# School of Mathematics

## Prof Chris A Jones

Professor of Applied Nonlinear Dynamics

Applied Mathematics

### Contact details

Room: 8.32

Tel: +44 (0)113 3435107

Email: C.A.Jones @ maths.leeds.ac.uk

### Keywords

Magnetic field generation in the Earth and other planets

Thermal convection in rotating and magnetic systems

Winds in the giant planets

The solar dynamo

Pattern formation in strongly nonlinear systems

## Research interests

My interests are in Geophysical and Astrophysical fluid dynamics. The Earth's core is continually stirred by convection as heat escapes from the deep interior. Since the core is mostly molten iron, these flows can generate electric currents which produce the Earth's magnetic field. By solving the equations governing convection in a rotating magnetic environment, we can understand the flow patterns, and hence discover how the Earth's magnetic field is created. The field patterns that emerge from the models can be compared with observed geomagnetic data, so we can use this data to probe the physical conditions in the core.

Similar ideas can be used to study the magnetic fields of other planets, and also to understand the origin of the very fast east-west winds that are seen on the giant outer planets. Since the density varies dramatically over the convecting regions in giant planets, I have been involved in developing computational methods based on the anelastic equations of fluid dynamics, which take the large density variation into account.

The mathematical part of this work involves understanding the behaviour of convection in the presence of rotation and magnetic field, both near onset and in the strongly nonlinear regime. This involves studying the bifurcations to new flow and field patterns, and hence the mathematics of nonlinear dynamics.

I am an Editor of the journal 'Physics of the Earth and Planetary Interiors, and an Associate Editor of the journal 'Geophysical and Astrophysical Fluid Dynamics'.

### Useful links

Link to personal pages about my research and teaching

Link to Physics of the Earth and Planetary Interiors

Link to Geophysical and Astrophysical Fluid Dynamics

## Current postgraduate students

Joshua Kirk (2014)

Luke Robins (2013)

## Publications

**Márquez-Artavia X, Jones CA, Tobias SM** Rotating magnetic shallow water waves and instabilities in a sphere *Geophysical and Astrophysical Fluid Dynamics*, **111**, 282-322, 2017

DOI:10.1080/03091929.2017.1301937

View abstract

**Jones CA, Holme R** A close-up view of Jupiter's magnetic field from Juno: New insights into the planet's deep interior *Geophysical Research Letters*, **44**, 5355-5359, 2017

DOI:10.1002/2017GL074200

View abstract

**Guervilly C, Hughes DW, Jones CA** Large-scale-vortex dynamos in planar rotating convection *Journal of Fluid Mechanics*, **815**, 333-360, 2017

DOI:10.1017/jfm.2017.56

View abstract

**Matsui H, Heien E, Aubert J, Aurnou JM, Avery M, Brown B, Buffett BA, Busse F, Christensen UR, Davies CJ, Featherstone N, Gastine T, Glatzmaier GA, Gubbins D, Guermond JL, Hayashi YY, Hollerbach R, Hwang LJ, Jackson A, Jones CA, Jiang W, Kellogg LH, Kuang W, Landeau M, Marti P, Olson P, Ribeiro A, Sasaki Y, Schaeffer N, Simitev RD, Sheyko A, Silva L, Stanley S, Takahashi F, Takehiro SI, Wicht J, Willis AP** Performance benchmarks for a next generation numerical dynamo model *Geochemistry, Geophysics, Geosystems*, **17**, 1586-1607, 2016

DOI:10.1002/2015GC006159

View abstract

**Hori K, Jones CA, Teed RJ** Slow magnetic Rossby waves in the Earth's core *Geophysical Research Letters*, **42**, 6622-6629, 2015

DOI:10.1002/2015GL064733

View abstract

**Teed RJ, Jones CA, Tobias SM** The transition to Earth-like torsional oscillations in magnetoconvection simulations *Earth and Planetary Science Letters*, **419**, 22-31, 2015

DOI:10.1016/j.epsl.2015.02.045

View abstract

**Guervilly C, Hughes DW, Jones CA** Generation of magnetic fields by large-scale vortices in rotating convection *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, **91**, 2015

DOI:10.1103/PhysRevE.91.041001

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**Jones CA** A dynamo model of Jupiter's magnetic field *Icarus*, **241**, 148-159, 2014

DOI:10.1016/j.icarus.2014.06.020

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**Welsh S, Kersale E, Jones CA** Compressible Taylor-Couette flow - instability mechanism and codimension 3 points *JOURNAL OF FLUID MECHANICS*, **750**, 555-577, 2014

DOI:10.1017/jfm.2014.279

**Guervilly C, Hughes DW, Jones CA** Large-scale vortices in rapidly rotating Rayleigh-Bénard convection *Journal of Fluid Mechanics*, **758**, 407-435, 2014

DOI:10.1017/jfm.2014.542

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**Teed RJ, Jones CA, Tobias SM** The dynamics and excitation of torsional waves in geodynamo simulations *Geophysical Journal International*, **196**, 724-735, 2013

DOI:10.1093/gji/ggt432

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**Teed RJ, Jones CA, Hollerbach R** On the necessary conditions for bursts of convection within the rapidly rotating cylindrical annulus *Physics of Fluids*, **24**, 2012

DOI:10.1063/1.4711398

View abstract

**Jones CA, Boronski P, Brun AS, Glatzmaier GA, Gastine T, Miesch MS, Wicht J** Anelastic convection-driven dynamo benchmarks *Icarus*, **216**, 120-135, 2011

DOI:10.1016/j.icarus.2011.08.014

**Jones CA, Sreenivasan B** Helicity generation and subcritical behaviour in rapidly rotating dynamos *Journal of Fluid Mechanics*, **688**, 5-30, 2011

DOI:10.1017/jfm.2011.233

**Jones CA** Planetary Magnetic Fields and Fluid Dynamos *ANNU REV FLUID MECH*, **43**, 583-614, 2011

DOI:10.1146/annurev-fluid-122109-160727

**Jones CA, Thompson MJ, Tobias SM** The Solar Dynamo *SPACE SCI REV*, **152**, 591-616, 2010

DOI:10.1007/s11214-009-9579-5

**Teed RJ, Jones CA, Hollerbach R** Rapidly rotating plane layer convection with zonal flow *GEOPHYS ASTRO FLUID*, **104**, 457-480, 2010

DOI:10.1080/03091929.2010.512290

**Jones CA, Kuzanyan KM** Compressible convection in the deep atmospheres of giant planets *ICARUS*, **204**, 227-238, 2009

DOI:10.1016/j.icarus.2009.05.022

**Jones CA, Kuzanyan KM, Mitchell RH** Linear theory of compressible convection in rapidly rotating spherical shells, using the anelastic approximation *J FLUID MECH*, **634**, 291-319, 2009

DOI:10.1017/S0022112009007253

**Jones CA** Course 2 Dynamo theory *Les Houches Summer School Proceedings*, **88**, 45-135, 2008

DOI:10.1016/S0924-8099(08)80006-6

**Rashid FQ, Jones CA, Tobias SM** Hydrodynamic instabilities in the solar tachocline *ASTRON ASTROPHYS*, **488**, 819-827, 2008

DOI:10.1051/0004-6361:200810039

**Chen QN, Jones CA** Similarity and dynamic similarity models for large-eddy simulations of a rotating convection-driven dynamo *GEOPHYS J INT*, **172**, 103-114, 2008

DOI:10.1111/j.1365-246X.2007.03621.x

**Livermore PW, Jones CA, Worland SJ** Spectral radial basis functions for full sphere computations *J COMPUT PHYS*, **227**, 1209-1224, 2007

DOI:10.1016/j.jcp.2007.08.026

**Jones CA** Thermal and Compositional Convection in the Outer Core In *Treatise on Geophysics*, **8**, 131-185, 2007

DOI:10.1016/B978-044452748-6.00130-9

View abstract

**Rogers TM, Glatzmaier GA, Jones CA** Numerical simulations of penetration and overshoot in the sun *ASTROPHYS J*, **653**, 765-773, 2006

**Rotvig J, Jones CA** Multiple jets and bursting in the rapidly rotating convecting two-dimensional annulus model with nearly plane-parallel boundaries *J FLUID MECH*, **567**, 117-140, 2006

DOI:10.1017/S0022112006002254

**Eltayeb IA, Jones CA** Special issue: Modelling dynamo processes - Introduction *GEOPHYS ASTRO FLUID*, **100**, 279-279, 2006

DOI:10.1080/03091920600997111

**Gillet N, Jones CA** The quasi-geo strophic model for rapidly rotating spherical convection outside the tangent cylinder *J FLUID MECH*, **554**, 343-369, 2006

DOI:10.1017/S0022112006009219

**Sreenivasan B, Jones CA** The role of inertia in the evolution of spherical dynamos *Geophysical Journal International*, **164**, 467-476, 2006

DOI:10.1111/j.1365-246X.2005.02845.x

View abstract

**Sharif BW, Jones CA** Rotational and magnetic instability in the diffusive tachocline *GEOPHYS ASTRO FLUID*, **99**, 493-511, 2005

DOI:10.1080/03091920500372084

**Sreenivasan B, Jones CA** Structure and dynamics of the polar vortex in the Earth's core *Geophysical Research Letters*, **32**, 1-4, 2005

DOI:10.1029/2005GL023841

View abstract

**Anufriev AP, Jones CA, Soward AM** The Boussinesq and anelastic liquid approximations for convection in the Earth's core *Physics of the Earth and Planetary Interiors*, **152**, 163-190, 2005

DOI:10.1016/j.pepi.2005.06.004

View abstract

**Jones CA, Roberts PH** Turbulence models and Plane layer dynamos In *Fluid Dynamics and Dynamos in Astrophysics and Geophysics*, **12**, 295-330, 2005

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**Burkert A, Lin DNC, Bodenheimer PH, Jones CA, Yorke HW** On the surface heating of synchronously-spinning short-period Jovian planets *Advances in Applied Mathematics*, **618**, 512-523, 2005

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**Dormy E, Soward AM, Jones CA, Jault D, Cardin P** The onset of thermal convection in rotating spherical shells *Journal of Fluid Mechanics*, **501**, 43-70, 2004

DOI:10.1017/S0022112003007316

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**Chan KH, Liao X, Zhang K, Jones CA** Non-axisymmetric spherical interface dynamos *Astronomy and Astrophysics*, **423**, L37-40, 2004

DOI:10.1051/0004-6361:200400034

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**Jones CA, Rotvig J, Abdulrahman A** Multiple jets and zonal flow on Jupiter *Geophysical Research Letters*, **30**, pp.1731, 2003

DOI:10.1029/2003GL016980

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**Jones CA, Mussa AI, Worland SJ** Magnetoconvection in a rapidly rotating sphere: the weak-field case *Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences*, **459**, 773-797, 2003

DOI:10.1098/rspa.2002.1048

View abstract

**Jones CA** Dynamos in Planets In *Stellar Astrophysical Fluid Dynamics*, 159-176, 2003

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**Roberts PH, Jones CA, Calderwood AR** Energy Fluxes and Ohmic dissipation in the Earth's core In *Earth's Core and Lower Mantle*, 100-129, 2003

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**Rotvig J, Jones CA** Rotating convection-driven dynamos at low Ekman number *Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics)*, **66**, 1-15, 2002

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**Starchenko S, Jones CA** Typical velocities and magnetic field strengths in planetary interiors *Icarus*, **157**, 426-435, 2002

DOI:10.1006/icar.2002.6842

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**Wicht J, Jones CA, Zhang K** Instability of zonal flows in rotating spherical shells, an application to Jupiter *Icarus*, **155**, 425-435, 2002

DOI:10.1006/icar.2001.6733

View abstract

**Hori K, Teed RJ, Jones CA** The dynamics of magnetic Rossby waves in spherical dynamo simulations: a signature of strong-field dynamos? *Physics of the Earth and Planetary Interiors*

DOI:10.1016/j.pepi.2017.07.008

View abstract

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