# School of Mathematics

## Prof Rainer Hollerbach

Professor in Astrophysical Fluid Dynamics

Applied Mathematics

### Contact details

Room: 9.17

Tel: +44 (0)113 3435134

Email: R.Hollerbach @ leeds.ac.uk

### Keywords

Magnetohydrodynamics

Dynamo theory

Hydrodynamic stability theory

## Research interests

The Earth's magnetic field is created by so-called dynamo action, involving fluid motions in its molten iron core. The Sun's magnetic field is similarly created by flows of electrically conducting plasmas in its interior. My research goal is to understand the dynamics underlying some of these processes, and involves large-scale numerical solutions of the governing partial differential equations for the fluid flow and the magnetic field. I am particularly interested in geophysically or astrophysically motivated liquid metal laboratory experiments, and some of my theoretical predictions have lead directly to the design of new experiments, e.g. on the helical magnetorotational instability in a Taylor-Couette device.

### Useful links

## Current postgraduate students

Adam Child (2013)

Floriane Gidel (2014)

## Publications

**Kim E-J, Hollerbach R** Geometric structure and information change in phase transitions. *Physical review. E*, **95**, 062107, 2017

DOI:10.1103/physreve.95.062107

View abstract

**Kim EJ, Hollerbach R** Geometric structure and information change in phase transitions *Physical Review E*, **95**, 2017

DOI:10.1103/PhysRevE.95.062107

View abstract

**Hollerbach R, Kim EJ** Information geometry of non-equilibrium processes in a bistable system with a cubic damping *Entropy*, **19**, 2017

DOI:10.3390/e19060268

View abstract

**Child A, Hollerbach R, Kersalé E** Axisymmetric pulse train solutions in narrow-gap spherical Couette flow *Physica D: Nonlinear Phenomena*, **348**, 54-59, 2017

DOI:10.1016/j.physd.2017.02.009

View abstract

**Hollerbach R, Sibanda N, Kim EJ** Absolute versus convective helical magnetorotational instabilities in Taylor-Couette flows *Fluid Dynamics Research*, **49**, 2017

DOI:10.1088/1873-7005/aa6e61

View abstract

**Feudel F, Tuckerman LS, Zaks M, Hollerbach R** Hysteresis of dynamos in rotating spherical shell convection *PHYSICAL REVIEW FLUIDS*, **2**, 2017

DOI:10.1103/PhysRevFluids.2.053902

**Kim EJ, Hollerbach R** Signature of nonlinear damping in geometric structure of a nonequilibrium process *Physical Review E*, **95**, 2017

DOI:10.1103/PhysRevE.95.022137

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**Livermore PW, Hollerbach R, Finlay CC** An accelerating high-latitude jet in Earth's core *Nature Geoscience*, **10**, 62-68, 2017

DOI:10.1038/ngeo2859

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**Guseva A, Hollerbach R, Willis AP, Avila M** Azimuthal magnetorotational instability at low and high magnetic Prandtl numbers *Magnetohydrodynamics*, **53**, 25-33, 2017

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**Sood A, Kim EJ, Hollerbach R** DYNAMICAL MODEL for SPINDOWN of SOLAR-TYPE STARS *Astrophysical Journal*, **832**, 2016

DOI:10.3847/0004-637X/832/2/97

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**Kim EJ, Hollerbach R** Time-dependent probability density function in cubic stochastic processes *Physical Review E*, **94**, 2016

DOI:10.1103/PhysRevE.94.052118

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**Sood A, Hollerbach R, Kim EJ** Suppression of a laminar kinematic dynamo by a prescribed large-scale shear *Journal of Physics A: Mathematical and Theoretical*, **49**, 2016

DOI:10.1088/1751-8113/49/42/425501

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**Hollerbach R, Hulot D** Shercliff layers in strongly magnetic cylindrical Taylor-Couette flow *Comptes Rendus - Mecanique*, **344**, 502-509, 2016

DOI:10.1016/j.crme.2016.02.012

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**Kim EJ, Lee U, Heseltine J, Hollerbach R** Geometric structure and geodesic in a solvable model of nonequilibrium process *Physical Review E*, **93**, 2016

DOI:10.1103/PhysRevE.93.062127

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**Gellert M, Rüdiger G, Schultz M, Guseva A, Hollerbach R** Nonaxisymmetric mhd instabilities of chandrasekhar states in taylor-couette geometry *Astrophysical Journal*, **823**, 2016

DOI:10.3847/0004-637X/823/2/99

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**Child A, Hollerbach R, Marston B, Tobias S** Generalised quasilinear approximation of the helical magnetorotational instability *Journal of Plasma Physics*, **82**, 2016

DOI:10.1017/S0022377816000556

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**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

**Gourgouliatos KN, Wood TS, Hollerbach R** Magnetic field evolution in magnetar crusts through three-dimensional simulations *Proceedings of the National Academy of Sciences of the United States of America*, **113**, 3944-3949, 2016

DOI:10.1073/pnas.1522363113

View abstract

**Livermore PW, Bailey LM, Hollerbach R** A comparison of no-slip, stress-free and inviscid models of rapidly rotating fluid in a spherical shell *Scientific Reports*, **6**, 2016

DOI:10.1038/srep22812

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**Hollerbach R, Khan F** Phase slip solutions in magnetically modulated Taylor–Couette flow *Acta Mechanica*, **227**, 311-319, 2016

DOI:10.1007/s00707-015-1447-7

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**Gourgouliatos KN, Hollerbach R** Resistive tearing instability in electron MHD: Application to neutron star crusts *Monthly Notices of the Royal Astronomical Society*, **463**, 3381-3389, 2016

DOI:10.1093/mnras/stw2309

View abstract

**Child A, Kersalé E, Hollerbach R** Nonaxisymmetric linear instability of cylindrical magnetohydrodynamic Taylor-Couette flow *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, **92**, 2015

DOI:10.1103/PhysRevE.92.033011

View abstract

**Guseva A, Willis AP, Hollerbach R, Avila M** Transition to magnetorotational turbulence in Taylor-Couette flow with imposed azimuthal magnetic field *New Journal of Physics*, **17**, 2015

DOI:10.1088/1367-2630/17/9/093018

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**Child A, Kersale E, Hollerbach R** Nonaxisymmetric linear instability of cylindrical magnetohydrodynamic Taylor-Couette flow *Physical Review E*, **92**, 2015

DOI:10.1103/PhysRevE.92.033011

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**Wood TS, Hollerbach R** Three dimensional simulation of the magnetic stress in a neutron star crust *Physical Review Letters*, **114**, 2015

DOI:10.1103/PhysRevLett.114.191101

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**Gourgouliatos KN, Kondić T, Lyutikov M, Hollerbach R** Magnetar activity via the density-shear instability in Hall-MHD *Monthly Notices of the Royal Astronomical Society: Letters*, **453**, L93-L97, 2015

DOI:10.1093/mnrasl/slv106

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**Seilmayer M, Galindo V, Gerbeth G, Gundrum T, Stefani F, Gellert M, Rüdiger G, Schultz M, Hollerbach R** Experimental evidence for nonaxisymmetric magnetorotational instability in a rotating liquid metal exposed to an azimuthal magnetic field. *Phys Rev Lett*, **113**, 024505, 2014

DOI:10.1103/PhysRevLett.113.024505

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**Cébron D, Hollerbach R** Tidally driven dynamos in a rotating sphere *Astrophysical Journal Letters*, **789**, 2014

DOI:10.1088/2041-8205/789/1/L25

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**Marti P, Schaeffer N, Hollerbach R, Cébron D, Nore C, Luddens F, Guermond JL, Aubert J, Takehiro S, Sasaki Y, Hayashi YY, Simitev R, Busse F, Vantieghem S, Jackson A** Full sphere hydrodynamic and dynamo benchmarks *Geophysical Journal International*, **197**, 119-134, 2014

DOI:10.1093/gji/ggt518

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**Rüdiger G, Gellert M, Schultz M, Hollerbach R, Stefani F** Astrophysical and experimental implications from the magnetorotational instability of toroidal fields *Monthly Notices of the Royal Astronomical Society*, **438**, 271-277, 2014

DOI:10.1093/mnras/stt2171

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**Wood TS, Hollerbach R, Lyutikov M** Density-shear instability in electron magneto-hydrodynamics *Physics of Plasmas*, **21**, 2014

DOI:10.1063/1.4879810

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**Livermore PW, Jackson A, Hollerbach R** 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**, 2013

DOI:10.1073/pnas.1307825110

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**Rüdiger G; Kitchatinov LL; Hollerbach R ** *Magnetic Processes in Astrophysics: Theory, Simulations, Experiments*. 2013

DOI:10.1002/9783527648924

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**Hollerbach R, Wei X, Noir J, Jackson A** Electromagnetically driven zonal flows in a rapidly rotating spherical shell *JOURNAL OF FLUID MECHANICS*, **725**, 428-445, 2013

DOI:10.1017/jfm.2013.195

**Koch S, Harlander U, Egbers C, Hollerbach R** Inertial waves in a spherical shell induced by librations of the inner sphere: experimental and numerical results *FLUID DYNAMICS RESEARCH*, **45**, 2013

DOI:10.1088/0169-5983/45/3/035504

**Hollerbach R, Nore C, Marti P, Vantieghem S, Luddens F, Léorat J** Parity-breaking flows in precessing spherical containers *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, **87**, 2013

DOI:10.1103/PhysRevE.87.053020

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**Hollerbach R, Nore C, Marti P, Vantieghem S, Luddens F, Léorat J** Parity-breaking flows in precessing spherical containers. *Phys Rev E Stat Nonlin Soft Matter Phys*, **87**, 053020, 2013

DOI:10.1103/PhysRevE.87.053020

View abstract

**Futterer B, Krebs A, Plesa AC, Zaussinger F, Hollerbach R, Breuer D, Egbers C** Sheet-like and plume-like thermal flow in a spherical convection experiment performed under microgravity *Journal of Fluid Mechanics*, **735**, 647-683, 2013

DOI:10.1017/jfm.2013.507

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**Wei X, Jackson A, Hollerbach R** Kinematic dynamo action in spherical Couette flow *Geophysical and Astrophysical Fluid Dynamics*, **106**, 681-700, 2012

DOI:10.1080/03091929.2011.620569

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**Richardson KJ, Hollerbach R, Proctor MRE** From large-scale to small-scale dynamos in a spherical shell *Physics of Fluids*, **24**, 2012

DOI:10.1063/1.4757661

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**Livermore PW, Hollerbach R** Successive elimination of shear layers by a hierarchy of constraints in inviscid spherical-shell flows *Journal of Mathematical Physics*, **53**, 2012

DOI:10.1063/1.4736990

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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

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**von Larcher T, Fournier A, Hollerbach R** The influence of a sloping bottom endwall on the linear stability in the thermally driven baroclinic annulus with a free surface *Theoretical and Computational Fluid Dynamics*, 1-19, 2012

DOI:10.1007/s00162-012-0289-3

View abstract

**Koch S, Harlander U, Hollerbach R, Egbers C** Laboratory experiments and numerical simulations of inertial wave-interactions in a rotating spherical shell *Journal of Physics: Conference Series*, **318**, 2011

DOI:10.1088/1742-6596/318/8/082022

View abstract

**Gellert M, Rudiger G, Hollerbach R** Helicity and alpha-effect by current-driven instabilities of helical magnetic fields *MON NOT R ASTRON SOC*, **414**, 2696-2701, 2011

DOI:10.1111/j.1365-2966.2011.18583.x

**Feudel F, Bergemann K, Tuckerman LS, Egbers C, Futterer B, Gellert M, Hollerbach R** Convection patterns in a spherical fluid shell *PHYS REV E*, **83**, 2011

DOI:10.1103/PhysRevE.83.046304

**Koch S; Harlander U; Hollerbach R; Egbers C ** *Laboratory experiments and numerical simulations of inertial wave-interactions in a rotating spherical shell*13TH EUROPEAN TURBULENCE CONFERENCE (ETC13): CONVECTION, ROTATION, STRATIFICATION AND BUOYANCY EFFECTS, ARTN 082022 2011

DOI:10.1088/1742-6596/318/8/082022

**Wei X, Hollerbach R** Magnetic spherical Couette flow in linear combinations of axial and dipolar fields *ACTA MECH*, **215**, 1-8, 2010

DOI:10.1007/s00707-010-0299-4

**Rüdiger G, Gellert M, Schultz M, Hollerbach R** Erratum: Publisher's Note: Dissipative Taylor-Couette flows under the influence of helical magnetic fields (Physical Review E - Statistical, Nonlinear, and Soft Matter Physics (2010) 82 (016319)) *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, **82**, 2010

DOI:10.1103/PhysRevE.82.029901

**Rudiger G, Gellert M, Schultz M, Hollerbach R** Dissipative Taylor-Couette flows under the influence of helical magnetic fields *PHYS REV E*, **82**, 2010

DOI:10.1103/PhysRevE.82.016319

**Wareing CJ, Hollerbach R** Cascades in decaying three-dimensional electron magnetohydrodynamic turbulence *J PLASMA PHYS*, **76**, 117-128, 2010

DOI:10.1017/S0022377809990158

**Hollerbach R, Teeluck V, Rudiger G** Nonaxisymmetric Magnetorotational Instabilities in Cylindrical Taylor-Couette Flow *PHYS REV LETT*, **104**, 2010

DOI:10.1103/PhysRevLett.104.044502

**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

**Jehring L, Egbers C, Beltrame P, Chossat P, Feudel F, Hollerbach R, Mutabazi I, Tuckerman LS** Geoflow: First results from geophysical motivated experiments inside the Fluid Science Laboratory of Columbus *47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition*, 2009

View abstract

**Stefani F, Gerbeth G, Gundrum T, Hollerbach R, Priede J, Rudiger G, Szklarski J** Helical magnetorotational instability in a Taylor-Couette flow with strongly reduced Ekman pumping *PHYS REV E*, **80**, 2009

DOI:10.1103/PhysRevE.80.066303

**Wareing CJ, Hollerbach R** Hall cascades versus instabilities in neutron star magnetic fields *ASTRON ASTROPHYS*, **508**, L39-L42, 2009

DOI:10.1051/0004-6361/200913452

**Hollerbach R, Cally PS** Nonlinear Evolution of Axisymmetric Twisted Flux Tubes in the Solar Tachocline *SOL PHYS*, **260**, 251-260, 2009

DOI:10.1007/s11207-009-9447-1

**Hollerbach R** Instabilities of Taylor columns in a rotating stratified fluid *PHYS LETT A*, **373**, 3775-3778, 2009

DOI:10.1016/j.physleta.2009.08.026

**Hollerbach R** Non-axisymmetric instabilities in magnetic spherical Couette flow *P R SOC A*, **465**, 2003-2013, 2009

DOI:10.1098/rspa.2009.0004

**Stefani F; Gerbeth G; Gundrum T; Szklarski J; Rudiger G; Hollerbach R ** *LIQUID METAL EXPERIMENTS ON THE HELICAL MAGNETOROTATIONAL INSTABILITY*MAGNETOHYDRODYNAMICS, 135-143 2009

**Wareing CJ, Hollerbach R** Forward and inverse cascades in decaying two-dimensional electron magnetohydrodynamic turbulence *PHYS PLASMAS*, **16**, 2009

DOI:10.1063/1.3111033

**Stefani F, Gerbeth G, Gundrum T, Szklarski J, Rudiger G, Hollerbach R** Results of a modified PROMISE experiment *ASTRON NACHR*, **329**, 652-658, 2008

DOI:10.1002/asna.200811023

**Wei X, Hollerbach R** Instabilities of Shercliffe and Stewartson layers in spherical Couette flow *PHYS REV E*, **78**, 2008

DOI:10.1103/PhysRevE.78.026309

**Futterer B; Hollerbach R; Egbers C ** *GeoFlow: 3D numerical simulation of supercritical thermal convective states - art. no. 012026*15TH INTERNATIONAL COUETTE-TAYLOR WORKSHOP, 12026-12026 2008

**Rudiger G, Hollerbach R** Comment on "Helical magnetorotational instability in magnetized Taylor-Couette flow" *PHYS REV E*, **76**, 2007

DOI:10.1103/PhysRevE.76.068301

**Hollerbach R, Canet E, Fournier A** Spherical Couette flow in a dipolar magnetic field *EUR J MECH B-FLUID*, **26**, 729-737, 2007

DOI:10.1016/j.euromechflu.2007.02.002

**Rüdiger G, Schultz M, Shalybkov D, Hollerbach R** Theory of current-driven instability experiments in magnetic Taylor-Couette flows. *Phys Rev E Stat Nonlin Soft Matter Phys*, **76**, 056309, 2007

DOI:10.1103/PhysRevE.76.056309

View abstract

**Ruediger G; Hollerbach R; Gellert M; Schultz M ** *The azimuthal magnetorotational instability (AMRI)*ASTRONOMISCHE NACHRICHTEN, 1158-1161 2007

DOI:10.1002/asna.200710852

**Futterer B, Brucks A, Hollerbach R, Egbers C** Thermal blob convection in spherical shells *INT J HEAT MASS TRAN*, **50**, 4079-4088, 2007

DOI:10.1016/j.ijheatmasstransfer.2006.12.036

**Stefani F, Gundrum T, Gerbeth G, Rudiger G, Szklarski J, Hollerbach R** Experiments on the magnetorotational instability in helical magnetic fields *NEW J PHYS*, **9**, 2007

DOI:10.1088/1367-2630/9/8/295

**Rudiger G, Hollerbach R, Schultz M, Elstner D** Destabilization of hydrodynamically stable rotation laws by azimuthal magnetic fields *MON NOT R ASTRON SOC*, **377**, 1481-1487, 2007

DOI:10.1111/j.1365-2966.2007.11682.x

**Stefani F, Gundrum T, Gerbeth G, Rudiger G, Schultz M, Szklarski J, Hollerbach R** Experimental evidence for magnetorotational instability in a Taylor-Couette flow under the influence of a helical magnetic field *PHYS REV LETT*, **97**, 2006

DOI:10.1103/PhysRevLett.97.184502

**Fournier A, Bunge HP, Hollerbach R, Vilotte JP** A Fourier-spectral element algorithm for thermal convection in rotating axisymmetric containers *J COMPUT PHYS*, **204**, 462-489, 2005

DOI:10.1016/j.jcp.204.10.020

**Egbers C; Beyer W; Bonhage A; Hollerbach R; Beltrame P ** *The GEOFLOW-experiment on ISS (part I): Experimental preparation and design of laboratory testing hardware*GRAVITATIONAL EFFECTS IN PHYSICO-CHEMICAL PROCESSES, 171-180 2003

DOI:10.1016/S0273-1177(03)00385-5

**Travnikov V; Egbers C; Hollerbach R ** *The GEOFLOW-experiment on ISS (part II): Numerical simulation*GRAVITATIONAL EFFECTS IN PHYSICO-CHEMICAL PROCESSES, 181-189 2003

DOI:10.1016/S0273-1177(03)00386-7

**Beltrame P; Egbers C; Hollerbach R ** *The GEOFLOW-experiment on ISS (part III): Bifurcation analysis*GRAVITATIONAL EFFECTS IN PHYSICO-CHEMICAL PROCESSES, 191-197 2003

DOI:10.1016/S0273-1177(03)00387-9

**Hollerbach R ** *Magnetohydrodynamic flows in spherical shells*PHYSICS OF ROTATING FLUIDS, 295-316 2000

Kondić T; Rüdiger G; Hollerbach R The shear-Hall instability in newborn neutron stars.

DOI:10.1051/0004-6361/201116776

View abstract

**Kim EJ, Tenkes LM, Hollerbach R, Radulescu O** Far-from-Equilibrium Time Evolution between two Gamma Distributions *Entropy*

**Guseva A, Hollerbach R, Willis AP, Avila M** Dynamo action in a quasi-Keplerian Taylor-Couette flow *Physical Review Letters*

View abstract

**Guseva A, Willis AP, Hollerbach R, Avila M** Transport Properties of the Azimuthal Magnetorotational Instability *Astrophysical Journal*

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