FDEPS Kyoto: Bibliography for the lecture notes
Planetary interiors: Magnetic fields, Convection and Dynamo Theory
Chris Jones, University of Leeds, UKNovember 2017

1. Observational background to planetary structure
The 2nd edition of the ‘Treatise on Geophysics’ 2015, edited by G. Schubert, published by Elsevier,is an excellent source for many of the topics in Lecture 1. Referred to below as TOG2.
1.1 Interior of the EarthInternal structure of the Earth from seismology:
Article by Brian Kennett 'Earth structure: major divisions' in the Encyclopaedia of Geomagnetism
and Paleomagnetism, eds D. Gubbins and E. Herrero-Bervera, Springer, 2007.
Dziewonski, A.M. and Anderson, D.L., 1981. Preliminary reference Earth model (PREM).
Phys. Earth Planet. Inter. 25, 297-356.
Length of Day long term:
Article by L.V Morrison and F.R. Stephenson, 'Length of day variations: long term' inEncyclopaedia of Geomagnetism and Paleomagnetism, eds D. Gubbins and E. Herrero-Bervera,Springer, 2007.
Length of Day decadal variations:
Jault, D., Gire, C. and LeMouel, J.L. 1988. Nature, 333, 353-356.
Holme, R. and DeViron, O. 2013. Nature, 499, 202-204.
Precession and Nutation signals:
Dehant, V. and Matthews P.M. 2015. TOG2 volume 3, chapter 3.10, p 263-305.
Thermal convection in the core:
Jones, C.A. 2015. TOG2 volume 8, chapter 8.05, p 115-159.
Nimmo, F. 2015. TOG2 volume 8, chapter 8.02, p 27-55.
Mantle convection and the Core-Mantle Boundary heat flux:
Hernlund, J.W. and McNamara, A.K. 2015 TOG2 volume 7, chapter 7.11, p 461-519.

1.2 Interiors of other planets
Plate tectonics on other planets: Structure of terrestrial planets and their history:Gregg, T.K.P., 2015 TOG2 volume 10, chapter 10.09, p307-325.
Internal structure of the giant planets.
Guillot, T., and Gautier, D., 2015 TOG2 volume 10, chapter 10.16, p 529-557.
1.3 Earth's magnetic field
Radial field at the surface: Extrapolating the field to the Core-Mantle Boundary:
Secular variation.
Jackson, A. 2003, Intense equatorial flux spots on the surface of the Earth’s core
Nature, 424, p 760-763
Jackson, A. Jonkers, A.R.T. and Walker, M. 2000. Four centuries of geomagnetic secular variationfrom historical records. Phil. Trans. R. Soc. Lond. A, 358, p 957–990.
Induction equation and magnetic Reynolds number:
An Introduction to Magnetohydrodynamics. P.A. Davidson, 2001,Cambridge University Press.
Core-flow inversion techniques:
Holme, R. 2015 TOG2 volume 8, chapter 8.04, p 91-113.
Energy source for the geodynamo: convection
Article by Stephane Labrosse 'Geodynamo: energy sources' in Encyclopaedia of Geomagnetism andPaleomagnetism, eds D. Gubbins and E. Herrero-Bervera, Springer, 2007.
Energy source for the geodynamo: precession
Tilgner, A. 2015 TOG2 volume 8, chapter 8.07, p 183-212
Reversals and Excursions:Glatzmaier, G.A., and Coe, R.S. 2015 TOG2 volume 8, chapter 8.11, p 279-295.
1.4 Magnetic fields of other planets:
Connerney, J.E.P. 2015 TOG2 volume 10, chapter 10.06, p 195-237.
1.5 Zonal winds on the giant planets.
Jupiter, edited by Fran Bagenal, Timothy Dowling and William McKinnon. 2004. Chapter 6.
'Dynamics of Jupiter's atmosphere'. Cambridge University Press.

Jones, C.A. and Kuzanyan, K.M., 2009. Compressible convection in the deep atmospheres of giantplanets. Icarus, 204, p 227-238.
Zhang K, Kong D, Schubert G. (2017) Shape, Internal Structure, Zonal Winds, and GravitationalField of Rapidly Rotating Jupiter-Like Planets, Annual Review of Earth and Planetary Sciences,volume 45, pages 419-446.

2. Convection in planetary interiors
2.1 Boussinesq Rayleigh-Benard convection.
Hydrodynamic and Hydromagnetic Stability. S Chandrasekhar, S., 1961. Oxford University Press.
(available online). This is the fundamental source for the linear theory of convection. Referred tobelow as HHS.
Laboratory experiments and astrophysical and geophysical applications;
A.V. Getling (1998). Rayleigh-Bénard Convection: Structures and Dynamics (World Scientific).
2.2 Stability of the basic state:
HHS.
2.3 Nonlinear Rayleigh-Bénard convection
Heat transport, Nusselt number: Nu - Ra relations: Malkus-Howard theory:
Siggia, E. D. 1994. High Rayleigh number convection. Ann. Rev. Fluid Mech. 26, p137-168.
Dissipation integrals and the Grossmann-Lohse theory:
Grossmann, S. and Lohse, D., 2000. J. Fluid Mech., 407, p27-56
2.4 Rotating flows.
Taylor-Proudman theorem. Geostrophic flow. Rotating flow experiments.
Greenspan, H.P., The Theory of Rotating Fluids. 1968. Cambridge University Press, New York.
2.5 Plane layer rotating convection
Plane convection model: Vorticity equation and inertial waves. Dispersion relation for the Rayleighnumber. Steady and oscillatory modes. Small Ekman number limit:
HHS.
2.6 Nonlinear rotating convection
Tall thin columns. Formation of large scale vortices:
Busse, F.H. Thermal instabilities of rapidly rotating systems. J. Fluid Mech. 44, p441-460.

Nusselt number - Rayleigh number relations from experiments.
Formation of large scale vortices:
Guervilly, C., Hughes, D.W. and Jones, C.A. 2014. Large-scale vortices in rapidly rotating
Rayleigh-Bénard convection. Journal of Fluid Mechanics 758, 407-435.
2.7 Rotating spherical convection
The Busse annulus:
Busse, F.H. Thermal instabilities of rapidly rotating systems. J. Fluid Mech. 44, p441-460.
Jones, C.A. 2015. TOG2 volume 8, chapter 8.05, p 115-159.
Experiments in rotating convection: columnar flow:
Busse, F.H. and Carrigan, C.R. 1976. Science, 191, p 81-83.
Zonal jet formation in the Busse annulus model:
Rotvig, J. and Jones, C.A., 2006. Multiple jets and bursting in the rapidly rotating convecting twodimensional annulus model with nearly plane-parallel boundaries. Journal of Fluid Mechanics 567,
117 - 140.
Quasi-geostrophic approximation:
Gillet, N and Jones, C.A., 2006. The quasi-geostrophic model for rapidly rotating sphericalconvection outside the tangent cylinder. Journal of Fluid Mechanics 554, 343 - 369.
Onset of convection in a rapidly rotating sphere:
Dormy, E., Soward, A.M., Jones, C.A., Jault, D. and Cardin, P., 2004. The onset of thermal
convection in rotating spherical shells. Journal of Fluid Mechanics, 501, 43-70.
Jones, C.A., Soward, A.M. and Mussa, A.I., 2000. The onset of convection in a rapidly rotatingsphere. Journal of Fluid Mechanics, 405, 157-179.
Scaling laws in convection. Inertial theory of rapidly rotating convection:
Jones, C.A. 2015. TOG2 volume 8, chapter 8.05, p 115-159.
3. How planetary magnetic fields are generated
This lecture is an updated version of my article in Chapter 2. Dynamo Theory, which appeared inDynamos: Les Houches Session LXXXVIII, eds. Ph Cardin and L.F. Cugliando. Elsevier 2008.
Chapter 2 is p 45-132. References to the original papers are given there.
3.1 Fundamentals of MHD and Maxwell's equations.
The MHD equations. Ohm's law and the induction equation. Magnetic Reynolds number.

Frozen flux, Alfvén's theorem. Flux expulsion:
An Introduction to Magnetohydrodynamics. P.A. Davidson, 2001,Cambridge University Press.
3.2 Kinematic dynamo problem
Definition of kinematic dynamos: the four anti-dynamo theorems:
Cowling T.G., The magnetic field of sunspots, Mon. Not. R. Astr. Soc. 94, p 39-48 (1934).
Zeldovich, Ya. B., 1957. Sov. Phys. JETP, 4, p 460-462.
3.3 Working kinematic dynamos.
Ponomarenko dynamo and the Riga dynamo experiment:
Ponomarenko Yu. B., On the theory of hydromagnetic dynamo, J. Appl. Mech. Tech. Phys.
14, 775 (1973).
Gailitis, A. et al. 2008. History and results of the Riga dynamo experiments. Comptes Rendus
Physique, 9, Pages 721-728.
The G.O. Roberts periodic dynamo:
Roberts G.O., Spatially periodic dynamos, Phil. Trans. R. Soc. Lond., A 266, 535-558 (1970).
Spherical dynamo models and the Dudley-James dynamos:Dudley M.L. \& R.W. James, Time-dependent kinematic dynamos with stationary flows,
Proc. R. Soc. Lond., A 425, 407-429 (1989)
3.4 Field generation in numerical geodynamo models.
Creation of meridional and azimuthal field:
U. Christensen, P. Olson and G. A. Glatzmaier 1999. Geophys. J. Int. (1999) 138, p 393-409.
3.5 Fast and slow dynamos.
ABC dynamos and the Galloway-Proctor dynamo:
Galloway D.J. and Proctor M.R.E., Numerical calculations of fast dynamos for smooth velocity
fields with realistic diffusion, Nature, 356, 691-693 (1992).
3.6 Mean-field dynamo theory.
Mean and fluctuating parts in the induction equation. Scale separation and derivation of the alphaand beta effects:
Krause F. and Radler K.-H., Mean field magnetohydrodynamics and dynamo theory, Pergamon
Press (New-York, 1980).

3.7 Mean field α-effect dynamos
Axisymmetric mean field dynamos. The Omega-effect. Dynamo waves. Spherical αω-dynamos:
Parker E.N., Cosmical Magnetic Fields: Their Origin and Their Activity. (1979) Oxford UniversityPress.
Parker E.N., Hydromagnetic dynamo models, Astrophys. J., 122, 293-314 (1955).
Roberts P.H., Kinematic Dynamo Models. Phil. Trans. R. Soc. Lond., A 272, 663-703.
4. Core dynamics: Rotation and Magnetic fields
4.1 Rotating magnetoconvection.
Plane layer models. Non-rotating limit and sunspots. Alfvén waves, magnetic field lines as
stretched strings:
HHS.
Elsasser number and the breaking of the Taylor-Proudman constraint.
Jones, C.A. 2015. TOG2 volume 8, chapter 8.05, p 115-159.
4.2 Waves in rotating MHD.
Types of wave found in the core. MC waves and their dispersion relation. Slow magnetic Rossby
waves:
D. Jault, C.C. Finlay, 2015 TOG2 Chapter 8.09 - Waves in the Core and Mechanical Core–MantleInteractions, Pages 225-244.
Malkus model:,Malkus, W.V.R., Hydromagnetic planetary waves. J. Fluid Mech. (1967), 28, pp. 793-802.
4.3 Torsional waves in the core.
Dynamics of torsional waves. Observations of torsional waves in secular variation and length ofday.
Roberts, P.H. and Aurnou, J., On the theory of core-mantle coupling.
Geophysical & Astrophysical Fluid Dynamics, 106, p 157-230. (2012)
Torsional waves in dynamo models and magnetoconvection models.
Teed, R.J., Jones, C.A. and Tobias, S.M. 2014. The dynamics and excitation of torsional waves ingeodynamo simulations. Geophysical Journal International 196, 724-735.

Teed, R.J., Jones, C.A. and Tobias, S.M. 2015. The transition to Earth-like torsional oscillations inmagnetoconvection simulations. Earth and Planetary Science Letters 419, 22-31.
4.4 Magnetic Rossby waves in the core.
Secular variation: waves or flow? Magnetic Rossby waves in a thick shell. Magnetic Rossby waves
in simulations:Hori, K., Jones, C.A. and Teed, R.J. 2015. Slow magnetic Rossby waves in the Earth's core
Geophysical Research Letters 42, Art No. 10.1002/2015GL064733
4.5 Shallow water MHD model
Gilman shallow water MHD equations:Gilman, P. A., 2000. Magnetohydrodynamic “Shallow Water” equations for the solar tachocline.
Astrophys. J. Lett., 544, l79.
Linearised model, and the types of wave that occur. Magnetic instabilities:
Marquez-Artavia, X., Jones, C.A., and Tobias, S.M. 2017. Rotating magnetic shallow water waves
and instabilities in a sphere. Geophysical & Astrophysical Fluid Dynamics 111, 282-322.

Lecture 5 Thursday 30th November 2pm - 5pm
How numerical dynamo models are constructed and what they produce
5.1 Spherical geodynamo models
Boussinesq spherical dynamo models. Basic state and boundary conditions. Dimensionlessparameters:
U.R. Christensen, J. Wicht., 2015. TOG2 Volume 8, Chapter 8.10 - Numerical Dynamo
Simulations, Pages 245-277.

5.2 Pseudo-spectral method for Boussinesq dynamo models
Poloidal-Toroidal decomposition. Expansion in spherical harmonics. Deriving the scalar
equations. Solution using the influence matrix method. Radial dependence and time-stepping:
Magnetic boundary conditions:Gubbins, D., Willis, A.P. and Sreenivasan B., 2007. Phys. Earth Planet Inter. 162, 256-260.

5.3 Results from Boussinesq dynamo codes. Dipolar, non-dipolar solutions. Variation with Ekman
and Magnetic Prandtl number. Earth-like geodynamo models, subcriticality and helicity. Scalinglaws for geodynamo models:Jones, C.A., 2011. Planetary magnetic fields and fluid dynamos. Annual Review of Fluid
Mechanics, 43, 583-614.

Christensen, U.R., Aubert, J. and Hulot, G., 2010. Conditions for Earth-like geodynamo models.
Earth and Planetary Science Letters, 296, p 487-496.
Sreenivasan, B. and Jones, C.A., 2011. Helicity generation and subcritical behaviour in rapidly
rotating dynamos. Journal of Fluid Mechanics 688, 5-30.
Davidson, P.A. 2013. Scaling laws for planetary dynamos. Geophys. J. Int. 195, p 67-74.
5.4 Compressible convection equations.
Fluid mechanics, Landau, L.D. and Lifshitz, E.M., 1959. Pergamon Press.
5.5 Anelastic convection equations. Anelastic approximation. Entropy diffusion. Lantz-Braginsky
Roberts approximation.
Jones, C.A., Boronski, P., Brun, A.S., Glatzmaier, G.A., Gastine, T., Miesch, M.S. and Wicht, J.
Anelastic convection-driven dynamo benchmarks. Icarus 216, 120-135.
Jones, C.A., 2014. A dynamo model of Jupiter's magnetic field. Icarus 241, 148-159.
5.6 Pseudo-spectral method for anelastic convection. Poloidal-Toroidal decomposition. Deriving
the scalar equations in the entropy-diffusion model.
5.7 Anelastic dynamo benchmark.
Need for benchmarks. Hydrodynamic benchmark. The steady dynamo benchmark:Jones, C.A., Boronski, P., Brun, A.S., Glatzmaier, G.A., Gastine, T., Miesch, M.S. and Wicht, J.
Anelastic convection-driven dynamo benchmarks. Icarus 216, 120-135.

Research Seminar Friday 1st December 9am-11am
Anelastic spherical dynamos with variable conductivity
A series of numerical simulations of the dynamos of gas giant planets has been performed. We usean anelastic, fully nonlinear, three-dimensional, benchmarked MHD code to evolve the flow,entropy and magnetic field. Our models take into account the varying electrical conductivity, highin the ionised metallic hydrogen region, low in the molecular outer region. Our suite of electricalconductivity models ranges from Jupiter-like, where the outer hydrodynamic region is quite thin, toSaturn-like, where there is a thick non-conducting shell. The rapid rotation leads to two distinct
dynamical regimes forming which are separated by a magnetic tangent cylinder - mTC. Outside themTC there are strong zonal flows, where Reynolds stress balances turbulent viscosity, but inside themTC Lorentz force reduces the zonal flow. We find a rich diversity of magnetic field morphologies.
There are Jupiter-like steady dipolar fields, and a belt of quadrupolar dominated dynamos spanning
the range of models between Jupiter-like and Saturn-like conductivity profiles. This diversity may
be linked to the appearance of reversed sign helicity in the metallic regions of our dynamos. With
Saturn-like conductivity profiles we find models with dipolar magnetic fields, whose axisymmetriccomponents resemble those of Saturn, and which oscillate on a very long time-scale. However, thenonaxisymmetric field components of our models are at least ten times larger than those of Saturn,possibly due to the absence of any stably stratified layer.