Skip to main content
SpringerLink
Log in

Numerical Dynamo Simulations: From Basic Concepts to Realistic Models

  • Living reference work entry
  • First Online:
Handbook of Geomathematics

  • 431 Accesses

Abstract

The last years have witnessed an impressive growth in the number and quality of numerical dynamo simulations. The numerical models successfully describe many aspects of the geomagnetic field and also set out to explain the various fields of other planets. The success is somewhat surprising since numerical limitations force dynamo modelers to run their models at unrealistic parameters. In particular the Ekman number, a measure for the relative importance of viscous to Coriolis forces, is many orders of magnitude too large: Earth’s Ekman number is \(\mbox{ E} = 10^{-15}\), while even today’s most advanced numerical simulations have to content themselves with \(\mbox{ E} = 10^{-6}\). After giving a brief introduction into the basics of modern dynamo simulations, we discuss the fundamental force balances and address the question how well the modern models reproduce the geomagnetic field. First-level properties like the dipole dominance, realistic Elsasser and magnetic Reynolds numbers, and an Earth-like reversal behavior are already captured by larger Ekman number simulations around \(\mbox{ E} = 10^{-3}\). However, low Ekman numbers are required for modeling torsional oscillations which are thought to be an important part of the decadal geomagnetic field variations. Moreover, only low Ekman number models seem to retain the huge dipole dominance of the geomagnetic field once the Rayleigh number has been increased to values where field reversals happen. These cases also seem to resemble the low-latitude field found at Earth’s core-mantle boundary more closely than larger Ekman number cases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Note that Ra is defined similar to Eq. (14), with ℓ replaced by the layer depth. Furthermore, possible oscillatory modes are omitted from Fig. 8a for simplicity. See Hori and Wicht (2013) for details.

References

  • Alboussière T, Deguen R, Melzani M (2010) Melting-induced stratification above the Earth’s inner core due to convective translation. Nature 466:744–747

    Google Scholar 

  • Amit H, Aubert J, Hulot G (2010a) Stationary, oscillating or drifting geomagnetic flux patches? J Geophys Res 115:B07108

    Google Scholar 

  • Amit H, Aubert J, Hulot G, Olson P (2008) A simple model for mantle-driven flow at the top of Earth’s core. Earth Planets Space 60:845–854

    Google Scholar 

  • Amit H, Choblet G (2009) Mantle-driven geodynamo features – effects of post-perovskite phase transition. Earth Planets Space 61:1255–1268

    Google Scholar 

  • Amit H, Choblet G (2012) Mantle-driven geodynamo features – effects of compositional and narrow D” anomalies. Phys Earth Planet Inter 190:34–43

    Google Scholar 

  • Amit H, Korte M, Aubert J, Constable C, Hulot G (2011) The time-dependence of intense archeomagnetic flux patches. J Geophys Res 116(B15):B12106

    Google Scholar 

  • Amit H, Leonhardt R, Wicht J (2010b) Polarity reversals from paleomagnetic observations and numerical dynamo simulations. Space Sci Rev 155:293–335

    Google Scholar 

  • Amit H, Olson P (2006) Time-average and time-dependent parts of core flow. Phys Earth Planet Inter 155:120–139

    Google Scholar 

  • Amit H, Olson P (2008) Geomagnetic dipole tilt changes induced by core flow. Phys Earth Planet Inter 166:226–238

    Google Scholar 

  • Aubert J (2013) Flow throughout the Earth’s core inverted from geomagnetic observations and numerical dynamo models. Geophys J Int 192:1537–556

    Google Scholar 

  • Aubert J, Amit H, Hulot G (2007) Detecting thermal boundary control in surface flows from numerical dynamos. Phys Earth Planet Inter 160:143–156

    Google Scholar 

  • Aubert J, Amit H, Hulot G, Olson P (2008a) Thermochemical flows couple the Earth’s inner core growth to mantle heterogeneity. Nature 454:758–761

    Google Scholar 

  • Aubert J, Aurnou J, Wicht J (2008b) The magnetic structure of convection-driven numerical dynamos. Geophys J Int 172:945–956

    Google Scholar 

  • Aubert J, Labrosse S, Poitou C (2009) Modelling the paleo-evolution of the geodynamo. Geophys J Int 179:1414–1429

    Google Scholar 

  • Aubert J, Wicht J (2004) Axial versus equatorial dynamo models with implications for planetary magnetic fields. Earth Planet Sci Lett 221:409–419

    Google Scholar 

  • Biggin AJ, Steinberger B, Aubert J et al (2012) Possible links between long-term geomagnetic variations and wholemantle convection processes. Nat Geosci 5:674

    Google Scholar 

  • Bloxham J, Zatman S, Dumberry M (2002) The origin of geomagnetic jerks. Nature 420:65–68

    Google Scholar 

  • Braginsky S (1970) Torsional magnetohydrodynamic vibrations in the Earth’s core and variation in day length. Geomag Aeron 10:1–8

    Google Scholar 

  • Braginsky S, Roberts P (1995) Equations governing convection in Earths core and the geodynamo. Geophys Astrophys Fluid Dyn 79:1–97

    Google Scholar 

  • Breuer M, Manglik A, Wicht J et al (2010) Thermochemically driven convection in a rotating spherical shell. Geophys J Int 183:150–162

    Google Scholar 

  • Breuer M, Wesseling S, Schmalzl J, Hansen U (2002) Effect of inertia in Rayleigh-Bénard convection. Phys Rev E 69:026320/1–10

    Google Scholar 

  • Bullard EC, Gellman H (1954) Homogeneous dynamos and terrestrial magnetism. Proc R Soc Lond A A 247:213–278

    MathSciNet  MATH  Google Scholar 

  • Busse FH, Simitev R (2005a) Convection in rotating spherical fluid shells and its dynamo states. In: Soward AM, Jones CA, Hughes DW, Weiss NO (eds) Fluid dynamics and dynamos in astrophysics and geophysics. CRC Press, Boca Rato, pp 359–392

    Google Scholar 

  • Busse FH, Simitev R (2005b) Dynamos driven by convection in rotating spherical shells. Atronom Nachr 326:231–240

    MATH  Google Scholar 

  • Carlut J, Courtillot V (1998) How complex is the time-averaged geomagnetic field over the past 5 Myr? Geophys J Int 134:527–544

    Google Scholar 

  • Chan K, Li L, Liao X (2006) Phys Modelling the core convection using finite element and finite difference methods. Earth Planet Inter 157:124–138

    Google Scholar 

  • Chandrasekhar S (1961) Hydrodynamic and hydromagnetic stability. Clarendon Press, Oxford

    MATH  Google Scholar 

  • Christensen UR (2002) Zonal flow driven by strongly supercritical convection in rotating spherical shells. J Fluid Mech 470:115–133

    MathSciNet  MATH  Google Scholar 

  • Christensen UR (2006) A deep dynamo generating Mercury’s magnetic field. Nature 444:1056–1058

    Google Scholar 

  • Christensen UR (2010) Accepted for publication at Space Sci Rev

    Google Scholar 

  • Christensen U, Aubert J (2006) Scaling properties of convection-driven dynamos in rotating spherical shells and applications to planetary magnetic fields. Geophys J Int 116:97–114

    Google Scholar 

  • Christensen UR, Aubert J, Busse FH et al (2001) A numerical dynamo benchmark. Phys Earth Planet Inter 128:25–34

    Google Scholar 

  • Christensen UR, Aubert J, Hulot G (2010) Conditions for Earth-like geodynamo models. Earth Planet Sci Lett 296:487–496

    Google Scholar 

  • Christensen UR, Holzwarth V, Reiners A (2009) Energy flux determines magnetic field strength of planets and stars. Nature 457:167–169

    Google Scholar 

  • Christensen U, Olson P (2003) Secular variation in numerical geodynamo models with lateral variations of boundary heat flow. Phys Earth Planet Inter 138:39–54

    Google Scholar 

  • Christensen U, Olson P, Glatzmaier G (1999) Numericalmodeling of the geodynamo: a systematic parameter study. Geophys J Int 138:393–409

    Google Scholar 

  • Christensen U, Tilgner A (2004) Power requirement of the geodynamo from Ohmic losses in numerical and laboratory dynamos. Nature 429:169–171

    Google Scholar 

  • Christensen U, Wicht J (2007) Numerical dynamo simulations. In: Olson P (eds) Core dynamics. Treatise on geophysics, vol 8. Elsevier, Amsterdam/Boston, pp 245–282

    Google Scholar 

  • Christensen UR, Wardinski I, Lesur V (2012) Time scales of geomagnetic secular acceleration in satellite field models and geodynamo models. Geophys J Int 190:243–254

    Google Scholar 

  • Clement B (2004) Dependency of the duration of geomagnetic polarity reversals on site latitude. Nature 428:637–640

    Google Scholar 

  • Clune T, Eliott J, Miesch M, Toomre J, Glatzmaier G (1999) Computational aspects of a code to study rotating turbulent convection in spherical shells. Parallel Comput 25:361–380

    MATH  Google Scholar 

  • Coe R, Hongre L, Glatzmaier A (2000) An examination of simulated geomagnetic reversals from a paleomagnetic perspective. Philos Trans R Soc Lond A 358:1141–1170

    Google Scholar 

  • Constable C (2000) On the rate of occurence of geomagnetic reversals. Phys Earth Planet Inter 118:181–193

    Google Scholar 

  • Cowling T (1957) The dynamo maintainance of steady magnetic fields. Q J Mech Appl Math 10:129–136

    MathSciNet  MATH  Google Scholar 

  • Dormy E, Cardin P, Jault D (1998) Mhd flow in a slightly differentially rotating spherical shell, with conducting inner core, in a dipolar magnetic field. Earth Planet Sci Lett 158:15–24

    Google Scholar 

  • Fearn D (1979) Thermal and magnetic instabilities in a rapidly rotating fluid sphere. Geophys Astrophys Fluid Dyn 14:103–126

    MATH  Google Scholar 

  • Fournier A, Bunge H-P, Hollerbach R, Vilotte J-P (2005) A Fourier-spectral element algorithm for thermal convection in rotating axisymmetric containers. J Comput Phys 204:462–489

    MathSciNet  MATH  Google Scholar 

  • Gastine T, Duarte L, Wicht J (2012) Dipolar versus multipolar dynamos: the influence of the background density stratification. Astron Atrophys 546:A19

    Google Scholar 

  • Gastine T, Wicht J (2012) Effects of compressibility on driving zonal flow in gas giants. Icarus 219:428–442

    Google Scholar 

  • Gilbert AD, Frisch U, Pouquet A (1988) Helicity is unnecessary for alpha effect dynamos, but it helps. Geophys Astrophys Fluid Dyn 42(1–2):151–161

    MATH  Google Scholar 

  • Gillet N, Brito D, Jault D, Nataf H (2007) Experimental and numerical studies of convection in a rapidly rotating spherical shell. J Fluid Mech 580:83

    MathSciNet  MATH  Google Scholar 

  • Gillet N, Jault D, Canet E, Fournier A (2010) Fast torsional waves and strong magnetic fields within the Earths core. Nature 465:74–77

    Google Scholar 

  • Glatzmaier G (1984) Numerical simulation of stellar convective dynamos. 1. The model and methods. J Comput Phys 55:461–484

    Google Scholar 

  • Glatzmaier G (2002) Geodynamo simulations how realistic are they? Annu Rev Earth Planet Sci 30:237–257

    Google Scholar 

  • Glatzmaier G, Coe R (2007) Magnetic polarity reversals in the core. In: Olson P (eds) Core dynamics. Treatise on geophysics, vol 8. Elsevier, Amsterdam/Boston, pp 283–297

    Google Scholar 

  • Glatzmaier G, Coe R, Hongre L, Roberts P (1999) The role of the Earth’s mantle in controlling the frequency of geomagnetic reversals. Nature 401:885-890

    Google Scholar 

  • Glatzmaier G, Roberts P (1995) A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle. Phys Earth Planet Inter 91:63–75

    Google Scholar 

  • Glatzmaier G, Roberts P (1996) An anelastic evolutionary geodynamo simulation driven by compositional and thermal convection. Physica D 97:81–94

    Google Scholar 

  • Gubbins D (2001) The Rayleigh number for convection in the Earth’s core. Phys Earth Planet Inter 128:3–12

    Google Scholar 

  • Gubbins D, Davies CJ (2013) The stratified layer at the core-mantle boundary caused by barodiffusion of oxygen, sulphur and silicon. Phys Earth Planet Inter 215:21–28

    Google Scholar 

  • Gubbins D, Kelly P (1993) Persistent patterns in the geomagnetic field over the past 2.5 ma. Nature 365:829–832

    Google Scholar 

  • Gubbins D, Love J (1998) Preferred vgp paths during geomagnetic polarity reversals: symmetry considerations. Geophys Res Lett 25:1079–1082

    Google Scholar 

  • Gubbins D, Willis AP, Sreenivasan B (2007) Correlation of Earth’s magnetic field with lower mantle thermal and seismic structure. Phys Earth Planet Inter 162:256–260

    Google Scholar 

  • Harder H, Hansen U (2005) A finite-volume solution method for thermal convection and dynamo problems in spherical shells. Geophys J Int 161:522–532

    Google Scholar 

  • Heimpel M, Aurnou J, Wicht J (2005) Simulation of equatorial and high-latitude jets on Jupiter in a deep convection model. Nature 438:193–196

    Google Scholar 

  • Hejda P, Reshetnyak M (2003) Control volume method for the dynamo problem in the sphere with the free rotating inner core. Stud Geophys Geod 47:147–159

    Google Scholar 

  • Hejda P, Reshetnyak M (2004) Control volume method for the thermal convection problem in a rotating spherical shell: test on the benchmark solution. Stud Geophys Geod 48:741–746

    Google Scholar 

  • Hongre L, Hulot G, Khokholov A (1998) An analysis of the geomangetic field over the past 2000 years. Phys Earth Planet Inter 106:311–335

    Google Scholar 

  • Hori K, Wicht J (2013) Subcritical dynamos in the early Mars core: Implications for cessation of the past Martian dynamo. Phys Earth Planet Inter 219:21–33

    Google Scholar 

  • Hori K, Wicht J, Christensen UR (2010) The effect of thermal boundary conditions on dynamos driven by internal heating. Phys Earth Planet Inter 182:85–97

    Google Scholar 

  • Hori K, Wicht J, Christensen UR (2012) The influence of thermo-compositional boundary conditions on convection and dynamos in a rotating spherical shell. Phys Earth Planet Inter 196:32–48

    Google Scholar 

  • Hulot G, Bouligand C (2005) Statistical paleomagnetic field modelling and symmetry considerations. Geophys J Int 161. doi:10.1111/j.1365

    Google Scholar 

  • Hulot G, Finlay C, Constable C, Olsen N, Mandea M (2010) The magnetic field of planet Earth. Space Sci Rev. doi: 10.1007/s11,214–010–9644–0

    Google Scholar 

  • Isakov A, Descombes S, Dormy E (2004) An integro-differential formulation of magnet induction in bounded domains: boundary element-finite volume method. J Comput Phys 197:540–554

    MathSciNet  Google Scholar 

  • Ivers D, James R (1984) Axisymmetric antidynamo theorems in non-uniform compressible fluids. Philos Trans R Soc Lond A 312:179–218

    MathSciNet  MATH  Google Scholar 

  • Jackson A (1997) Time dependence of geostrophic core-surface motions. Phys Earth Planet Inter 103:293–311

    Google Scholar 

  • Jackson A (2003) Intense equatorial flux spots on the surface of the Earth’s core. Nature 424:760–763

    Google Scholar 

  • Jackson A, Finlay C (2007) Geomagnetic secular variation and applications to the core. In: Kono M (ed) Geomagnetism. Treatise on geophysics, vol 5. Elsevier, Amsterdam, pp 147–193

    Google Scholar 

  • Jackson A, Jonkers A, Walker M (2000) Four centuries of geomagnetic secular variation from historical records. Philos Trans R Soc Lond A358:957–990

    Google Scholar 

  • Jault D (2003) Electromagnetic and topographic coupling, and LOD variations. In: Jones CA, Soward AM, Zhang K (eds) Earth’s core and lower mantle. Taylor & Francis, London/New York, pp 56–76

    Google Scholar 

  • Jault D, Gire C, LeMouël J-L (1988) Westward drift, core motion and exchanges of angular momentum between core and mantle. Nature 333:353–356

    Google Scholar 

  • Johnson C, Constable C (1995) Time averaged geomagnetic field as recorded by lava flows over the past 5 Myr. Geophys J Int 122:489–519

    Google Scholar 

  • Johnson C, Constable C, Tauxe L (2003) Mapping long-term changed in Earth’s magnetic field. Science 300:2044–2045

    Google Scholar 

  • Johnson CL, McFadden P (2007) Time-averaged field and paleosecular variation. In: Kono M (ed) Geomagnetism. Treatise on geophysics, vol 5. Elsevier, Amsterdam, pp 217–254

    Google Scholar 

  • Jones C (2007) Thermal and compositional convection in the outer core. In: Olson P (eds) Core dynamics. Treatise on geophysics, vol 8. Elsevier, Amsterdam/Boston, pp 131–186

    Google Scholar 

  • Jones CA, Boronski P, Brun AS et al (2011) Anelastic convection-driven dynamo benchmarks. Icarus 216:120–135

    Google Scholar 

  • Jonkers A (2003) Long-range dependence in the cenozoic reversal record. Phys Earth Planet Inter 135:253–266

    Google Scholar 

  • Julien K, Knobloch E (1998) Strongly nonlinear convection cells in a rapidly rotating fluid layer: the tilted f-plane. J Fluid Mech 360:141–178

    MathSciNet  MATH  Google Scholar 

  • Julien K, Knobloch E, Werne J (1998) A new class of equations for rotationally constrained flows. Theor Comput Fluid Dyn 11(3–4):251–261

    MATH  Google Scholar 

  • Julien K, Rubio A, Grooms I, Knobloch E (2012) Statistical and physical balances in low Rossby number Rayleigh–Bénard convection. Geophys Astrophys Fluid Dyn 106(4–5):392–428

    MathSciNet  Google Scholar 

  • Kageyama A, Miyagoshi T, Sato T (2008) Formation of current coils in geodynamo simulations. Nature 454:1106–1109

    Google Scholar 

  • Kageyama A, Sato T (1995) Computer simulation of a magnetohydrodynamic dynamo. II. Phys Plasmas 2:1421–1431

    Google Scholar 

  • Kageyama A, Sato T (1997) Generation mechanism of a dipole field by a magnetohydrodynamic dynamo. Phys Rev E 55:4617–4626

    MathSciNet  Google Scholar 

  • Kageyama A, Watanabe K, Sato T (1993) Simulation study of a magnetohydrodynamic dynamo: convection in a rotating shell. Phys Fluids B 24(8):2793–2806

    Google Scholar 

  • Kageyama A, Yoshida M (2005) Geodynamo and mantle convection simulations on the Earth simulator using the yin-yang grid. J Phys Conf Ser 16:325–338

    Google Scholar 

  • Kaiser R, Schmitt P, Busse F (1994) On the invisible dynamo. Geophys Astrophys Fluid Dyn 77:93–109

    Google Scholar 

  • Kelly P, Gubbins D (1997) The geomagnetic field over the past 5 million years. Geophys J Int 128:315–330

    Google Scholar 

  • Kono M, Roberts P (2002) Recent geodynamo simulations and observations of the geomagnetic field. Rev Geophys 40:1013. doi:10.1029/2000RG000102

    Google Scholar 

  • Korte M, Constable C (2005) Continuous geomagnetic field models for the past 7 millennia: 2. cals7k. Geochem Geophys Geosys 6:Q02H16

    Google Scholar 

  • Korte M, Constable C, Donadini F, Holme R (2011) Reconstructing the Holocene geomagnetic field. Earth Planet Sci Lett 312:497–505

    Google Scholar 

  • Korte M, Genevey A, Constable C, Frank U, Schnepp E (2005) Continuous geomagnetic field models for the past 7 millennia: 1. A new global data compilation. Geochem Geophys Geosyst 6:Q02H15

    Google Scholar 

  • Korte M, Holme R (2010) On the persistence of geomagnetic flux lobes in global Holocene field models. Phys Earth Planet Inter 182:179–186

    Google Scholar 

  • Kuang W, Bloxham J (1997) An Earth-like numerical dynamo model. Nature 389:371–374

    Google Scholar 

  • Kuang W, Bloxham J (1999) Numerical modeling of magnetohydrodynamic convection in a rapidly rotating spherical shell: weak and strong field dynamo action. J Comput Phys 153:51–81

    MathSciNet  MATH  Google Scholar 

  • Kuang W, Jiang W, Wang T (2008) Sudden termination of martian dynamo? Implications from subcritical dynamo simulations. Geophys Res Lett 35(14):14,202

    Google Scholar 

  • Kutzner C, Christensen U (2000) Effects of driving mechanisms in geodynamo models. Geophys Res Lett 27:29–32

    Google Scholar 

  • Kutzner C, Christensen U (2002) From stable dipolar to reversing numerical dynamos. Phys Earth Planet Inter 131:29–45

    Google Scholar 

  • Kutzner C, Christensen U (2004) Simulated geomagnetic reversals and preferred virtual geomagnetic pole paths. Geophys J Int 157:1105–1118

    Google Scholar 

  • Lhuillier F, Fournier A, Hulot G, Aubert J (2011) The geomagnetic secular variation timescale in observations and numerical dynamo models. Geophys Res Lett 38:L09306

    Google Scholar 

  • Lillis R, Frey H, Manga M (2008) Rapid decrease in martian crustal magnetization in the noachian era: implications for the dynamo and climate of early mars. Geophys Res Lett 35(14):14,203

    Google Scholar 

  • Manglik A, Wicht J, Christensen UR (2010) A dynamo model with double diffusive convection for Mercurys core. Earth Planet Sci Lett 289:619–628

    Google Scholar 

  • Matsui H, Buffett B (2005) Sub-grid scale model for convection-driven dynamos in a rotating plane layer. Phys Earth Planet Inter 153:74–82

    Google Scholar 

  • Miyagoshi T, Kageyama A, Sato T (2010) Zonal flow formation in the Earth’s core. Nature 463(7282):793–796

    Google Scholar 

  • Miyagoshi T, Kageyama A, Sato T (2011) Formation of sheet plumes, current coils, and helical magnetic fields in a spherical magnetohydrodynamic dynamo. Phys Plasmas 18:072901

    Google Scholar 

  • Monnereau M, Calvet M, Margerin L, Souriau A (2010) Lopsided growth of Earth’s inner core. Science 328:1014

    Google Scholar 

  • Morin V, Dormy E (2009) The dynamo bifurcation in rotating spherical shells. Int J Mod Phys B 23(28n29):5467–5482

    Google Scholar 

  • Olsen N, Haagmans R, Sabaka TJ et al (2006) The Swarm End-to-End mission simulator study: a demonstration of separating the various contributions to Earth’s magnetic field using synthetic data. Earth Planets Space 58:359–370

    Google Scholar 

  • Olson P, Christensen U (2002) The time-averaged magnetic field in numerical dynamos with nonuniform boundary heat flow. Geophys J Int 151:809–823

    Google Scholar 

  • Olson P, Christensen U (2006) Dipole moment scaling for convection-driven planetary dynamos. Earth Planet Sci Lett 250:561–571

    Google Scholar 

  • Olson P, Christensen UR, Driscoll PE (2012) From superchrons to secular variation: a broadband dynamo frequency spectrum for the geomagnetic dipole. Earth Planet Sci Lett 319–320:75–82

    Google Scholar 

  • Olson P, Christensen U, Glatzmaier G (1999) Numerical modeling of the geodynamo: mechanism of field generation and equilibration. J Geophys Res 104:10383–10404

    Google Scholar 

  • Pozzo M, Davies C, Gubbins D, Alfè D (2012) Thermal and electrical conductivity of iron at Earth’s core conditions. Nature 485:355–358

    Google Scholar 

  • Proctor M (1994) Convection and magnetoconvection in a rapidly rotating sphere. In: Proctor MRE, Gilbert AD (eds) Lectures on solar and planetary dynamos, vol 1. Cambridge University Press, Cambridge/New York, p 97

    Google Scholar 

  • Roberts P (1972) Kinematic dynamo models. Philos Trans R Soc Lond A 271:663–697

    Google Scholar 

  • Roberts P (2007) Theory of the geodynamo. In: Olson P (eds) Core dynamics. Treatise on geophysics, vol 8. Elsevier, Amsterdam/Boston, pp 245–282

    Google Scholar 

  • Ryan DA, Sarson GR (2007) Are geomagnetic field reversals controlled by turbulence within the Earth’s core? Geophys Res Lett 34:2307

    Google Scholar 

  • Sakuraba A (2002) Linear magnetoconvection in rotating fluid spheres permeated by a uniform axial magnetic field. Geophys Astrophys Fluid Dyn 96:291–318

    MathSciNet  MATH  Google Scholar 

  • Sakuraba A, Kono M (2000) Effect of a uniform magnetic field on nonlinear magnetocenvection in a rotating fluid spherical shell. Geophys Astrophys Fluid Dyn 92:255–287

    MathSciNet  Google Scholar 

  • Sakuraba A, Roberts P (2009) Generation of a strong magnetic field using uniform heat flux at the surface of the core. Nat Geosci 2:802–805

    Google Scholar 

  • Schmalzl J, Breuer M, Hansen U (2002) The influence of the Prandtl number on the style of vigorous thermal convection. Geophys Astrophys Fluid Dyn 96:381–403

    MATH  Google Scholar 

  • Simitev R, Busse F (2005) Prandtl-number dependence of convection-driven dynamos in rotating spherical fluid shells. J Fluid Mech 532:365–388

    MathSciNet  MATH  Google Scholar 

  • Simitev RD, Busse FH (2009) Bistability and hysteresis of dipolar dynamos generated by turbulent convection in rotating spherical shells. Europhys Lett 85:19001

    Google Scholar 

  • Soderlund KM, King E, Aurnou JM (2012) The influence of magnetic fields in planetary dynamo models. Earth Planet Sci Lett 333–334:9–20

    Google Scholar 

  • Sprague M, Julien K, Knobloch E, Werne J (2006) Numerical simulation of an asymptotically reduced system for rotationally constrained convection. J Fluid Mech 551:141–174

    MathSciNet  MATH  Google Scholar 

  • Sreenivasan B (2009) On dynamo action produced by boundary thermal coupling. Phys Earth Planet Inter 177:130–138

    Google Scholar 

  • Sreenivasan B, Jones CA (2006) The role of inertia in the evolution of spherical dynamos. Geophys J Int 164:467–476

    Google Scholar 

  • Sreenivasan B, Jones CA (2011) Helicity generation and subcritical behaviour in rapidly rotating dynamos. J Fluid Mech 688:5–30

    MathSciNet  MATH  Google Scholar 

  • St Pierre M (1993) The strong field branch of the Childress-Soward dynamo. In: Proctor MRE et al (eds) Solar and planetary dynamos, Cambridge University Press, Cambridge, pp 329–337

    Google Scholar 

  • Stanley S, Bloxham J (2004) Convective-region geometry as the cause of Uranus’ and Neptune’s unusual magnetic fields. Nature 428:151–153

    Google Scholar 

  • Stanley S, Bloxham J, Hutchison W, Zuber M (2005) Thin shell dynamo models consistent with mercurys weak observed magnetic field. Earth Planet Sci Lett 234:341–353

    Google Scholar 

  • Stanley S, Glatzmaier G (2010) Dynamo models for planets other than Earth. Space Sci Rev 152:617–649

    Google Scholar 

  • Stellmach S, Hansen U (2004) Cartesian convection-driven dynamos at low ekman number. Phys Rev E 70:056312

    Google Scholar 

  • Stelzer Z, Jackson A (2013, in press) Extracting scaling laws from numerical dynamo models. Geophys J Int

    Google Scholar 

  • Stieglitz R, Müller U (2001) Experimental demonstration of the homogeneous two-scale dynamo. Phys Fluids 1:561–564

    Google Scholar 

  • Takahashi F, Matsushima M (2006) Dipolar and non-dipolar dynamos in a thin shell geometry with implications for the magnetic field of Mercury. Geophys Res Lett 33:L10202

    Google Scholar 

  • Takahashi F, Matsushima M, Honkura Y (2008a) Scale variability in convection-driven MHD dynamos at low Ekman number. Phys Earth Planet Inter 167:168–178

    Google Scholar 

  • Takahashi F, Tsunakawa H, Matsushima M, Mochizuki N, Honkura Y (2008b) Effects of thermally heterogeneous structure in the lowermost mantle on the geomagnetic field strength. Earth Planet Sci Lett 272:738–746

    Google Scholar 

  • Taylor J (1963) The magneto-hydrodynamics of a rotating fluid and the Earth’s dynamo problem. Proc R Soc Lond A 274:274–283

    MATH  Google Scholar 

  • Tilgner A (1996) High-Rayleigh-number convection in spherical shells. Phys Rev E 53:4847–4851

    Google Scholar 

  • Vallis GK (2006) Atmospheric and oceanic fluid dynamics: fundamentals and large-scale circulation. Cambridge University Press, Cambridge

    Google Scholar 

  • Wicht J (2002) Inner-core conductivity in numerical dynamo simulations. Phys Earth Planet Inter 132:281–302

    Google Scholar 

  • Wicht J (2005) Palaeomagnetic interpretation of dynamo simulations. Geophys J Int 162:371–380

    Google Scholar 

  • Wicht J, Aubert J (2005) Dynamos in action. GWDG-Bericht 68:49–66

    Google Scholar 

  • Wicht J, Christensen UR (2010) Torsional oscillations in dynamo simulations. Geophys J Int 181:1367–1380

    Google Scholar 

  • Wicht J, Mandea M, Takahashi F et al (2007) The origin of Mercurys internal magnetic field. Space Sci Rev 132:261–290

    Google Scholar 

  • Wicht J, Olson P (2004) A detailed study of the polarity reversalmechanism in a numerical dynamo model. Geochem Geophys Geosyst 5. doi:10.1029/2003GC000602

    Google Scholar 

  • Wicht J, Stellmach S, Harder H (2009) Numerical models of the geodynamo: from fundamental Cartesian models to 3d simulations of field reversals. In: Glassmeier K, Soffel H, Negendank J (eds) Geomagnetic field variations – space-time structure, processes, and effects on system Earth. Springer monograph. Springer, Berlin/Heidelberg/NewYork, pp 107–158

    Google Scholar 

  • Wicht J, Tilgner A (2010) Theory and modeling of planetary dynamos. Space Sci Rev 152:501–542

    Google Scholar 

  • Willis AP, Sreenivasan B, Gubbins D (2007) Thermal core mantle interaction: exploring regimes for locked dynamo action. Phys Earth Planet Inter 165:83–92

    Google Scholar 

  • Yadav RK, Gastine T, Christensen UR (2013) Scaling laws in spherical shell dynamos with freeslip boundaries. Icarus 225:185–193

    Google Scholar 

  • Zatman S, Bloxham J (1997) Torsional oscillations and the magnetic field within the Earth’s core. Nature 388:760–761

    Google Scholar 

  • Zhang K-K, Busse F (1988) Finite amplitude convection and magnetic field generation in in a rotating spherical shell. Geophys Astrophys Fluid Dyn 44:33–53

    MATH  Google Scholar 

  • Zhang K, Gubbins D (2000a) Is the geodynamo process intrinsically unstable? Geophys J Int 140:F1–F4

    Google Scholar 

  • Zhang K, Gubbins D (2000b) Scale disparities and magnetohydrodynamics in the Earth’s core. Philos Trans R Soc Lond A 358:899–920

    MathSciNet  MATH  Google Scholar 

  • Zhang K, Schubert G (2000) Magnetohydrodynamics in rapidly rotating spherical systems. Annu Rev Fluid Mech 32:409–443

    MathSciNet  Google Scholar 

Download references

Acknowledgements

Johannes Wicht thanks Uli Christensen for useful discussions and hints.

Author information

Authors and Affiliations

  1. Max-Planck Intitut für Sonnensystemforschung, Kaltenburg-Lindau, Germany

    Johannes Wicht

  2. Institut für Geophysik, Westfählische Wilhelms-Universität, Münster, Germany

    Stephan Stellmach

  3. Institut für Geophysik, Westfählische Wilhelms-Universität, Münster, Germany

    Helmut Harder

Authors
  1. Johannes Wicht
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stephan Stellmach
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Helmut Harder
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Johannes Wicht .

Editor information

Editors and Affiliations

  1. Geomathematische Gruppe, TU Kaiserslautern FB Mathematik, Kaiserslautern, Germany

    Willi Freeden

  2. University of Central Florida Dept. Mathematics, Orlando, Florida, USA

    M. Zuhair Nashed

  3. Inst. Analysis, TU Braunschweig FB 1 Mathematik und Informatik, Braunschweig, Germany

    Thomas Sonar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this entry

Cite this entry

Wicht, J., Stellmach, S., Harder, H. (2013). Numerical Dynamo Simulations: From Basic Concepts to Realistic Models. In: Freeden, W., Nashed, M., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27793-1_16-2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-27793-1_16-2

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Online ISBN: 978-3-642-27793-1

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation