The Simple Model of the Evolution of Magnetic and Kinetic Energy of Geodynamo

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

The induction and momentum equations are simplified to a dynamical system for the kinetic and magnetic energies in the Earth’s core. Stable stationary points of this system give a geomagnetic field of ~ 10 mT and the cosecant of the angle between the magnetic field vector and the fluid velocity vector is on average about 500 at a known speed of ~ 1 mm/sec and a generally accepted dynamo power of ~ 1 TW. With a generally known typical geomagnetic time of the order of a thousand years, harmonic secular variations of the order of several decades and rapid exponential changes of the order of several months, possibly associated with jerks, were obtained. All this is in good agreement with dynamo theory, paleomagnetic reconstructions, numerical modeling and observations. Geomagnetic energy ~ 10 mJ/kg is four orders of magnitude greater than kinetic energy. Under conditions of such dominance of magnetic energy, an analytical solution was obtained, which over time converges to stable stationary points. Apparently unlikely catastrophes with virtually zero magnetic energy near partially stable stationary points are discussed.

Full Text

Restricted Access

About the authors

S. V. Starchenko

Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the Russian Academy of Sciences

Author for correspondence.
Email: sstarchenko@mail.ru
Russian Federation, Troitsk

References

  1. Брагинский С.И., Магнитная гидродинамика земного ядра // Геомагнетизм и аэрономия. Т. 4. № 5. С. 898−916. 1964.
  2. Водинчар Г.М. Использование собственных мод колебаний вязкой вращающейся жидкости в задаче крупномасштабного динамо // Вестн. КРАУНЦ. Физ.-мат. науки. Выпуск 2(7). С. 33–42. 2013. https://doi.org/
  3. Старченко С.В., Рузмайкин А.А. Кинематическое – турбулентное геодинамо средних полей // Геомагнетизм и аэрономия. Т. 28. № 3. С. 475−490. 1988.
  4. Старченко С.В. Наблюдательная оценка магнитного поля и параметров геодинамо под поверхностью ядра Земли // Геомагнетизм и аэрономия. T. 55. № 5. С. 712−718. 2015. https://doi.org/10.7868/s0016794015050181
  5. Старченко С.В. Энергетические параметры геодинамо совместимые с аналитическими, численными, палеомагнитными моделями и наблюдениями // Физика Земли. № 5. С. 1−15. 2017. https://doi.org/10.7868/s0002333717050131
  6. Старченко С.В., Яковлева С.В. Двухвековая эволюция и статистика времен вариаций энергии потенциального геомагнитного поля // Геомагнетизм и аэрономия. T. 61. № 5. С. 661−671. 2021. https://doi.org/10.31857/s0016794021050138
  7. Старченко С.В., Смирнов А.Ю. Объемные токи современного магнитного диполя в ядре Земли // Физика Земли. № 4. С. 42-46. 2021. https://doi.org/10.31857/S0002333721040086
  8. Юшков Е.В., Соколов Д.Д. Инверсии геомагнитного поля и динамо-всплески в рамках простой модели геодинамо // Физика Земли. № 4. С. 121–126. 2018.
  9. Arneitz P., Leonhardt R., Egli R., Fabian K. Dipole and Nondipole Evolution of the Historical Geomagnetic Field From Instrumental, Archeomagnetic, and Volcanic Data // JGR Solid Earth. V. 126. issue 10 e2021JB022565. 2021. https://doi.org/10.1029/2021jb022565
  10. Aubert J. State and evolution of the geodynamo from numerical models reaching the physical conditions of Earth’s core // Geoph. J. Int. V. 235 (1). P. 468−487. 2023. https://doi.org/10.1093/gji/ggad229
  11. Aubert J., Finlay C.C. Geomagnetic jerks and rapid hydromagnetic waves focusing at Earth’s core surface // Nat. Geosci. V. 12. P. 393–398. 2019. https://doi.org/10.1038/s41561-019-0355-1
  12. Bouligand C., Gillet N., Jault D., Schaeffer N., Fournier A., Aubert J. Frequency spectrum of the geomagnetic field harmonic coefficients from dynamo simulations // Geoph. J. Int. V. 207. P. 1142–1157. 2016. https://doi.org/10.1093/gji/ggw326
  13. Braginsky S.I., Roberts P.H. Equations governing convection in the Earth’s core and the geodynamo // Geoph. Astroph. Fluid Dyn. V. 79. P. 1–97. 1995. https://doi.org/10.1080/03091929508228992
  14. Buffett B.A., Bloxham J. Energetics of numerical geodynamo models // Geoph. J. Int. V. 149. P. 211–224. 2002. https://doi.org/10.1046/j.1365-246x.2002.01644.x
  15. Christensen U., Aubert J., Hulot G. Conditions for Earth-like geodynamo models // Earth Planet. Sci. Lett. V. 296. P. 487–496. 2010. https://doi.org/10.1016/j.epsl.2010.06.009
  16. Dumberry M., Mound J. Inner core–mantle gravitational locking and the super-rotation of the inner core // Geophys. J. Int. V. 181. P. 806–817. 2010. https://doi.org/10.1111/j.1365-246x.2010.04563.x
  17. Glatzmaier G.A., Roberts P.H. A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle // Phys. Earth Planet. Int. V. 91(1–3). P. 63–75. 1995.
  18. Gwirtz K., Morzfeld M., Fournier A., Hulot G. Can one use Earth’s magnetic axial dipole field intensity to predict reversals? // Geophys. J. Int. V. 225. P. 277–297. 2021. https://doi.org/10.1093/gji/ggaa542
  19. Jacobs J.A. The Earth’s core // Academic Press, London, New York, San Francisco. 1975.
  20. Krause F., Rädler K.-H. Mean-field magnetohydrodynamics and dynamo theory // Pergamon Press, Oxford. 1980.
  21. Lowes F.J. Possible evidence on core evolution from geomagnetic dynamo theories // Phys. Earth Planet. Int. V. 2. P. 382–385. 1970.
  22. Moffatt K.H., Dormy E. Self-exciting fluid dynamos // Cambridge texts in applied mathematics. Cambridge University Press, Cambridge. 2019. https://doi.org/10.1080/03091929.2019.1690203
  23. Shebalin J.V. Magnetohydrodynamic turbulence and the geodynamo // Phys. Earth Planet. Inter. V. 285. P. 59−75. 2018. https://doi.org/10.3390/fluids6030099
  24. Panovska S., Finlay C.C., Hirt A.M. Observed periodicities and the spectrum of field variations in Holocene magnetic records // Earth Planet. Sci. Lett. V. 379. P. 88–94. 2013. https://doi.org/10.1016/j.epsl.2013.08.010
  25. Starchenko S.V. Analytic scaling laws in planetary dynamo models // Geoph. Astroph. Fluid Dyn. V. 113. № 1−2. P. 71−79. 2019. https://doi.org/10.1080/03091929.2018.1551531
  26. Starchenko S.V. Analytic base of geodynamo-like scaling laws in the planets, geomagnetic periodicities and inversions // Geomagnetism and Aeronomy. V. 54. № 6. P. 694–701. 2014. https://doi.org/10.1080/03091929.2018.1551531
  27. Starchenko S.V., Jones C.A. Typical velocities and magnetic field strengths in planetary interiors // Icarus. V. 157 (2). P. 426−435. 2002. https://doi.org/10.1006/icar.2002.6842
  28. Wicht J., Sanchez S. Advances in geodynamo modeling // Geoph. Astroph. Fluid Dyn., V. 113. № 1−2. P. 2−50. 2019. https://doi.org/10.1080/03091929.2019.1597074

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2024 Russian Academy of Sciences