hyperviscosity on geodynamo models , 1997 .

[10]  A. Longbottom,et al.  The influence of boundary region heterogeneities on the geodynamo , 1997 .

[11]  C. Jones,et al.  Influence of the Earth's inner core on geomagnetic fluctuations and reversals , 1993, Nature.

[12]  D. Gubbins.  The distinction between geomagnetic excursions and reversals , 1999 .

[13]  A. Longbottom,et al.  A self-consistent convection driven geodynamo model, using a mean field approximation , 1995 .

[14]  J. Bloxham,et al.  Energetics of numerical geodynamo models , 2002 .

[15]  Paul H. Roberts,et al.  A three-dimensional self-consistent computer simulation of a geomagnetic field reversal , 1995, Nature.

[16]  P. Roberts,et al.  The anisotropy of local turbulence in the Earth’s core , 1999 .

[17]  T. Williams,et al.  Geomagnetic field excursions occurred often during the last million years , 1998 .

[18]  K. Hunkins.  Ekman drift currents in the Arctic Ocean , 1966 .

[19]  Masaru Kono,et al.  Effect of the inner core on the numerical solution of the magnetohydrodynamic dynamo , 1999 .

[20]  F. Busse,et al.  On Convection Driven Dynamos in Rotating Spherical Shells , 1998 .

[21]  Peter A. Gilman,et al.  Three-dimensional Spherical Simulations of Solar Convection. I. Differential Rotation and Pattern Evolution Achieved with Laminar and Turbulent States , 2000 .

[22]  G. Glatzmaier,et al.  An examination of simulated geomagnetic reversals from a palaeomagnetic perspective , 2000, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[23]  Paul H. Roberts,et al.  Geodynamo theory and simulations , 2000 .

[24]  A. Tilgner,et al.  Spectral methods for the simulation of incompressible flows in spherical shells , 1999 .

[25]  Gary A. Glatzmaier,et al.  Numerical Simulations of Stellar Convective Dynamos , 1984 .

[26]  Keisuke Araki,et al.  Periodic Reversals of Magnetic Field Generated by Thermal Convection in a Rotating Spherical Shell , 1997 .

[27]  Akira Kageyama,et al.  Generation mechanism of a dipole field by a magnetohydrodynamic dynamo , 1997 .

[28]  J. Bloxham.  The effect of thermal core–mantle interactions on the palaeomagnetic secular variation , 2000, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[29]  Paul G. Richards,et al.  Seismological evidence for differential rotation of the Earth's inner core , 1996, Nature.

[30]  Ulrich R. Christensen,et al.  Numerical modelling of the geodynamo: a systematic parameter study , 1999 .

[31]  U. Christensen,et al.  Numerical modeling of the geodynamo: Mechanisms of field generation and equilibration , 1999 .

[32]  S. I. Braginsky,et al.  Local turbulence in the Earth's core , 1990 .

[33]  F. Busse,et al.  Generation of magnetic fields by convection in a rotating sphere, I , 1981 .

[34]  Friedrich H. Busse,et al.  Effects of hyperdiffusivities on dynamo simulations , 2000 .

[35]  G. Glatzmaier,et al.  A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle , 1995 .

[36]  D. Fearn,et al.  The influence of Rayleigh number, azimuthal wavenumber and inner core radius on 2- D hydromagnetic dynamos , 2000 .

[37]  F. Busse.  Homogeneous Dynamos in Planetary Cores and in the Laboratory , 2000 .

[38]  Paul H. Roberts,et al.  The role of the Earth's mantle in controlling the frequency of geomagnetic reversals , 1999, Nature.

[39]  J. Aurnou,et al.  Control of inner core rotation by electromagnetic, gravitational and mechanical torques , 2000 .

[40]  Masaru Kono,et al.  A numerical dynamo benchmark , 2001 .

[41]  M. Gillan,et al.  The viscosity of liquid iron at the physical conditions of the Earth's core , 1998, Nature.

[42]  G. Glatzmaier,et al.  Simulating the geodynamo , 1997 .

[43]  Jeremy Bloxham,et al.  Sensitivity of the geomagnetic axial dipole to thermal core–mantle interactions , 2000, Nature.

[44]  Ulrich R. Christensen,et al.  A dynamo model interpretation of geomagnetic field structures , 1998 .

[45]  M. Matsushima,et al.  Some characteristics of magnetic field behavior in a model of MHD dynamo thermally driven in a rotating spherical shell , 1999 .

[46]  E. Dormy,et al.  Numerical models of the geodynamo and observational constraints , 2000 .

[47]  Rainer Hollerbach.  ON THE THEORY OF THE GEODYNAMO , 1996 .

[48]  P. Gilman,et al.  Dynamically consistent nonlinear dynamos driven by convection in a rotating spherical shell , 1981 .

[49]  Steven A. Orszag,et al.  Numerical simulation of incompressible flows within simple boundaries: accuracy , 1971, Journal of Fluid Mechanics.

[50]  Masaru Kono,et al.  Dynamo simulation and palaeosecular variation models , 2000, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[51]  F. Busse,et al.  Finite amplitude convection and magnetic field generation in a rotating spherical shell , 1988 .

[52]  F. Busse,et al.  Regular and chaotic spherical dynamos , 2000 .

[53]  D. Fearn.  Hydromagnetic flow in planetary cores , 1998 .

[54]  R. Parker,et al.  A statistical analysis of magnetic fields from some geodynamo simulations , 2001 .

[55]  G. Glatzmaier,et al.  A test of the frozen-flux approximation using a new geodynamo model , 2000, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[56]  Keke Zhang,et al.  Magnetohydrodynamics in Rapidly Rotating spherical Systems , 2000 .