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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

Personal home page

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
View abstract

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
View abstract

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

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
View abstract

Kim EJ, Hollerbach R Time-dependent probability density function in cubic stochastic processes Physical Review E, 94, 2016
DOI:10.1103/PhysRevE.94.052118
View abstract

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
View abstract

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
View abstract

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
View abstract

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
View abstract

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
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

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
View abstract

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
View abstract

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
View abstract

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
View abstract

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
View abstract

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
View abstract

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
View abstract

Cébron D, Hollerbach R Tidally driven dynamos in a rotating sphere Astrophysical Journal Letters, 789, 2014
DOI:10.1088/2041-8205/789/1/L25
View abstract

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
View abstract

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
View abstract

Wood TS, Hollerbach R, Lyutikov M Density-shear instability in electron magneto-hydrodynamics Physics of Plasmas, 21, 2014
DOI:10.1063/1.4879810
View abstract

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
View abstract

Rüdiger G; Kitchatinov LL; Hollerbach R Magnetic Processes in Astrophysics: Theory, Simulations, Experiments. 2013
DOI:10.1002/9783527648924
View abstract

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
View abstract

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
View abstract

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
View abstract

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
View abstract

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
View abstract

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

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 shell13TH 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 INSTABILITYMAGNETOHYDRODYNAMICS, 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. 01202615TH 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 hardwareGRAVITATIONAL 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 simulationGRAVITATIONAL 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 analysisGRAVITATIONAL EFFECTS IN PHYSICO-CHEMICAL PROCESSES, 191-197 2003
DOI:10.1016/S0273-1177(03)00387-9

Hollerbach R Magnetohydrodynamic flows in spherical shellsPHYSICS 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