Professor Andrew Gilbert | Mathematics and Statistics

Prof Andrew Gilbert

Professor

A.D.Gilbert@exeter.ac.uk

(Streatham) 5222

01392 725222

Overview

After spending my formative years at Bury Grammar School, I took my first degree in Mathematics in Cambridge (first class each year) followed by the Certificate of Advanced Study in Mathematics ('Part III') for which I was awarded a Distinction and the Mayhew Prize.

I then worked for a PhD in DAMTP, Cambridge under the supervision of Prof. Keith Moffatt. After a year as a Researcher at the Observatoire de Nice (with Uriel Frisch) and 3 years as a Research Fellow at Gonville and Caius College, Cambridge, I moved to Exeter, where I am now a Professor of Mathematical Physics, with interests in fluid mechanics, magnetic field generation in fluid flows, mixing processes and dynamical systems.

I was pleased to be the recipient of a Leverhulme Trust Research Fellowship during 2019, and from this, I am continuing to work on problems of vortex stretching and reconnection with Steve Childress (New York University) and geometric fluid mechanics with Jacques Vanneste (Edinburgh University).

Research Interests

Fluid mechanics and magnetohydrodynamics (with Liam Wattts, Joanne Mason)
Geometric methods in ideal fluid flow and MHD (with Jacques Vanneste)
Vortex dynamics, stability and mixing (with Steve Childress)
Waves and instabilities (with Chen Wang, Azza Al Gatheem, Andrew Hillier)
Dynamo theory (modelling geophysical and astrophysical magnetic fields)
Magnetically driven swimmers in low Reynolds number flows (with Feodor Ogrin, Liz Martin)

Personnel

Azza Al Gatheem, PhD student, with Dr. Andrew Hillier
Liam Watts, PhD student (STFC), with Dr. Joanne Mason
Dr. Chen Wang, Postdoctoral Research Fellow (EPSRC), with Dr. Joanne Mason

Teaching Interests

I teach a range of modules, at present MTH1003 Mathematical Modelling, and NSC1002 Mathematics and computing for Natural Sciences, and supervise MMath projects. I am leading on the development of a new MSc in Weather and Climate Science.

Administration

I am currently an External Examiner in Applied Mathematics at Warwick University.

Other Relevant Information

1994 - Member, London Mathematical Society.

2001 - Fellow, Royal Astronomical Society.

2002 - Fellow, Institute of Mathematics and its Applications

2004 -15 Editor: Fluid Dynamics Research.

2017 - Senior Fellow, Higher Education Academy.

Qualifications: MA, PhD (Cantab), FIMA, CMath, FRAS, SFHEA.

Publications

_{Copyright Notice: Any articles made available for download are for personal use only. Any other use requires prior permission of the author and the copyright holder.}

| 2024 | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 | 2004 | 2003 | 2002 | 2001 | 2000 | 1999 | 1998 | 1997 | 1995 | 1994 | 1993 | 1992 | 1991 | 1990 | 1988 |

2024

Al Gatheem A. (2024) Jets and instabilities in forced magnetohydrodynamic flows.

2023

Algatheem AM, Gilbert AD, Hillier AS. (2023) Zonostrophic instabilities in magnetohydrodynamic Kolmogorov flow. [PDF]
Gilbert AD, Vanneste J. (2023) A Geometric Look at Momentum Flux and Stress in Fluid Mechanics, Journal of Nonlinear Science, volume 33, no. 2, article no. 31, DOI:10.1007/s00332-023-09887-0. [PDF]

2022

Wang C, Gilbert A, Mason J. (2022) Critical-layer instability of shallow water magnetohydrodynamic shear flows, DOI:10.48550/arxiv.2202.06272.
Wang C, Gilbert A, Mason J. (2022) An analytical study of the MHD clamshell instability on a sphere, Journal of Fluid Mechanics, DOI:10.1017/jfm.2022.973.
Wang C, Gilbert A, Mason J. (2022) An analytical study of the MHD clamshell instability on a sphere, Journal of Fluid Mechanics, volume 953, DOI:10.1017/jfm.2022.973.
Wang C, Gilbert AD, Mason J. (2022) An analytical study of the MHD clamshell instability on a sphere. [PDF]
Wang C, Gilbert A, Mason J. (2022) Critical-layer instability of shallow water magnetohydrodynamic shear flows. [PDF]

2021

Bryan MT, Martin EL, Pac A, Gilbert AD, Ogrin FY. (2021) Metachronal waves in magnetic micro-robotic paddles for artificial cilia, Communications Materials, volume 2, no. 1, article no. 14, DOI:10.1038/s43246-021-00120-7. [PDF]
Gilbert AD, Vanneste J. (2021) A geometric look at MHD and the Braginsky dynamo, Geophysical and Astrophysical Fluid Dynamics, volume 115, no. 4, pages 436-471, DOI:10.1080/03091929.2020.1839896.

2020

Childress S, Gilbert AD. (2020) A filamentary cascade model of the inertial range, Fluid Dynamics Research, volume 52, no. 3, DOI:10.1088/1873-7005/ab8547.

2019

Gilbert AD, Vanneste J. (2019) A geometric look at MHD and the Braginsky dynamo. [PDF]

2018

Hamilton J, Petrov P, Gilbert A, Ogrin F. (2018) Torque driven ferromagnetic swimmers, Physics of Fluids, volume 30, pages 092001-092001, DOI:10.1063/1.5046360.
Hamilton J, Bryan MT, Gilbert AD, Myers TO, Ogrin FY. (2018) A new class of magnetically actuated pumps and valves for microfluidic applications, Scientific Reports, volume 8, pages 1-12, article no. 933, DOI:10.1038/s41598-018-19506-8.
Gilbert AD, Vanneste J. (2018) Geometric generalised Lagrangian-mean theories, Journal of Fluid Mechanics, volume 839, pages 95-134, DOI:10.1017/jfm.2017.913.
Childress S, Gilbert AD. (2018) Eroding dipoles and vorticity growth for Euler flows in ℝ³: The hairpin geometry as a model for finite-time blowup, Fluid Dynamics Research, volume 50, no. 1, DOI:10.1088/1873-7005/aa9880.

2017

Hamilton JK, Petrov PG, Winlove CP, Gilbert AD, Bryan MT, Ogrin FY. (2017) Magnetically controlled ferromagnetic swimmers, Sci Rep, volume 7, DOI:10.1038/srep44142. [PDF]
Bryan MT, Shelley SR, Parish MJ, Petrov PG, Winlove CP, Gilbert AD, Ogrin FY. (2017) Emergent propagation modes of ferromagnetic swimmers in constrained geometries, Journal of Applied Physics, volume 121, no. 7, DOI:10.1063/1.4976103.

2016

Childress S, Gilbert AD, Valiant P. (2016) Eroding dipoles and vorticity growth for Euler flows in ℝ³: Axisymmetric flow without swirl, Journal of Fluid Mechanics, volume 805, pages 1-30, DOI:10.1017/jfm.2016.573.
Gilbert AD, Mason J, Tobias SM. (2016) Flux Expulsion with Dynamics, Journal of Fluid Mechanics, volume 791, pages 568-588, DOI:10.1017/jfm.2016.60. [PDF]

2015

Childress S, Gilbert AD, Valiant P. (2015) Eroding dipoles and vorticity growth for Euler flows in $ \scriptstyle{\mathbb{R}}^3$ I. Axisymmetric flow without swirl, DOI:10.48550/arxiv.1512.07898.

2014

Riedinger X, Gilbert AD. (2014) Critical layer and radiative instabilities in shallow-water shear flows, Journal of Fluid Mechanics, volume 751, pages 539-569, DOI:10.1017/jfm.2014.303.
Gilbert AD, Riedinger X, Thuburn J. (2014) On the form of the viscous term for two dimensional Navier-Stokes flows, Quarterly Journal of Mechanics and Applied Mathematics, volume 67, no. 2, pages 205-228, DOI:10.1093/qjmam/hbu004.
Jones SE, Gilbert AD. (2014) Dynamo action in the ABC flows using symmetries, Geophysical and Astrophysical Fluid Dynamics, volume 108, no. 1, pages 83-116, DOI:10.1080/03091929.2013.832762.

2012

Zaggout FA, Gilbert AD. (2012) Passive scalar decay in chaotic flows with boundaries, Fluid Dynamics Research, volume 44, no. 2, DOI:10.1088/0169-5983/44/2/025504.
Gilbert AD, Ogrin FY, Petrov PG, Winlove CP. (2012) THEORY OF FERROMAGNETIC MICROSWIMMERS (vol 64, pg 239, 2011), QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, volume 65, no. 1, pages 181-181, DOI:10.1093/qjmam/hbr024. [PDF]

2011

Gilbert A, Klapper I, Thiffeault JL, Wang J. (2011) Preface, Physica D: Nonlinear Phenomena, volume 240, no. 20, pages 1565-1566, DOI:10.1016/j.physd.2011.08.002.
Gilbert AD, Ogrin FY, Petrov PG, Winlove CP. (2011) Motion and mixing for multiple ferromagnetic microswimmers, European Physical Journal E, volume 34, article no. 121.
Gilbert AD, Pauls W. (2011) Complex manifolds for the Euler equations: a hierarchy of ODEs and the case of vanishing angle in two dimensions, Fluid Dyn Res, volume 43, article no. 025505.
Gilbert AD, Ogrin FY, Petrov PG, Winlove CP. (2011) Theory of ferromagnetic microswimmers, The Quarterly Journal of Mechanics and Applied Mathematics, volume 64, no. 3, pages 239-263.

2010

Gilbert AD, Ponty Y, Zheligovsky V. (2010) Dissipative structures in a nonlinear dynamo, DOI:10.48550/arxiv.1005.5259.

2009

Peyrot M, Gilbert A, Plunian F. (2009) Oscillating Ponomarenko dynamo in the highly conducting limit, DOI:10.48550/arxiv.0905.0415.
Barenghi C, Dritschel D, Gilbert A. (2009) Vortex Dynamics from Quantum to Geophysical Scales Introduction, GEOPHYS ASTRO FLUID, volume 103, no. 2-3, pages 111-111, DOI:10.1080/03091920802682628.
Hall O, Hills CP, Gilbert AD. (2009) Nonaxisymmetric stokes flow between concentric cones, Q J MECH APPL MATH, volume 62, no. 2, pages 131-148, DOI:10.1093/qjmam/hbp002.
Hall O, Gilbert AD, Hills CP. (2009) Converging flow between coaxial cones, FLUID DYN RES, volume 41, no. 1, article no. 011402, DOI:10.1088/0169-5983/41/1/011402.
Turner MR, Thuburn J, Gilbert AD. (2009) The influence of periodic islands in the flow on a scalar tracer in the presence of a steady source, PHYS FLUIDS, volume 21, no. 6, article no. 067103, DOI:10.1063/1.3159615.
Turner MR, Bassom AP, Gilbert AD. (2009) Diﬀusion and the formation of vorticity staircases in randomly strained two-dimensional vortices, J. Fluid Mech, volume 638, pages 49-72, DOI:10.1017/S0022112009990875.
TURNER MR, GILBERT AD. (2009) Spreading of two-dimensional axisymmetric vortices exposed to a rotating strain field, Journal of Fluid Mechanics, volume 630, pages 155-177, DOI:10.1017/s0022112009006855. [PDF]

2008

Turner MR, Gilbert AD, Bassom AP. (2008) Neutral modes of a two-dimensional vortex and their link to persistent cat's eyes, Phys. Fluids, volume 20, no. 2. [PDF]
Turner MR, Gilbert AD. (2008) Thresholds for the formation of satellites in two-dimensional vortices, J. Fluid Mech, volume 614, pages 381-405, DOI:10.1017/S0022112008003558. [PDF]
Peyrot M, Gilbert A, Plunian F. (2008) Oscillating Ponomarenko dynamo in the highly conducting limit, Phys Plasma, volume 15, article no. 122104.
Turner MR, Gilbert AD, Thuburn J. (2008) Effective diffusion of scalar fields in a chaotic flow, Phys. Fluids, volume 20, no. 10, pages 107103-1107103. [PDF]

2007

Blockley E, Bassom AP, Gilbert AD, Soward AM. (2007) Pulse-train solutions of a spatially heterogeneous amplitude equation arising in the subcritical instability of a narrow gap-spherical Couette flow, PHYSICA D, volume 228, no. 1, pages 1-30, DOI:10.1016/j.physd.2007.01.005.
Turner MR, Gilbert AD. (2007) "Linear and nonlinear decay of cat's eyes in two-dimensional vortices, and the link to Landau poles", J. Fluid Mech, volume 593, pages 255-279, DOI:10.1017/S0022112007008944. [PDF]
Desjardins B, Dormy E, Gilbert AD, Proctor MRE. (2007) Introduction to self-excited dynamo action, Mathematical Aspects of Natural Dynamos, Taylor and Francis/CRC Press, 3-57.
Hall O, Hills CP, Gilbert AD. (2007) Slow flow between concentric cones, Q J MECH APPL MATH, volume 60, pages 27-48, DOI:10.1093/qjman/hbl024.

2006

Zhang P, Gilbert AD, Zhang K. (2006) Nonlinear dynamo action in rotating convection and shear, J. Fluid Mech, volume 546, pages 25-49.
Gilbert AD. (2006) Advected fields in maps: III. Passive scalar decay in baker's maps, Dynamical Systems: An International Journal, volume 21, no. 1, pages 25-71, DOI:10.1080/14689360500288813.
Zhang P, Gilbert AD. (2006) Nonlinear dynamo action in hydrodynamic instabilities driven by shear, Geophys. Astrophys. Fluid Dynam.

2005

Courvoisier A, Gilbert AD, Ponty Y. (2005) Dynamo action in flows with cat's eyes, Geophys. Astrophys. Fluid Dynam, volume 99, pages 413-429.
Gilbert AD. (2005) Advected fields in maps: II. Dynamo action in the stretch-fold-shear map, Geophysical and Astrophysical Fluid Dynamics, volume 99, no. 3, pages 241-269, DOI:10.1080/03091920500087716.

2004

Bajer K, Bassom AP, Gilbert AD. (2004) Advection-diffusion of a passive scalar in the flow of a decaying vortex, Fluid Mechanics and its Applications, volume 71, pages 31-36, DOI:10.1007/0-306-48420-x_5.
Bajer K, Bassom, A.P., Gilbert AD. (2004) Vortex motion in a weak background shear flow, Journal of Fluid Mechanics, volume 509, pages 281-304.

2003

Gilbert AD. (2003) Chapter 9 Dynamo Theory, volume 2, pages 355-441, DOI:10.1016/S1874-5792(03)80011-3.
Hall IM, Bassom AP, Gilbert AD. (2003) The effect of viscosity on the stability of planar vortices with fine structure, Quart. Jl. Mechanics and Applied Mathematics, volume 56, pages 649-657.
Gilbert AD. (2003) Dynamo Theory, Handbook of Mathematical Fluid Dynamics, Elsevier Science BV, 355-441.
Gilbert AD, Ponty Y, Soward AM. (2003) The onset of thermal convection in Ekman--Couette shear flow with oblique rotation, Journal of Fluid Mechanics, volume 487, pages 91-123, DOI:10.1017/S0022112003004622.
Bajer K, Bassom AP, Gilbert AD. (2003) Mixing and diffusion in planar vortices, "Tubes, Sheets and Singularities in Fluid Dynamics (ed. K. Bajer, H.K. Moffatt), Zakopane, Poland", pages 31-36.
Hall IM, Bassom AP, Gilbert AD. (2003) The effect of fine structure on the stability of planar vortices, European Journal of Mechanics/B Fluids, volume 22, pages 179-198.

2002

Gilbert AD. (2002) Magnetic helicity in fast dynamos, Geophysical and Astrophysical Fluid Dynamics, volume 96, no. 2, pages 135-151, DOI:10.1080/03091920290027952.
Bajer K, Bassom AP, Gilbert AD. (2002) Concentrated vortex in a Poiseuille flow, Advances in Turbulence IX CIMNE, pages 483-486.
Macaskill C, Bassom AP, Gilbert AD. (2002) Nonlinear wind-up in a strained planar vortex, European J of Mechanics B/Fluids, volume 21, pages 293-306.
Gilbert AD. (2002) Advected fields in maps - I. Magnetic flux growth in the stretch-fold-shear map, Physica D: Nonlinear Phenomena, volume 166, no. 3-4, pages 167-196, DOI:10.1016/S0167-2789(02)00444-X.

2001

Ponty Y, Gilbert AD, Soward AM. (2001) Kinematic dynamo action in large magnetic Reynolds number flows driven by shear and convection, J FLUID MECH, volume 435, pages 261-287, DOI:10.1017/S0022112001003755.
Bajer K, Bassom AP, Gilbert AD. (2001) Accelerated diffusion in the centre of a vortex, Journal of Fluid Mechanics, volume 437, pages 395-411, DOI:10.1017/S0022112001004232.
Ponty Y, Gilbert AD, Soward AM. (2001) Dynamo action due to Ekman layer instability, "Dynamo and Dynamics, a Mathematical Challenge, NATO Science Series II: Mathematics, Physics and Chemistry. Kluwer Academic Publishers", volume 26, pages 75-82.
Childress S, Kerswell RR, Gilbert AD. (2001) Bounds on dissipation for Navier-Stokes flow with Kolmogorov forcing, Physica D, volume 158, pages 105-128.

2000

Bassom AP, Gilbert AD. (2000) The relaxation of vorticity fluctuations in locally elliptical streamlines, Proc. Roy. Soc. A, volume 456, pages 295-314.
Bajer K, Bassom AP, Gilbert AD. (2000) Decay of perturbations near the centre of a strong vortex, "Advances in Turbulence VIII, Barcelona, Spain, 2000", pages 729-732.
Gilbert AD, Ponty Y. (2000) Dynamos on stream surfaces of a highly conducting fluid, Geophysical and Astrophysical Fluid Dynamics, volume 93, no. 1-2, pages 55-95, DOI:10.1080/03091920008203722.

1999

Bassom AP, Gilbert AD. (1999) The spiral wind-up and dissipation of vorticity and a passive scalar in a strained planar vortex, J. Fluid Mech, volume 398, pages 245-270.
Maksymczuk J, Gilbert AD. (1999) Fast dynamo equilibration in a simplified nonlinear model, "Stellar Dynamos: Nonlinearity and Chaotic Flows (ed. M Nunez, A. Ferriz-Mas), Medina del Campo, Spain, 1998", pages 97-106.

1998

Maksymczuk J, Gilbert AD. (1998) Remarks on the equilibration of high conductivity dynamos, Geophys. Astrophys. Fluid Dyn, volume 90, pages 127-137.
Bassom AP, Gilbert AD. (1998) The spiral wind-up of vorticity in an inviscid planar vortex, J. Fluid Mech, volume 371, pages 109-140.

1997

Gilbert AD, Soward AM, Childress S. (1997) A fast dynamo of αω-type, Geophysical and Astrophysical Fluid Dynamics, volume 85, no. 3-4, pages 279-314, DOI:10.1080/03091929708208992.
Gilbert AD, Soward AM, Childress S. (1997) A fast dynamo of alpha omega-type, GEOPHYSICAL AND ASTROPHYSICAL FLUID DYNAMICS, volume 85, no. 3-4, pages 279-314, DOI:10.1080/03091929708208992. [PDF]
Bassom AP, Gilbert AD. (1997) Nonlinear equilibration of a dynamo in a smooth helical flow, J. Fluid Mech, volume 343, pages 375-406.

1995

Childress S, Gilbert AD. (1995) Stretch, twist, fold: the fast dynamo, Springer Verlag.

1994

Proctor MRE, Gilbert AD. (1994) Lectures on Solar and Planetary Dynamos, Cambridge University Press.

1993

Aurell E, Gilbert AD. (1993) Fast dynamos and determinants of singular integral operators, Geophys. Astrophys. Fluid Dynam, volume 73, pages 5-32.
GILBERT AD. (1993) TOWARDS A REALISTIC FAST DYNAMO - MODELS BASED ON CAT MAPS AND PSEUDO-ANOSOV MAPS, PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, volume 443, no. 1919, pages 585-606, DOI:10.1098/rspa.1993.0164. [PDF]
Gilbert AD. (1993) A cascade interpretation of Lundgren’s stretched spiral vortex model for turbulent ﬁne structure,, Phys. Fluids A, volume 5, pages 2831-2834.
Friedlander S, Gilbert AD, Vishik MM. (1993) Hydrodynamic instability for certain ABC ﬂows, Geophys. Astrophys. Fluid Dynam, volume 73, pages 97-107.
Gilbert AD, Froeschle C, Frisch U. (1993) Wavelet analysis of the standard map: structure and scaling, Celestial Mechanics & Dynamical Astronomy, volume 56, pages 263-272.

1992

Gilbert AD, Bayly BJ. (1992) Magnetic ﬁeld intermittency and fast dynamo action in random helical ﬂows, J. Fluid Mech, volume 241, pages 199-214.
Gilbert AD. (1992) Magnetic ﬁeld evolution in steady chaotic ﬂows, Phil. Trans. R. Soc. Lond. A, volume 339, pages 627-656.

1991

Gilbert AD. (1991) Fast dynamo action in a steady chaotic ﬂow, Nature, volume 350, pages 483-485.
Gilbert AD, Galanti B, Sulem PL. (1991) Inverse cascades and time-dependent dynamos in MHD ﬂows,, Physica D, volume 47, pages 416-426.

1990

Gilbert AD, Childress S. (1990) Evidence for fast dynamo action in a chaotic web, Phys. Rev. Lett, volume 65, pages 2133-2136.
CHILDRESS S, COLLET P, FRISCH U, GILBERT AD, MOFFATT HK, ZASLAVSKY GM. (1990) REPORT ON WORKSHOP ON SMALL-DIFFUSIVITY DYNAMOS AND DYNAMIC-SYSTEMS HELD AT OBSERVATOIRE-DE-NICE 25-30 JUNE 1989, GEOPHYSICAL AND ASTROPHYSICAL FLUID DYNAMICS, volume 52, no. 4, pages 263-270, DOI:10.1080/03091929008219507. [PDF]
Gilbert AD, Sulem PL. (1990) On inverse cascades in alpha eﬀect dynamos, Geophys. Astrophys. Fluid Dynam, volume 51, pages 243-261.

1988

Gilbert AD. (1988) Fast dynamo action in the Ponomarenko dynamo, Geophys. Astrophys. Fluid Dynam, volume 44, pages 241-258.
Gilbert AD, Frisch U, Pouquet A. (1988) Helicity is unnecessary for alpha eﬀect dynamos, but it helps, Geophys. Astrophys. Fluid Dynam, volume 42, pages 151-161.
Gilbert AD. (1988) Spiral structures and spectra in two-dimensional turbulence, J. Fluid Mech, volume 193, pages 475-497.