Hydromagnetic quasi-geostrophic modes in rapidly rotating planetary cores

Physics of the Earth and Planetary Interiors

Volumn 229, Issue , 2014, Pages 1-15

  Canet, E ^a   Finlay, C C ^a,b   Fournier, A ^c  

^a ETH ZURICH   (Switzerland)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^c INSTITUT DE PHYSIQUE DU GLOBE DE PARIS   (France)

Author keywords

Core dynamics; Earth; Ganymede; Mercury; Planetary magnetic fields

Indexed keywords

ASTROPHYSICS; DIFFUSION; EARTH (PLANET); MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; MERCURY (METAL); SPHERES;

AZIMUTHAL WAVENUMBERS; CONTINUOUS TRANSITIONS; CORE DYNAMICS; GANYMEDE; INTERNAL MAGNETIC FIELDS; MAGNETIC DISSIPATION; NON-DIMENSIONAL PARAMETERS; PLANETARY MAGNETIC FIELDS;

ELECTROMAGNETIC FIELD EFFECTS;

CORE (PLANETARY); DISSIPATION; GANYMEDE; MAGNETIC FIELD; MERCURY (PLANET); QUASI-GEOSTROPHIC FLOW;

EID: 84897102485     PISSN: 00319201     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pepi.2013.12.006     Document Type: Article

References (51)

1. Acheson D.J. On hydromagnetic stability of a rotating fluid annulus. J. Fluid Mech. 1972, 52:529-541. 10.1017/S0022112072001570.
2. Alfvén H. Existence of electromagnetic-hydrodynamic waves. Nature 1942, 150:405-406. 10.1038/150405d0.
3. Anderson B.J., Acuña M.H., Korth H., Purucker M.E., Johnson C.L., Slavin J.A., Solomon S.C., McNutt R.L. The structure of Mercury's magnetic field from MESSENGER's first flyby. Science 2008, 321(5885):82-85. 10.1126/science.1159081.
4. Anderson B.J., Johnson C.L., Korth H., Winslow R.M., Borovsky J.E., Purucker M.E., Slavin J.A., Solomon S.C., Zuber M.T., McNutt R.L. Low-degree structure in Mercury's planetary magnetic field. J. Geophys. Res. 2012, 117:E00L12. 10.1029/2012JE004159.
5. Braginsky S.I. Magnetohydrodynamics of the Earth's core. Geomag. Aeron. 1964, 4:698-712.
6. Buffett B.A., Mound J., Jackson A. Inversion of torsional oscillations for the structure and dynamics of earth's core. Geophys. J. Int. 2009, 177(3):878-890. 10.1111/j.1365-246X.2009.04129.x.
7. Busse F.H. Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 1970, 44:441-460. 10.1017/S0022112070001921.
8. Busse F.H. Generation of planetary magnetism by convection. Phys. Earth Planet. Int. 1976, 12:350-358.
9. Busse F.H., Zhang K., Liao X. On slow inertial waves in the solar convection zone. Astr. J. 2005, 631:L171-L174. 10.1086/497300.
10. Canet E., Fournier A., Jault D. Forward and adjoint quasi-geostrophic models of the geomagnetic secular variation. J. Geophys. Res. 2009, 114:B11101. 10.1029/2008JB006189.
11. Cébron D., Le Bars M., Moutou C., Le Gal P. Elliptical instability in terrestrial planets and moons. Astron. Astrophys. 2012, 539:1-16. 10.1086/497300.
12. de Koker N., Steinle-Neumann G., Vlček V. Electrical resistivity and thermal conductivity of liquid fe alloys at high p and t, and heat flux in Earth's core. Proc. Natl. Acad. Sci. 2012, 109:4070-4073. 10.1073/pnas.1111841109.
13. Deng L., Seagle C., Fei Y., Shahar A. High pressure and temperature electrical resistivity of iron and implications for planetary cores. Geophys. Res. Lett. 2013, 40(1):33-37. 10.1029/2012GL054347.
14. Dougherty, M., Grasset, O., Erd, C., Titov, D., Bunce, E., Coustenis, A., Blanc, M., Coates, A., Drossart, P., Fletcher, L., Hussmann, H., Jaumann, R., Krupp, N., Prieto-Ballesteros, O., Tortora, P., Tosi, F., van Hoolst, T., 2012. JUpiter ICy moons Explorer (JUICE): An ESA L-Class Mission Candidate to the Jupiter System. In: Lunar and Planetary Institute Science Conference Abstracts, vol. 43, p. 1806.
15. Dumberry M., Mound J.E. Constraints on core-mantle electromagnetic coupling from torsional oscillation normal modes. J. Geophys. Res. 2008, 113(B03102). 10.1029/2007JB005135.
16. Fearn D.R., Proctor M.R.E. Hydromagnetic waves in a differentially rotating sphere. J. Fluid Mech. 1983, 128:1-20. 10.1017/S0022112083000348.
17. Gillet N., Jault D., Canet E., Fournier A. Fast torsional waves and strong magnetic field within the Earth's core. Nature 2010, 465:74-77. 10.1038/nature09010.
18. Gillet N., Jones C. The quasi-geostrophic model for rapidly rotating spherical convection outside the tangent cylinder. J. Fluid Mech. 2006, 554:343-369. 10.1086/346226.
19. Gillet N., Schaeffer N., Jault D. Rationale and geophysical evidence for quasi-geostrophic rapid dynamics within the earth's outer core. Phys. Earth Planet. Int. 2011, 187(3):380-390. 10.1016/j.pepi.2012.03.006.
20. Greenspan H.P. The Theory of Rotating Fluids 1968, Cambridge University Press.
21. Hauck S.A., Aurnou J.M., Dombard A.J. Sulfur's impact on core evolution and magnetic field generation on ganymede. J. Geophys. Res. 2006, 111(E09008). 10.1029/2005JE002557.
22. Hauck, S.A., Margot, J.-L., Solomon, S.C., Phillips, R.J., Johnson, C.L., Lemoine, F.G., Mazarico, E., McCoy, T.J., Padovan, S., Peale, S.J., Perry, M.E., Smith, D.E., Zuber, M.T., 2013. The curious case of mercury's internal structure. J. Geophys. Res. 118 (Planets), 1204-1220. doi:10.1002/jgre.20091.
23. Hide R. Free hydromagnetic oscillations of the Earth's core and the theory of geomagnetic secular variation. Phil. Trans. R. Soc. Lond. A 1966, 259:615-647. 10.1098/rsta.1966.0026.
24. Hulot G., Finlay C.C., Constable C.G., Olsen N., Mandea M. The magnetic field of planet Earth. Space Sci. Rev. 2010, 152(1-4):159-222. 10.1007/s11214-010-9644-0.
25. Jault D. Axial invariance of rapidly varying diffusionless motions in the Earth's core interior. Phys. Earth Planet. Int. 2008, 166:67-76. 10.1016/j.pepi.2007.11.001.
26. Jones, C., 2003. Dynamos in planets. In: M. J. Thompson, J. Christensen-Dalsgaard (eds.), Stellar Astrophysical Fluid Dynamics, Cambridge University Press, pp. 159-176.
27. Kivelson M.G., Khurana K.K., Volwerk M. The permanent and inductive magnetic moments of Ganymede. Icarus 2002, 157(2):507-522. 10.1006/icar.2002.6834.
28. Kono M., Roberts P.H. Recent geodynamo simulations and observations of the geomagnetic field. Rev. Geophys. 2002, 40(4):1013. 10.1029/2000RG00102.
29. Lehnert B. Magnetohydrodynamic waves under the action of the coriolis force. Astr. J. 1954, 119:647-654.
30. Longuet-Higgins M.S. Planetary waves on a rotating sphere. Proc. R. Soc. Lond. A 1964, 279:446-473. 10.1098/rspa.1964.0116.
31. Malkus W.V.R. Hydromagnetic planetary waves. J. Fluid Mech. 1967, 28:793-802. 10.1017/S0022112067002447.
32. Nornberg M., Ji H., Schartman E., Roach A., Goodman J. Observation of magnetocoriolis waves in a liquid metal Taylor-Couette experiment. Phys. Rev. Lett. 2010, 104(7):074501. 10.1103/PhysRevLett.104.074501.
33. Olson, P., 2007. Overview. In: Treatise on Geophysics, vol. 8: Core Dynamics. ed. Olson, P., Elsevier, Oxford, pp. 1-30.
34. Pais A., Jault D. Quasi-geostrophic flows responsible for the secular variation of the Earth's magnetic field. Geophys. J. Int. 2008, 173:421-443. 10.1111/j.1365-246X.2008.03741.x.
35. Plaut E., Busse F. Low-prandtl-number convection in a rotating cylindrical annulus. J. Fluid Mech. 2002, 464:345-363. 10.1017/S0022112002008923.
36. Pozzo M., Davies C., Gubbins D., Alfè D. Thermal and electrical conductivity of iron at Earth's core conditions. Nature 2012, 485:355-358. 10.1038/nature11031.
37. Rüdiger, G., Hollerbach, R., 2004. The Magnetic Universe. Wiley-VCH, Ch. 2: Earth and Planets, pp. 3-46.
38. Schaeffer N., Cardin P. Quasi-geostrophic model of the instabilities of the Stewartson layer in flat and depth varying containers. Phys. Fluids 2005, 17:104111. 10.1063/1.2073547.
39. Schmitt D. Magneto-inertial waves in a rotating sphere. Geophys. Astrophys. Fluid Dyn. 2010, 104:135-151. 10.1080/03091920903439746.
40. Schmitt D. Quasi-free-decay magnetic modes in planetary cores. Geophys. Astrophys. Fluid Dyn. 2012, 106:660-680. 10.1080/03091929.2012.681306.
41. Schmitt D., Alboussière T., Brito D., Cardin P., Gagnière N., Jault D., Nataf H.-C. Rotating spherical Couette flow in a dipolar magnetic field: experimental study of magneto-inertial waves. J. Fluid Mech. 2008, 604:175-197. 10.1017/S0022112008001298.
42. Stevenson D. Planetary magnetic fields. Earth Planet. Sci. Lett. 2003, 208:1-11. 10.1016/S0012-821X(02)01126-3.
43. Tobias S., Diamond P., Hughes D. β-plane magnetohydrodynamic turbulence in the solar tachocline. Astrophys. J. Lett. 2007, 667(1):L113.
44. Trefethen, L.N., 2000. Spectral methods in MATLAB. Vol. 10. Society for Industrial and Applied Mathematics.
45. Wicht J., Mandea M., Takahashi F., Christensen U., Matsushima M., Langlais B. The origin of Mercury's internal magnetic field. Space Sci. Rev. 2007, 132:261-290. 10.1007/s11214-007-9280-5.
46. Williams P., Read P., Haine T., 3 Testing the limits of quasi-geostrophic theory: application to observed laboratory flows outside the quasi-geostrophic regime. J. Fluid Mech. 2010, 649:187-203. 10.1017/S0022112008001298.
47. Yamakawa H., Ogawa H., Kasaba Y., Hayakawa H., Mukai T., Adachi M. Current status of the bepicolombo/mmo spacecraft design. Adv. Space Res. 2004, 33(12):2133-2141.
48. Zhang K. Spherical shell rotating convection in the presence of a toroidal magnetic field. Proc. R. Soc. Lond. 1995, 448:245-268. 10.1098/rspa.1995.0015.
49. Zhang K., Earnshaw P., Liao X., Busse F. On inertial waves in a rotating fluid sphere. J. Fluid Mech. 2001, 437:103-119. 10.1017/S0022112008001298.
50. Zhang K., Fearn D.R. Hydromagnetic waves in rapidly rotating spherical shells, generated by magnetic toroidal decay modes. Geophys. Astrophys. Fluid Dyn. 1994, 77:133-157.
51. Zhang K., Liao X., Schubert G. Non-axisymmetric instabilities of a torioidal magnetic field in a rotating sphere. Astr. J. 2003, 585:1124-1137. 10.1086/346226.