# School of Mathematics

## Prof David W Hughes

Professor of Applied Mathematics

Applied Mathematics

### Contact details

Room: 8.16

Tel: +44 (0)113 3435105

Email: D.W.Hughes @ leeds.ac.uk

## Current postgraduate students

Thomas Goodfellow (2014)

Joshua Kirk (2014)

## Publications

**Cattaneo F, Hughes DW** Dynamo action in rapidly rotating Rayleigh-Bénard convection at infinite Prandtl number *Journal of Fluid Mechanics*, **825**, 385-411, 2017

DOI:10.1017/jfm.2017.385

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**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

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**Hughes DW, Cattaneo F** Strong-field dynamo action in rapidly rotating convection with no inertia *Physical Review E*, **93**, 2016

DOI:10.1103/PhysRevE.93.061101

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**Kondić T, Hughes DW, Tobias SM** THE DECAY of A WEAK LARGE-SCALE MAGNETIC FIELD in TWO-DIMENSIONAL TURBULENCE *Astrophysical Journal*, **823**, 2016

DOI:10.3847/0004-637X/823/2/111

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**Mak J, Griffiths SD, Hughes DW** Shear flow instabilities in shallow-water magnetohydrodynamics *Journal of Fluid Mechanics*, **788**, 767-796, 2016

DOI:10.1017/jfm.2015.718

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**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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**Hughes DW, Vladimirov VA, Proctor MRE** Vortex Dynamics of Oscillating Flows *Arnold Mathematical Journal*, **1**, 113-126, 2015

DOI:10.1007/s40598-015-0010-x

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**Bowker JA, Hughes DW, Kersalé E** Incorporating velocity shear into the magneto-Boussinesq approximation *Geophysical and Astrophysical Fluid Dynamics*, **108**, 553-567, 2014

DOI:10.1080/03091929.2014.917296

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**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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**Mizerski KA, Davies CR, Hughes DW** Short-wavelength magnetic buoyancy instability *Astrophysical Journal, Supplement Series*, **205**, 2013

DOI:10.1088/0067-0049/205/2/16

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**Hughes DW, Proctor MRE** The effect of velocity shear on dynamo action due to rotating convection *Journal of Fluid Mechanics*, **717**, 395-416, 2013

DOI:10.1017/jfm.2012.584

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**Mizerski KA, Davies CR, Hughes DW** The short-wavelength instability of magnetically buoyant layer *Journal of Physics: Conference Series*, **318**, 2011

DOI:10.1088/1742-6596/318/7/072033

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**Hood AW, Hughes DW** Solar magnetic fields *PHYS EARTH PLANET IN*, **187**, 78-91, 2011

DOI:10.1016/j.pepi.2011.04.010

**Hughes DW, Proctor MRE, Cattaneo F** The alpha-effect in rotating convection: a comparison of numerical simulations *MON NOT R ASTRON SOC*, **414**, L45-L49, 2011

DOI:10.1111/j.1745-3933.2011.01053.x

**Hughes DW, Proctor MRE, Cattaneo F** Theα-effect in rotating convection: A comparison of numerical simulations *Monthly Notices of the Royal Astronomical Society: Letters*, **414**, 2011

DOI:10.1111/j.1745-3933.2011.01053.x

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**Davies CR, Hughes DW** Erratum: The mean electromotive force resulting from magnetic buoyancy instability (Astrophysical Journal (2011) 727 (112)) *Astrophysical Journal*, **730**, 2011

DOI:10.1088/0004-637X/730/1/60

**Davies CR, Hughes DW** THE MEAN ELECTROMOTIVE FORCE RESULTING FROM MAGNETIC BUOYANCY INSTABILITY *ASTROPHYS J*, **730**, 2011

DOI:10.1088/0004-637X/727/2/112

**Davies CR, Hughes DW** THE MEAN ELECTROMOTIVE FORCE RESULTING FROM MAGNETIC BUOYANCY INSTABILITY *ASTROPHYS J*, **727**, 2011

DOI:10.1088/0004-637X/727/2/112

**Mizerski KA; Davies CR; Hughes DW ** *The short-wavelength instability of magnetically buoyant layer*13TH EUROPEAN TURBULENCE CONFERENCE (ETC13): GEOPHYSICAL AND MAGNETOHYDRODYNAMIC TURBULENCE, ARTN 072033 2011

DOI:10.1088/1742-6596/318/7/072033

**Courvoisier A, Hughes DW, Proctor MRE** A self-consistent treatment of the electromotive force in magnetohydrodynamics for large diffusivities *ASTRON NACHR*, **331**, 667-670, 2010

DOI:10.1002/asna.201011358

**Proctor MRE, Hughes DW** Competing kinematic dynamo mechanisms in rotating convection with shear *Proceedings of the International Astronomical Union*, **6**, 239-246, 2010

DOI:10.1017/S1743921311017662

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**Livermore PW, Hughes DW, Tobias SM** Nonlinear generation of large-scale magnetic fields in forced spherical shell dynamos *PHYS FLUIDS*, **22**, 2010

DOI:10.1063/1.3313930

**Courvoisier A, Hughes DW, Proctor MRE** Self-consistent mean-field magnetohydrodynamics *P R SOC A*, **466**, 583-601, 2010

DOI:10.1098/rspa.2009.0384

**Hughes DW, Proctor MRE** Turbulent Magnetic Diffusivity Tensor for Time-Dependent Mean Fields *PHYS REV LETT*, **104**, 2010

DOI:10.1103/PhysRevLett.104.024503

**Hughes DW ** *Large- and Small-Scale Dynamo Action*NUMERICAL MODELING OF SPACE PLASMA FLOWS ASTRONUM-2009, 79-84 2010

**Mizerski KA, Hughes DW** Compressible Ekman-Hartmann boundary layers *GEOPHYS ASTRO FLUID*, **104**, 403-418, 2010

DOI:10.1080/03091921003698983

**Courvoisier A, Hughes DW, Tobias SM** Mean induction and diffusion: the influence of spatial coherence *J FLUID MECH*, **627**, 403-421, 2009

DOI:10.1017/S0022112009005783

**Hughes DW, Proctor MRE** Dynamo action in the presence of an imposed magnetic field *P R SOC A*, **465**, 1599-1616, 2009

DOI:10.1098/rspa.2008.0493

**Cattaneo F, Hughes DW** Problems with kinematic mean field electrodynamics at high magnetic Reynolds numbers *MON NOT R ASTRON SOC*, **395**, L48-L51, 2009

DOI:10.1111/j.1745-3933.2009.00639.x

**Hughes DW, Proctor MRE** Large-Scale Dynamo Action Driven by Velocity Shear and Rotating Convection *PHYS REV LETT*, **102**, 2009

DOI:10.1103/PhysRevLett.102.044501

**Hughes DW ** *The mean electromotive force at high magnetic Reynolds numbers*PLASMA PHYSICS AND CONTROLLED FUSION, 124021 2008

DOI:10.1088/0741-3335/50/12/124021

**Mason J, Hughes DW, Tobias SM** The effects of flux transport on interface dynamos *MON NOT R ASTRON SOC*, **391**, 467-480, 2008

DOI:10.1111/j.1365-2966.2008.13918.x

**Hughes DW, Cattaneo F** The alpha-effect in rotating convection: size matters *J FLUID MECH*, **594**, 445-461, 2008

DOI:10.1017/S0022112007009214

**Tobias SM, Diamond PH, Hughes DW** beta-plane magnetohydrodynamic turbulence in the solar tachocline *ASTROPHYS J*, **667**, L113-L116, 2007

**Tobias SM, Diamond PH, Hughes DW** β-plane magnetohydrodynamic turbulence in the solar tachocline *Astrophysical Journal*, **667**, 2007

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**Kersalé E, Hughes DW, Tobias SM** The Nonlinear Evolution of Instabilities Driven by Magnetic Buoyancy: A New Mechanism for the Formation of Coherent Magnetic Structures *The Astrophysical Journal*, **663**, L113-L116, 2007

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**Livermore PW, Hughes DW, Tobias SM** The role of helicity and stretching in forced kinematic dynamos in a spherical shell *PHYS FLUIDS*, **19**, 2007

DOI:10.1063/1.2717947

**Hughes DW; Rosner R; Weiss NO ** *The Solar Tachocline*. Cambridge University Press 2007

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**Hughes DW** Magnetic buoyancy instabilities in the tachocline In *The Solar Tachocline*, 275-298, 2007

DOI:10.1017/CBO9780511536243.012

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**Hughes DW; Rosner R; Weiss NO ** *Preface*. 9780521861014, Cambridge University Press 2007

DOI:10.1017/CBO9780511536243.001

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**Hughes DW; Rosner R; Weiss NO ** *Preface*. 2007

DOI:10.1017/CBO9780511536243.001

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**Livermore PW, Hughes DW, Tobias SM** The role of kinetic helicity in spherical shell dynamos *European Space Agency, (Special Publication) ESA SP*, 2006

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**Cattaneo F, Hughes DW** Dynamo action in a rotating convective layer *J FLUID MECH*, **553**, 401-418, 2006

DOI:10.1017/S0022112006009165

**Kersalé E, Hughes DW, Ogilvie GI, Tobias SM** Global Magnetorotational Instability with Inflow. II. The Nonlinear Development of Axisymmetric Wall Modes *The Astrophysical Journal*, **638**, 382-390, 2006

DOI:10.1086/498704

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**Courvoisier A, Hughes DW, Tobias SM** α effect in a family of chaotic flows *Physical Review Letters*, **96**, 2006

DOI:10.1103/PhysRevLett.96.034503

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**Tobias S, Hughes D, Weiss N** Unpredictable Sun leaves researchers in the dark *Nature*, **442**, 26-26, 2006

DOI:10.1038/442026c

**Hughes D, Rosner R, Weiss N** Magnetohydrodynamics of stellar interiors *Astronomy and Geophysics*, **46**, 2005

DOI:10.1111/j.1468-4004.2005.46435.x

**Tobias SM, Hughes DW** The Influence of Velocity Shear on Magnetic Buoyancy Instability in the Solar Tachocline *The Astrophysical Journal*, **603**, 785-802, 2004

DOI:10.1086/381492

**Kersale E, Hughes DW, Ogilvie GI, Tobias SM, Weiss NO** Global magnetorotational instability with inflow. I. Linear theory and the role of boundary conditions *ASTROPHYS J*, **602**, 892-903, 2004

**Diamond PH, Hughes DW, Kim E** Self-consistent mean field electrodynamics in two and three dimensions In *Astrophysical and Geophysical Fluid Dynamics, and Dynamos*, 2004

**Soward AM; Jones CA; Hughes DW; Weiss NO ** *Fluid Dynamics and Dynamos in Astrophysics and Geophysics*. Taylor and Francis 2004

**Hughes DW, Kim E, Soward AM** A nonlinear dynamo driven by rapidly rotating convection *Geophysical and Astrophysical Fluid Dynamics*, 2004

**Tanner SEM, Hughes DW** Fast dynamo action in a family of parameterized flows *None*, **586**, 685-691, 2003

**Mason J, Hughes DW, Tobias SM** The competition in the solar dynamo between surface and deep-seated alpha-effects *The Astrophysical Journal*, **580**, L89-L92, 2002

DOI:10.1086/345419

**Cattaneo F, Hughes DW, Thelen J** The nonlinear properties of a large-scale dynamo driven by helical forcing *Journal of Fluid Mechanics*, **456**, 219-237, 2002

DOI:10.1017/S0022112001007479

**Cattaneo F; Hughes DW; Thelen JC ** *On the nonlinear nature of the turbulent alpha-effect*HIGHLIGHTS OF ASTRONOMY, VOL 12, 733-735 2002

**Hughes DW, Tobias SM** On the instability of magnetohydrodynamic shear flows *P ROY SOC LOND A MAT*, **457**, 1365-1384, 2001

**Cattaneo F, Hughes DW** Solar dynamo theory: a new look at the origin of small-scale magnetic fields *ASTRON GEOPHYS*, **42**, 18-22, 2001

**Cattaneo F, Hughes DW** Solar dynamo theory: A new look at the origin of small-scale magnetic fields *Astronomy and Geophysics*, **42**, 318-325, 2001

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**Hughes DW; Cattaneo F; Thelen JC ** *Large- and small-scale dynamo action*NATO SCI SER II MATH, 199-206 2001

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**Hughes DW** Magnetic Buoyancy *None*, 2000

**Hughes DW, Matthews PC, Proctor MRE, Wissink JG** The three dimensional breakup of a magnetic layer *Monthly Notices of the Royal Astronomical Society.*, **318**, 501-510, 2000

**Hughes DW, Matthews PC, Proctor MRE, Wissink JG** Numerical simulation of buoyant magnetic flux tubes *None*, 2000

**Kim EJ, Hughes DW, Soward AM** An Investigation into High Conductivity Dynamo Action Driven by Rotating Convection *Geophysical and Astrophysical Fluid Dynamics*, **91**, 303-332, 1999

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**Hughes DW, Falle S** The Rise of Twisted Magnetic Flux Tubes: a High Reynolds Number Adaptive Grid Calculation *The Astrophysical Journal*, **509**, L57-L60, 1998

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**Hughes DW, Cattaneo F, Kim EJ** Nonlinear multi-cellular fast dynamos *Studia Geophysica et Geodaetica*, **42**, 328-334, 1998

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**Kim EJ, Hughes DW, Soward AM** On a physically realistic fast dynamo *Studia Geophysica et Geodaetica*, **42**, 335-342, 1998

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**Tanner SEM, Hughes DW** Generalisation of a nonlinear dynamo model *Studia Geophysica et Geodaetica*, **42**, 343-349, 1998

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**Hughes DW, Falle SAEG, Joarder P** The rise of twisted magnetic flux tubes *Monthly Notices of the Royal Astronomical Society*, **298**, 433-444, 1998

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**Kim EJ, Hughes DW** Flow helicity in a simplified statistical model of a fast dynamo *Physics Letters, Section A: General, Atomic and Solid State Physics*, **236**, 211-218, 1997

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**Hughes DW, Cattaneo F, Kim EJ** Kinetic helicity, magnetic helicity and fast dynamo action *Physics Letters, Section A: General, Atomic and Solid State Physics*, **224**, 167-172, 1997

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**Hughes DW, Cattaneo F, Kim EJ** Kinetic Helicity, Magnetic Helicity and Fast Dynamo Action *Physics Letters. Section A: General, Atomic and Solid State Physics*, **223**, 167-172, 1996

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**Cattaneo F, Hughes DW** Nonlinear Saturation of the Turbulent Alpha Effect *Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics)*, **54**, 4532-4535, 1996

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**Cattaneo F, Hughes DW, Kim EJ** Suppression of chaos in a simplified nonlinear dynamo model *Physical Review Letters*, **76**, 2057-2060, 1996

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**Matthews PC, Hughes DW, Proctor MRE** Magnetic buoyancy, vorticity, and three-dimensional flux-tube formation *Astrophysical Journal*, **448**, 938-941, 1995

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**Hughes DW, Weiss NO** Double-Diffusive Convection with Two Stabilizing Gradients: Strange Consequences of Magnetic Buoyancy *Journal of Fluid Mechanics*, **301**, 383-406, 1995

DOI:10.1017/S0022112095003946

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**Hughes DW, Proctor MRE** Non-symmetrical three-wave resonance *Wave Motion*, **20**, 201-209, 1994

DOI:10.1016/0165-2125(94)90047-7

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**Hughes DW, Proctor MRE** Nonlinear three-wave interaction with non-conservative coupling *Journal of Fluid Mechanics*, **244**, 583-604, 1992

DOI:10.1017/S0022112092003203

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**Hughes DW, Proctor MRE** A low-order model of the shear instability of convection: Chaos and the effect of noise *Nonlinearity*, **3**, 127-153, 1990

DOI:10.1088/0951-7715/3/1/008

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**Hughes DW, Proctor MRE** Chaos and the effect of noise in a model of three-wave mode coupling *Physica D: Nonlinear Phenomena*, **46**, 163-176, 1990

DOI:10.1016/0167-2789(90)90034-M

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**Cattaneo F, Chiuell T, Hughes DW** Buoyancy-driven instabilities and the nonlinear breakup of a sheared magnetic layer *Journal of Fluid Mechanics*, **219**, 1-23, 1990

DOI:10.1017/S0022112090002841

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**Cattaneo F, Hughes DW** The nonlinear breakup of a magnetic layer: instability to interchange modes *Journal of Fluid Mechanics*, **196**, 323-323, 1988

DOI:10.1017/S0022112088002721

**Hughes DW, Proctor MRE** Magnetic Fields in the Solar Convection Zone: Magnetoconvection and Magnetic Buoyancy *Annual Review of Fluid Mechanics*, **20**, 187-223, 1988

DOI:10.1146/annurev.fl.20.010188.001155

**Cattaneo F, Hughes DW, Proctor MRE** Mean advection effects in turbulence *Geophysical& Astrophysical Fluid Dynamics*, **41**, 335-342, 1988

DOI:10.1080/03091928808208855

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**Hughes DW** Finite-amplitude solutions for interchange instabilities driven by magnetic buoyancy *Geophysical& Astrophysical Fluid Dynamics*, **37**, 297-343, 1987

DOI:10.1080/03091928708210101

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**Hughes DW, Cattaneo F** A new look at the instability of a stratified horizontal magnetic field *Geophysical& Astrophysical Fluid Dynamics*, **39**, 65-81, 1987

DOI:10.1080/03091928708208806

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**Hughes DW** Magnetic Buoyancy Instabilities for a Static Plane Layer *Geophysical& Astrophysical Fluid Dynamics*, **32**, 273-316, 1985

DOI:10.1080/03091928508208787

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**Hughes DW** Magnetic Buoyancy Instabilities Incorporating Rotation *Geophysical& Astrophysical Fluid Dynamics*, **34**, 99-142, 1985

DOI:10.1080/03091928508245440

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