Abstract
With NASA’s Juno mission having arrived at its target and ESA’s JUICE mission in planning, the interest in state-of-the-art models for the interior structure and dynamics of Jupiter is increasing. This chapter reports on the related attempts within the Special Priority Program PlanetMag of the German Science Foundation and provides an up-to-date review of the topic. Refined interior models are discussed that are based on new ab initio calculations for the equations of state for hydrogen and helium. For the first time, the depth-dependent transport properties have also been calculated, most notably an electrical conductivity profile that captures the transition from the molecular outer to the metallic inner hydrogen-rich envelopes. Anelastic simulations of convection show that the strong density stratification causes flow amplitudes to increase with radius while the flow scale decreases. Zonal jet systems very similar to those observed on Jupiter or Saturn are found in simulations of the molecular hydrogen envelope. Dynamo simulations that include the whole gaseous envelope show strikingly Jupiter-like magnetic field configurations when the strong density stratification is combined with an electrical conductivity profile that includes the significant drop in the molecular layer. While the dipole-dominated large-scale field is produced at depth, the equatorial jet can give rise to a secondary dynamo process where it reaches down to regions of sizable electrical conductivity. The magnetic surface signatures of this secondary dynamo are banded but also have more localized wave number m = 1 and m = 2 concentrations at lower latitudes. By detecting these features, the Juno mission should be able to constrain the deep dynamics of the equatorial jet.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids. Oxford University Press, Oxford (1989)
Aubert, J., Aurnou, J., Wicht, J.: The magnetic structure of convection-driven numerical dynamos. Geophys. J. Int. 172, 945 (2008)
Aurnou, J., Heimpel, M., Wicht, J.: The effects of vigorous mixing in a convective model of zonal flow on the ice giants. Icarus 190, 110 (2007)
Ballot, J., Brun, A.S., Turck-Chièze, S.: Simulations of turbulent convection in rotating young solarlike stars: differential rotation and meridional circulation. Astrophys. J. 669, 1190 (2007)
Bassom, A.P., Kuzanyan, K.M., Sokoloff, D., Soward, A.M.: Non-axisymmetric α2Ω-dynamo waves in thin stellar shells. Geophys. Astrophys. Fluid Dyn. 99, 309 (2005)
Becker, A., Lorenzen, W., Fortney, J.J., Nettelmann, N., Schöttler, M., Redmer, R.: Ab initio equations of state for hydrogen (H-REOS.3) and helium (HE-REOS.3) and their implications for the interior of brown dwarfs. Astrophys. J. Suppl. Ser. 215, 14 (2014)
Bessolaz, N., Brun, A.S.: Hunting for giant cells in deep stellar convective zones using wavelet analysis. Astrophys. J. 728, 115 (2011)
Braginsky, S.I., Roberts, P.H.: Equations governing convection in Earth’s core and the geodynamo. Geophys. Astrophys. Fluid Dyn. 79, 1 (1995)
Brown, B.P.: Convection and dynamo action in rapidly rotating suns. Ph.D. thesis, University of Colorado (2009)
Browning, M.K.: Simulations of dynamo action in fully convective stars. Astrophys. J. 676, 1262 (2008)
Brun, A.S., Palacios, A.: Numerical simulations of a rotating red giant star. I. Three-dimensional models of turbulent convection and associated mean flows. Astrophys. J. 702, 1078 (2009)
Busse, F.H.: Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 44, 441 (1970)
Busse, F.H.: Convective flows in rapidly rotating spheres and their dynamo action. Phys. Fluids 14, 1301 (2002)
Busse, F.H., Simitev, R.D.: Parameter dependences of convection-driven dynamos in rotating spherical fluid shells. Geophys. Astrophys. Fluid Dyn. 100, 341 (2006)
Busse, F.H., Simitev, R.D.: Quasi-geostrophic approximation of anelastic convection. J. Fluid Mech. 751, 216 (2014)
Caillabet, L., Mazevet, S., Loubeyre, P.: Multiphase equation of state of hydrogen from ab initio calculations in the range 0.2 to 5 g/cc up to 10 eV. Phys. Rev. B 83, 094101 (2011)
Cao, H., Russell, C.T., Wicht, J., Christensen, U.R., Dougherty, M.K.: Saturn’s high-degree magnetic moments: evidence for a unique planetary dynamo. Icarus 221, 388 (2012)
Chabrier, G., Saumon, D., Hubbard, W.B., Lunine, J.I.: The molecular-metallic transition of hydrogen and the structure of Jupiter and Saturn. Astrophys. J. 391, 817 (1992)
Chekhlov, A., Orszag, S.A., Sukoriansky, S., Galperin, B., Staroselsky, I.: The effect of small-scale forcing on large-scale structures in two-dimensional flows. Physica D 98, 321 (1996)
Christensen, U.R.: Zonal flow driven by deep convection in the major planets. Geophys. Res. Lett. 28, 2553 (2001)
Christensen, U.R.: Zonal flow driven by strongly supercritical convection in rotating spherical shells. J. Fluid Mech. 470, 115 (2002)
Christensen, U., Aubert, J.: Scaling properties of convection-driven dynamos in rotating spherical shells and applications to planetary magnetic fields. Geophys. J. Int. 116, 97 (2006)
Christensen, U.R., Wicht, J.: Models of magnetic field generation in partly stable planetary cores: applications to Mercury and Saturn. Icarus 196, 16 (2008)
Christensen, U., Wicht, J.: Numerical dynamo simulations. In: Olson, P. (ed.) Core Dynamics. Treatise on Geophysics, vol. 8, p. 245. Elsevier, Amsterdam (2015)
Connaughton, C., Nazarenko, S., Quinn, B.: Rossby and drift wave turbulence and zonal flows: the Charney-Hasegawa-Mima model and its extensions. Phys. Rep. 604, 1 (2015)
Connerney, J.E.P., Acuña, M.H., Ness, N.F., Satoh, T.: New models of Jupiter’s magnetic field constrained by the Io flux tube footprint. J. Geophys. Res. 103, 11929 (1998)
Danilov, S., Gryanik, V.M.: Barotropic beta-plane turbulence in a regime with strong zonal jets revisited. J. Atmos. Sci. 61, 2283 (2004)
Desjarlais, M.P.: Density-functional calculations of the liquid deuterium Hugoniot, reshock, and reverberation timing. Phys. Rev. B 68, 064204 (2003)
Desjarlais, M.P.: First-principles calculation of entropy for liquid metals. Phys. Rev. E 88, 062145 (2013)
Dias, R.P., Silvera, I.F.: Observation of the Wigner-Huntington transition to metallic hydrogen. Science (2017). ISSN:0036-8075
Dietrich, W., Gastine, T., Wicht, J.: Reversal and amplification of zonal flows by boundary enforced thermal wind. Icarus 282, 380 (2017)
Dormy, E., Soward, A.M., Jones, C.A., Jault, D., Cardin, P.: The onset of thermal convection in rotating spherical shells. J. Fluid Mech. 501, 43 (2004)
Dreizler, R.M., Gross, E.K.U.: Density Functional Theory. Springer, Berlin (1990)
Drew, S.J., Jones, C.A., Zhang, K.: Onset of convection in a rapidly rotating compressible fluid spherical shell. Geophys. Astrophys. Fluid Dyn. 80, 241 (1995)
Dritschel, D.G., McIntyre, M.E.: Multiple jets as PV staircases: the Phillips effect and the resilience of eddy-transport barriers. J. Atmos. Sci. 65, 855 (2008)
Duarte, L.D.V., Gastine, T., Wicht, J.: Anelastic dynamo models with variable electrical conductivity: an application to gas giants. Phys. Earth Planet. Inter. 222, 22 (2013)
Duarte, L.D.V., Wicht, J., Gastine, T.: Physical properties for Jupiter-like dynamo models. Icarus 229, 206–221 (2018)
Dubrovinsky, L., Dubrovinskaia, L.N., Prakapenka, V.B., Abakumov, A.M.: Implementation of micro-ball nanodiamond anvils for high-pressure studies above 6 Mbar. Nat. Commun. 3, 1163 (2012)
Evonuk, M.: The role of density stratification in generating zonal flow structures in a rotating fluid. Astrophys. J. 673, 1154 (2008)
Evonuk, M., Glatzmaier, G.A.: A 2D study of the effects of the size of a solid core on the equatorial flow in giant planets. Icarus 181, 458 (2006)
Evonuk, M., Samuel, H.: Simulating rotating fluid bodies: when is vorticity generation via density-stratification important? Earth Planet. Sci. Lett. 317, 1 (2012)
Feynman, R.P.: Forces in molecules. Phys. Rev. 56, 340 (1939)
Fortney, J.J., Hubbard, W.B.: Phase separation in giant planets: inhomogeneous evolution of Saturn. Icarus 164, 228 (2003)
Fortney, J.J., Nettelmann, N.: The interior structure, composition, and evolution of giant planets. Space Sci. Rev. 152, 423 (2010)
Fortov, V.E., Ilkaev, R.I., Arinin, V.A., Burtzev, V.V., Golubev, V.A., Iosilevskiy, I.L., Khrustalev, V.V., Mikhailov, A.L., Mochalov, M.A., Ternovoi, V.Y., Zhernokletov, M.V.: Phase transition in a strongly nonideal deuterium plasma generated by quasi-isentropical compression at megabar pressures. Phys. Rev. Lett. 99, 185001 (2007)
French, M., Becker, A., Lorenzen, W., Nettelmann, N., Bethkenhagen, M., Wicht, J., Redmer, R.: Ab initio simulations for material properties along the Jupiter adiabat. Astrophys. J. Suppl. Ser. 202, 5 (2012)
Galanti, E., Kaspi, Y.: Decoupling Jupiter’s deep and atmospheric flows using the upcoming Juno gravity measurements and a dynamical inverse model. Icarus 286, 46 (2017)
Gastine, T., Wicht, J.: Effects of compressibility on driving zonal flow in gas giants. Icarus 219, 428 (2012)
Gastine, T., Duarte, L., Wicht, J.: Dipolar versus multipolar dynamos: the influence of the background density stratification. Astron. Astrophys. 546, A19 (2012)
Gastine, T., Wicht, J., Aurnou, J.M.: Zonal flow regimes in rotating anelastic spherical shells: an application to giant planets. Icarus 225, 156 (2013)
Gastine, T., Heimpel, M., Wicht, J.: Zonal flow scaling in rapidly-rotating compressible convection. Phys. Earth Planet. Inter. 232, 36 (2014a)
Gastine, T., Wicht, J., Duarte, L.D.V., Heimpel, M., Becker, A.: Explaining Jupiter’s magnetic field and equatorial jet dynamics. Geophys. Res. Lett. 41, 5410 (2014b)
Gastine, T., Yadav, R.K., Morin, J., Reiners, A., Wicht, J.: From solar-like to antisolar differential rotation in cool stars. Mon. Not. R. Astron. Soc. 438, L76 (2014c)
Gilman, P.A.: Nonlinear dynamics of Boussinesq convection in a deep rotating spherical shell. I. Geophys. Astrophys. Fluid Dyn. 8, 93 (1977)
Gilman, P.A.: Model calculations concerning rotation at high solar latitudes and the depth of the solar convection zone. Astrophys. J. 231, 284 (1979)
Gilman, P.A., Foukal, P.V.: Angular velocity gradients in the solar convection zone. Astrophys. J. 229, 1179 (1979)
Glatzmaier, G.: Numerical simulation of stellar convective dynamos. I. The model and methods. J. Comput. Phys. 55, 461 (1984)
Glatzmaier, G.A., Gilman, P.A.: Compressible convection in a rotating spherical shell. II. A linear anelastic model. Astrophys. J. Suppl. Ser. 45, 351 (1981)
Glatzmaier, G.A., Evonuk, M., Rogers, T.M.: Differential rotation in giant planets maintained by density-stratified turbulent convection. Geophys. Astrophys. Fluid Dyn. 103, 31 (2009)
Gómez-Pérez, N., Heimpel, M., Wicht, J.: Effects of a radially varying electrical conductivity on 3D numerical dynamos. Phys. Earth Planet. Inter. 181, 42 (2010)
Greenwood, D.A.: The Boltzmann equation in the theory of electrical conduction in metals. Proc. Phys. Soc. 71, 585 (1958)
Grodent, D., Bonfond, B., GéRard, J.-C., Radioti, A., Gustin, J., Clarke, J.T., Nichols, J., Connerney, J.E.P.: Auroral evidence of a localized magnetic anomaly in Jupiter’s northern hemisphere. J. Geophys. Res. 113, A09201 (2008)
Grote, E., Busse, F.: Hemispherical dynamos generated by convection in rotating spherical shells. Phys. Rev. E 62, 4457 (2000)
Guillot, T.: The interior of giant planets: models and outstanding questions. Annu. Rev. Earth Planet. Sci. 33, 493 (2005)
Guillot, T., Gautier, D.: Giant planets. In: Spohn, T., Schubert, G. (eds.) Treatise on Geophysics, vol. 10, 2nd edn., p. 529. Elsevier, Amsterdam (2015)
Haas, P., Tran, F., Blaha, P.: Calculation of the lattice constant of solids with semilocal functionals. Phys. Rev. B 79, 085104 (2009)
Heimpel, M., Aurnou, J.: Turbulent convection in rapidly rotating spherical shells: a model for equatorial and high latitude jets on Jupiter and Saturn. Icarus 187, 540 (2007)
Heimpel, M., Gómez Pérez, N.: On the relationship between zonal jets and dynamo action in giant planets. Geophys. Res. Lett. 381, L14201 (2011)
Heimpel, M., Aurnou, J., Wicht, J.: Simulation of equatorial and high-latitude jets on Jupiter in a deep convection model. Nature 438, 193 (2005)
Helled, R., Stevenson, D.: The fuzziness of giant planets’ cores. Astrophys. J. Lett. L840, L4 (2017)
Hess, S.L.G., Bonfond, B., Zarka, P., Grodent, D.: Model of the Jovian magnetic field topology constrained by the Io auroral emissions. J. Geophys. Res. 116, A05217 (2011)
Hohenberg, P., Kohn, W.: Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964)
Holst, B., French, M., Redmer, R.: Electronic transport coefficients from ab initio simulations and application to dense liquid hydrogen. Phys. Rev. B 83, 235120 (2011)
Holst, B., Redmer, R., Gryaznov, V.K., Fortov, V.E., Iosilevskiy, I.L.: Hydrogen and deuterium in shock wave experiments, ab initio simulations and chemical picture modeling. Eur. Phys. J. D 66, 104 (2012)
Ingersoll, A.P., Pollard, D.: Motion in the interiors and atmospheres of Jupiter and Saturn: scale analysis, anelastic equations, barotropic stability criterion. Icarus 52, 62 (1982)
Jiang, J., Wang, J.: A non-axisymmetric spherical α2-dynamo. Chin. J. Astron. Astrophys. 6, 227 (2006)
Jones, C.A.: A dynamo model of Jupiter’s magnetic field. Icarus 241, 148 (2014)
Jones, C.A.: Thermal and compositional convection in the outer core. In: Olson, P. (ed.) Treatise on Geophysics, 2nd edn., p. 115. Elsevier, Oxford (2015)
Jones, C.A., Kuzanyan, K.M.: Compressible convection in the deep atmospheres of giant planets. Icarus 204, 227 (2009)
Jones, C.A., Soward, A.M., Mussa, A.I.: The onset of thermal convection in a rapidly rotating sphere. J. Fluid Mech. 405, 157 (2000)
Jones, C.A., Rotvig, J., Abdulrahman, A.: Multiple jets and zonal flow on Jupiter. Geophys. Res. Lett. 30, 1731 (2003)
Jones, C.A., Kuzanyan, K.M., Mitchell, R.H.: Linear theory of compressible convection in rapidly rotating spherical shells, using the anelastic approximation. J. Fluid Mech. 634, 291 (2009)
Jones, C.A., Boronski, P., Brun, A.S., Glatzmaier, G.A., Gastine, T., Miesch, M.S., Wicht, J.: Anelastic convection-driven dynamo benchmarks. Icarus 216, 120 (2011)
Juranek, H., Redmer, R., Rosenfeld, Y.: Fluid variational theory for pressure dissociation in dense hydrogen: multicomponent reference system and nonadditivity effects. J. Chem. Phys. 117, 1768 (2002)
Käpylä, P.J., Mantere, M.J., Guerrero, G., Brandenburg, A., Chatterjee, P.: Reynolds stress and heat flux in spherical shell convection. Astron. Astrophy. 531, A162 (2011)
Kaspi, Y.: Inferring the depth of the zonal jets on Jupiter and Saturn from odd gravity harmonics. Geophys. Res. Lett. 40, 676 (2013)
Kaspi, Y., Flierl, G.R., Showman, A.P.: The deep wind structure of the giant planets: results from an anelastic general circulation model. Icarus 202, 525 (2009)
Kaspi, Y., Hubbard, W.B., Showman, A.P., Flierl, G.R.: Gravitational signature of Jupiter’s internal dynamics. Geophys. Res. Lett. 37, L01204 (2010)
Kaspi, Y., Davighi, J.E., Galanti, E., Hubbard, W.B.: The gravitational signature of internal flows in giant planets: comparing the thermal wind approach with barotropic potential-surface methods. Icarus 276, 170 (2016)
Kerley, G.I., Christian-Frear, T.L.: Sandia Report No. SAND93–1206. Technical report, Sandia National Laboratories (1993)
King, E.M., Stellmach, S., Aurnou, J.M.: Heat transfer by rapidly rotating Rayleigh-Bénard convection. J. Fluid Mech. 691, 568 (2012)
Knudson, M.D., Desjarlais, M.P., Becker, A., Lemke, R.W., Cochrane, K.R., Savage, M.E., Bliss, D.E., Mattsson, T.R., Redmer, R.: Direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium. Science 348, 1455 (2015)
Kohanoff, J.: Electronic Structure Calculations for Solids and Molecules. Cambridge University Press, Cambridge (2006)
Kohn, W., Sham, L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965)
Kong, D., Zhang, K., Schubert, G.: On the variation of zonal gravity coefficients of a giant planet caused by its deep zonal flows. Astrophys. J. 748, 143 (2012)
Kong, D., Liao, X., Zhang, K., Schubert, G.: Gravitational signature of rotationally distorted Jupiter caused by deep zonal winds. Icarus 226, 1425 (2013)
Kong, D., Liao, X., Zhang, K., Schubert, G.: Equatorial zonal jets and Jupiter’s gravity. Astrophys. J. Lett. 791, L24 (2014)
Kong, D., Zhang, K., Schubert, G.: Odd gravitational harmonics of Jupiter: effects of spherical versus nonspherical geometry and mathematical smoothing of the equatorially antisymmetric zonal winds across the equatorial plane. Icarus 277, 416 (2016)
Kong, D., Zhang, K., Schubert, G.: On the gravitational signature of zonal flows in Jupiter-like planets: an analytical solution and its numerical validation. Phys. Earth Planet. Inter. 263, 1 (2017)
Kubo, R.: Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn. 12, 570 (1957)
Lantz, S.R., Fan, Y.: Anelastic magnetohydrodynamic equations for modeling solar and stellar convection zones. Astrophys. J. Suppl. Ser. 121, 247 (1999)
Lesur, V., Wardinski, I., Rother, M., Mandea, M.: GRIMM: the GFZ Reference Internal Magnetic Model based on vector satellite and observatory data. Geophys. J. Int. 173, 382 (2008)
Lian, Y., Showman, A.P.: Generation of equatorial jets by large-scale latent heating on the giant planets. Icarus 207, 373 (2010)
Liu, J., Goldreich, P.M., Stevenson, D.J.: Constraints on deep-seated zonal winds inside Jupiter and Saturn. Icarus 196, 653 (2008)
Lorenzen, W., Holst, B., Redmer, R.: Demixing of hydrogen and helium at megabar pressures. Phys. Rev. Lett. 102, 115701 (2009)
Lorenzen, W., Holst, B., Redmer, R.: First-order liquid-liquid phase transition in dense hydrogen. Phys. Rev. B 82, 195107 (2010)
Lorenzen, W., Holst, B., Redmer, R.: Metallization in hydrogen-helium mixtures. Phys. Rev. B 84, 235109 (2011)
Lyon, S.P., Johnson, J.D.: Los Alamos Report No. LA-UR-92–3407. Technical report, Los Alamos National Lab (1992)
Marx, D., Hutter, J.: Ab Initio Molecular Dynamics. Cambridge University Press, Cambridge (2009)
Matt, S.P., Do Cao, O., Brown, B.P., Brun, A.S.: Convection and differential rotation properties of G and K stars computed with the ASH code. Astron. Nachr. 332, 897 (2011)
McMahon, J.M., Morales, M.A., Pierleoni, C., Ceperley, D.M.: The properties of hydrogen and helium under extreme conditions. Rev. Mod. Phys. 84, 1607 (2012)
Mermin, N.D.: Thermal properties of the inhomogeneous electron gas. Phys. Rev. 137, A1441 (1965)
Miguel, Y., Guillot, T., Fayon, L.: Jupiter internal structure: the effect of different equations of state. Astron. Astrophys. 596, A114 (2016)
Militzer, B., Hubbard, W.B.: Ab initio equation of state for hydrogen–helium mixtures with recalibration of the giant-planet mass–radius relation. Astrophys. J. 774, 148 (2013)
Militzer, B., Hubbard, W.B., Vorberger, J., Tamblyn, I., Bonev, S.A.: A massive core in Jupiter predicted from first-principles simulations. Astrophys. J. 688, L45 (2008)
Morales, M.A., Schwegler, E., Ceperley, D., Pierleoni, C., Hamel, S., Caspersen, K.: Phase separation in hydrogen–helium mixtures at Mbar pressures. Proc. Natl. Acad. Sci. USA 106, 1324 (2009)
Morales, M.A., Pierleoni, C., Schwegler, E., Ceperley, D.M.: Evidence for a first-order liquid-liquid transition in high-pressure hydrogen from ab initio simulations. Proc. Natl. Acad. Sci. USA 107, 12799 (2010)
Morales, M.A., Hamel, S., Caspersen, K., Schwegler, E.: Hydrogen-helium demixing from first principles: from diamond anvil cells to planetary interiors. Phys. Rev. B 87, 174105 (2013)
Moses, E.: The National Ignition Facility: an experimental platform for studying behavior of matter under extreme conditions. Astrophys. Space Sci. 336, 3 (2011)
Nettelmann, N., Becker, A., Holst, B., Redmer, R.: Jupiter models with improved hydrogen EOS (H-REOS.2). Astrophys. J. 750, 52 (2012)
Nettelmann, N., Püstow, R., Redmer, R.: Saturn structure and homogeneous evolution models with different EOS. Icarus 225, 548 (2013)
Perdew, J.P., Burke, K., Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996)
Pierleoni, C., Morales, M.A., Rillo, G., Holzmann, M., Ceperley, D.M.: Liquid–liquid phase transition in hydrogen by coupled electron–ion Monte Carlo simulations. Proc. Natl. Acad. Sci. USA 113, 4953 (2016)
Porco, C.C., West, R.A., McEwen, A., Del Genio, A.D., Ingersoll, A.P., Thomas, P., Squyres, S., Dones, L., Murray, C.D., Johnson, T.V., Burns, J.A., Brahic, A., Neukum, G., Veverka, J., Barbara, J.M., Denk, T., Evans, M.L., Ferrier, J.J., Geissler, P., Helfenstein, P., Roatsch, T., Throop, H., Tiscareno, M., Vasavada, A.R.: Cassini imaging of Jupiter’s atmosphere, satellites, and rings. Science 299, 1541 (2003)
Püstow, R., Nettelmann, W., Lorenzen, N., Redmer, R.: H/He demixing and the cooling behavior of Saturn. Icarus 267, 323 (2016)
Raynaud, R., Petitdemange, L., Dormy, E.: Dipolar dynamos in stratified systems. Mon. Not. R. Astron. Soc. 448, 2055 (2015)
Read, P.L., Dowling, T.E., Schubert, G.: Saturn’s rotation period from its atmospheric planetary-wave configuration. Nature 460, 608 (2009)
Rhines, P.B.: Waves and turbulence on a beta-plane. J. Fluid Mech. 69, 417 (1975)
Ridley, V.A., Holme, R.: Modeling the Jovian magnetic field and its secular variation using all available magnetic field observations. J. Geophys. Res. 121, 309 (2016)
Rotvig, J., Jones, C.: Multiple jets and bursting in the rapidly rotating convecting two-dimensional annulus model with nearly plane-parallel boundaries. J. Fluid Mech. 567, 117 (2006)
Rüdiger, G., Elstner, D., Ossendrijver, M.: Do spherical α2-dynamos oscillate? Astron. Astrophys. 406, 15 (2003)
Sasaki, Y., Takehiro, S.-I., Kuramoto, K., Hayashi, Y.-Y.: Weak-field dynamo emerging in a rotating spherical shell with stress-free top and no-slip bottom boundaries. Phys. Earth Planet. Inter. 188, 203 (2011)
Saumon, D., Guillot, T.: Shock compression of deuterium and the interiors of Jupiter and Saturn. Astrophys. J. 609, 1170 (2004)
Saumon, D., Chabrier, G., van Horn, H.M.: An equation of state for low-mass stars and giant planets. Astrophys. J. Suppl. Ser. 99, 713 (1995)
Schrinner, M., Petitdemange, L., Dormy, E.: Dipole collapse and dynamo waves in global direct numerical simulations. Astrophys. J. 752, 121 (2012)
Schrinner, M., Petitdemange, L., Raynaud, R., Dormy, E.: Topology and field strength in spherical, anelastic dynamo simulations. Astron. Astrophys. 564, A78 (2014)
Scott, R.K., Polvani, L.M.: Equatorial superrotation in shallow atmospheres. Geophys. Res. Lett. 35, L24202 (2008)
Showman, A.P., Kaspi, Y., Flierl, G.R.: Scaling laws for convection and jet speeds in the giant planets. Icarus 211, 1258 (2011)
Simitev, R., Busse, F.: Patterns of convection in rotating spherical shells. New J. Phys. 5, 97 (2003)
Simitev, R., Busse, F.: Prandtl-number dependence of convection-driven dynamos in rotating spherical fluid shells. J. Fluid Mech. 532, 365 (2005)
Simitev, R.D., Busse, F.H.: Bistability and hysteresis of dipolar dynamos generated by turbulent convection in rotating spherical shells. Europhys. Lett. 85, 19001 (2009)
Soderlund, K.M., Heimpel, M.H., King, E.M., Aurnou, J.M.: Turbulent models of ice giant internal dynamics: dynamos, heat transfer, and zonal flows. Icarus 224, 97 (2013)
Stanley, S., Bloxham, J.: Convective-region geometry as the cause of Uranus’ and Neptune’s unusual magnetic fields. Nature 428, 151 (2004)
Stanley, S., Zuber, M.T., Bloxham, J.: Using reversed magnetic flux spots to determine a planet’s inner core size. Geophys. Res. Lett. 34, 19205 (2007)
Stevenson, D.J.: Reducing the non-axisymmetry of a planetary dynamo and an application to Saturn. Geophys. Astrophys. Fluid Dyn. 21, 113 (1982)
Stevenson, D., Salpeter, E.: The phase diagram and transport properties for hydrogen-helium fluid planets. Astrophys. J. Suppl. S. 35, 221 (1977a)
Stevenson, D., Salpeter, E.: The dynamics and helium distribution in hydrogen-helium fluid plantes. Astrophys. J. Suppl. S. 35, 221 (1977b)
Sukoriansky, S., Dikovskaya, N., Galperin, B.: On the arrest of inverse energy cascade and the Rhines scale. J. Atmos. Sci. 64, 3312 (2007)
Tamblyn, I., Bonev, S.A.: Structure and phase boundaries of compressed liquid hydrogen. Phys. Rev. Lett. 104, 065702 (2010)
Teed, R.J., Jones, C.A., Hollerbach, R.: On the necessary conditions for bursts of convection within the rapidly rotating cylindrical annulus. Phys. Fluids 24, 066604 (2012)
Vallis, G.K.: Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge University Press, Cambridge (2006)
Vallis, G.K., Maltrud, M.E.: Generation of mean flows and jets on a beta plane and over topography. J. Phys. Oceanogr. 23, 1346 (1993)
Vasavada, A.R., Showman, A.P.: Jovian atmospheric dynamics: an update after Galileo and Cassini. Rep. Prog. Phys. 68, 1935 (2005)
Verhoeven, J., Stellmach, S.: The compressional β-effect: a source of zonal winds in planets? Icarus 237, 143 (2014)
Weir, S.T., Mitchell, A.C., Nellis, W.J.: Metallization of fluid molecular hydrogen at 140 GPa (1.4 Mbar). Phys. Rev. Lett. 76, 1860 (1996)
Wicht, J.: Inner-core conductivity in numerical dynamo simulations. Phys. Earth Planet. Inter. 132, 281 (2002)
Wicht, J., Christensen, U.R.: Torsional oscillations in dynamo simulations. Geophys. J. Int. 181, 1367 (2010)
Williams, G.P.: Planetary circulations: I. Barotropic representation of Jovian and terrestrial turbulence. J. Atmos. Sci. 35, 1399 (1978)
Wilson, H.F., Militzer, B.: Sequestration of noble gases in giant planet interiors. Phys. Rev. Lett. 104, 121101 (2010)
Yadav, R.K., Gastine, T., Christensen, U.R., Duarte, L.D.V.: Consistent scaling laws in anelastic spherical shell dynamos. Astrophys. J. 774, 6 (2013)
Zhang, K.: Spiralling columnar convection in rapidly rotating spherical fluid shells. J. Fluid Mech. 236, 535 (1992)
Acknowledgements
The work presented here was extensively supported by the German Science Foundation within the Special Priority Program 1488 “PlanetMag.” Most of the numerical dynamo and flow simulations have been performed at the “Gesellschaft für Wissenschaftliche Datenverarbeitung” in Göttingen and the “Max Planck Computing and Data Facility” in Garching.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Wicht, J. et al. (2018). Modeling the Interior Dynamics of Gas Planets. In: Lühr, H., Wicht, J., Gilder, S.A., Holschneider, M. (eds) Magnetic Fields in the Solar System. Astrophysics and Space Science Library, vol 448. Springer, Cham. https://doi.org/10.1007/978-3-319-64292-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-64292-5_2
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-64291-8
Online ISBN: 978-3-319-64292-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)