# Dr Phil Livermore

## Associate Professor

**Telephone number:**
+44(0) 113 34
30379

**Email address:** p.w.livermore@leeds.ac.uk

**Room:** 8.137

**Affiliation:** Institute of Geophysics and Tectonics

#### Biography

4/2014 - present Associate Professor

7/2009 - 4/2014 NERC advanced research fellow.

7/2009 - 9/2009 Senior Scientist, ETH Zurich, Switzerland.

8/2007 - 7/2009 Postdoctoral Research Fellow, Institute of Geophysics and Planetary Physics, University of California, San Diego, USA.

03/2004 - 07/2007 Postdoctoral research assistant and teaching fellow, School of Mathematics, University of Leeds.

#### Research Interests

Earth's magnetic field is a fundamental characteristic of our planet - important both for navigation and in protecting the surface from harmful radiation. Is it is generated within the liquid core of our planet, by a process termed the "geodynamo". Observations of both how the surface magnetic field is structured and how these structures change over time help constrain the geodynamo mechanism which is hidden from view.

My research interests are focussed on the dynamics of the Earth's core and the structure and behaviour through time of the geomagnetic field. Specifically, I study

- Numerical and theoretical low-viscosity models of the Earth's core
- Rapid dynamics in the Earth's core, such as waves.
- Predicting the Earth's internal magnetic field and its impact on space weather.
- Analysing change in the ancient magnetic field.
- Numerical methods and computing.

I am a member of the deep-Earth research group that straddles the School of Earth and Environment and the School of Mathematics.

At Leeds I co-supervise PhD student Maurits Metman, Siohban Prise and Colin Hardy.

Previous PhD students who have now graduated are: Grace Cox (now at Liverpool) and Will Brown (now at BGS).

## Software

A compendium of Galerkin polynomials can be found here.

#### Teaching Interests

I teach Mathematics and Matlab for the Masters Programme in Exploration Geophysics, Mathematics for undergraduates, and am the manager of the undergraduate module Applied Geophysics.

## Publications

- Chen L; Herreman W; Li K;
**Livermore PW**; Luo JW; Jackson A (2018) The optimal kinematic dynamo driven by steady flows in a sphere,*Journal of Fluid Mechanics*,**839**, pp.1-32. doi: 10.1017/jfm.2017.924 - Maffei S; Jackson A;
**Livermore PW**(2017) Characterization of columnar inertial modes in rapidly rotating spheres and spheroids,*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,**473**, . doi: 10.1098/rspa.2017.0181 **Livermore PW**; Hollerbach R; Finlay CC (2017) An accelerating high-latitude jet in Earth's core,*Nature Geoscience*,**10**, pp.62-68. doi: 10.1038/ngeo2859- Metman MC;
**Livermore PW**; Mound JE (2017) The reversed and normal flux contributions to axial dipole decay for 1880-2015,*Physics of the Earth and Planetary Interiors*, . doi: 10.1016/j.pepi.2017.06.007 - Cox GA;
**Livermore PW**; Mound JE (2016) The observational signature of modelled torsional waves and comparison to geomagnetic jerks,*Physics of the Earth and Planetary Interiors*,**255**, pp.50-65. doi: 10.1016/j.pepi.2016.03.012 **Livermore PW**; Bailey LM; Hollerbach R (2016) A comparison of no-slip, stress-free and inviscid models of rapidly rotating fluid in a spherical shell,*Scientific Reports*,**6**, . doi: 10.1038/srep22812- Fournier A; Gallet Y; Usoskin I;
**Livermore PW**; Kovaltsov GA (2015) The impact of geomagnetic spikes on the production rates of cosmogenic^{14}C and^{10}Be in the Earth's atmosphere,*Geophysical Research Letters*,**42**, pp.2759-2766. doi: 10.1002/2015GL063461 - Li K; Jackson A;
**Livermore PW**(2014) Variational data assimilation for a forced, inertia-free magnetohydrodynamic dynamo model,*Geophysical Journal International*,**199**, pp.1662-1676. doi: 10.1093/gji/ggu260 **Livermore PW**; Fournier A; Gallet Y (2014) Core-flow constraints on extreme archeomagnetic intensity changes,*Earth and Planetary Science Letters*,**387**, pp.145-156. doi: 10.1016/j.epsl.2013.11.020- Cox GA;
**Livermore PW**; Mound JE (2013) Forward models of torsional waves: dispersion and geometric effects,*Geophysical Journal International*, . doi: 10.1093/gji/ggt414 - Brown WJ; Mound JE;
**Livermore PW**(2013) Jerks abound: An analysis of geomagnetic observatory data from 1957 to 2008,*Physics of the Earth and Planetary Interiors*,**223**, pp.62-76. doi: 10.1016/j.pepi.2013.06.001 **Livermore PW**; Jackson A; Hollerbach R (2013) Electromagnetically driven westward drift and inner-core superrotation in Earth"s core,*Proceedings of the National Academy of Sciences of the United States of America*,**110**, . doi: 10.1073/pnas.1307825110**Livermore PW**(2012) The Spherical Harmonic Spectrum of a Function with Algebraic Singularities,*Journal of Fourier Analysis and Applications*,**18**, pp.1146-1166. doi: 10.1007/s00041-012-9236-3**Livermore PW**; Hollerbach R (2012) Successive elimination of shear layers by a hierarchy of constraints in inviscid spherical-shell flows,*Journal of Mathematical Physics*,**53**, . doi: 10.1063/1.4736990**Livermore PW**; Ierley G; Jackson A (2011) The evolution of a magnetic field subject to Taylor's constraint using a projection operator,*Geophysical Journal International*,**187**, pp.690-704. doi: 10.1111/j.1365-246X.2011.05187.x- Li K; Jackson A;
**Livermore PW**(2011) Variational data assimilation for the initial-value dynamo problem,*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,**84**, . doi: 10.1103/PhysRevE.84.056321 - Jackson A;
**Livermore PW**; Ierley G (2011) On Ohmic heating in the Earth's core II: Poloidal magnetic fields obeying Taylor's constraint,*PHYS EARTH PLANET IN*,**187**, pp.322-327. doi: 10.1016/j.pepi.2011.06.003 - Li KA;
**Livermore PW**; Jackson A (2010) An optimal Galerkin scheme to solve the kinematic dynamo eigenvalue problem in a full sphere,*J COMPUT PHYS*,**229**, pp.8666-8683. doi: 10.1016/j.jcp.2010.07.039 **Livermore PW**; Hughes DW; Tobias SM (2010) Nonlinear generation of large-scale magnetic fields in forced spherical shell dynamos,*PHYS FLUIDS*,**22**, . doi: 10.1063/1.3313930**Livermore PW**(2010) Galerkin orthogonal polynomials,*J COMPUT PHYS*,**229**, pp.2046-2060. doi: 10.1016/j.jcp.2009.11.022**Livermore PW**; Ierley GR (2010) Quasi-L^{p}norm orthogonal Galerkin expansions in sums of Jacobi polynomials: Orthogonal expansions,*Numerical Algorithms*,**54**, pp.533-569. doi: 10.1007/s11075-009-9353-5**Livermore PW**; Ierley GR; Jackson A (2010) The construction of exact Taylor states. II: The influence of an inner core,*PHYSICS OF THE EARTH AND PLANETARY INTERIORS*,**178**, pp.16-26. doi: 10.1016/j.pepi.2009.07.015**Livermore PW**; Ierley G; Jackson A (2009) The construction of exact Taylor states. I: The full sphere,*GEOPHYS J INT*,**179**, pp.923-928. doi: 10.1111/j.1365-246X.2009.04340.x**Livermore PW**; Ierley GR (2009) A new hypergeometric identity linking coefficients of a certain class of homogeneous polynomials motivated from magneto hydrodynamics,*ADV APPL MATH*,**43**, pp.390-393. doi: 10.1016/j.aam.2009.06.001**Livermore P**; Ierley G (2009) Quasi Lp norm orthogonal Galerkin expansions in sums of Jacobi polynomials.,*Num. Alg.*, . doi: 10.1007/s11075-009-9353-5**Livermore P**(2009) A Compendium of Galerkin Orthogonal Polynomials., .- Jackson A;
**Livermore P**(2009) On Ohmic heating in the Earth's core I: nutation constraints,*GEOPHYS. J. INT.*,**177**, pp.367-382. doi: 10.1111/j.1365-246X.2008.04008.x **Livermore P**; Ierley G (2009) A new identity linking coefficients of a certain class of homogeneous polynomials and Gauss hypergeometric functions, .**Livermore PW**; Ierley G; Jackson A (2008) The structure of Taylor's constraint in three dimensions,*P R SOC A*,**464**, pp.3149-3174. doi: 10.1098/rspa.2008.0091**Livermore PW**; Jones CA; Worland SJ (2007) Spectral radial basis functions for full sphere computations,*J COMPUT PHYS*,**227**, pp.1209-1224. doi: 10.1016/j.jcp.2007.08.026**Livermore PW**; Hughes DW; Tobias SM (2007) The role of helicity and stretching in forced kinematic dynamos in a spherical shell,*PHYS FLUIDS*,**19**, . doi: 10.1063/1.2717947**Livermore P**(2007) Kinematic Dynamos, In: Gubbins DG; Herrero-Bervera E (Ed)*Encyclopedia of Geomagnetism and Paleomagnetism*, Springer, pp.188-192.**Livermore PW**(2007) An implementation of the exponential time differencing scheme to the magnetohydrodynamic equations in a spherical shell,*J COMPUT PHYS*,**220**, pp.824-838. doi: 10.1016/j.jcp.2006.05.029**Livermore PW**; Jackson A (2006) Transient magnetic energy growth in spherical stationary flows,*P R SOC A*,**462**, pp.2457-2479. doi: 10.1098/rspa.2005.1644**Livermore PW**; Hughes DW; Tobias SM (2006) The role of kinetic helicity in spherical shell dynamos,*European Space Agency, (Special Publication) ESA SP*, .**Livermore PW**; Jackson A (2005) A comparison of numerical schemes to solve the magnetic induction eigenvalue problem in a spherical geometry,*GEOPHYS ASTRO FLUID*,**99**, pp.467-480. doi: 10.1080/03091920500404861**Livermore PW**; Jackson A (2004) Preferential axisymmetric field growth in kinematic geodynamo models,*GEOPHYS RES LETT*,**31**, . doi: 10.1029/2004GL021397**Livermore PW**; Jackson A (2004) On magnetic energy instability in spherical stationary flows,*P ROY SOC LOND A MAT*,**460**, pp.1453-1476. doi: 10.1098/rspa.2003.1200- Li K; Jackson A;
**Livermore PW**(Accepted) Taylor state dynamos found by optimal control: axisymmetric examples,*Journal of Fluid Mechanics*, .