Imperial College London
Professor John Gibbon

ProfessorJohnGibbon

Faculty of Natural Sciences, Department of Mathematics

Senior Research Investigator
 
 
 
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Contact

 

j.d.gibbon Website

 
 
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Location

 

6M41Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

171 results found

Brindley J, Read P, Gibbon J, Soward Aet al., 2011, Introduction, Geophysical and Astrophysical Fluid Dynamics, Vol: 105, Pages: 113-116, ISSN: 0309-1929

Journal article

Gibbon JD, Holm DD, 2011, Extreme events in solutions of hydrostatic and non-hydrostatic climate models, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 369, Pages: 1156-1179, ISSN: 1364-503X

Journal article

Gibbon JD, Holm DD, 2011, The gradient of potential vorticity, quaternions and an orthonormal frame for fluid particles, GEOPHYSICAL AND ASTROPHYSICAL FLUID DYNAMICS, Vol: 105, Pages: 329-339, ISSN: 0309-1929

Journal article

Gibbon JD, 2010, Regularity and singularity in solutions of the three-dimensional Navier-Stokes equations, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 466, Pages: 2587-2604, ISSN: 1364-5021

Journal article

Gibbon JD, Holm DD, 2010, The dynamics of the gradient of potential vorticity, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 43, ISSN: 1751-8113

Journal article

Roulstone I, Banos B, Gibbon JD, Roubtsov VNet al., 2009, A geometric interpretation of coherent structures in Navier-Stokes flows, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 465, Pages: 2015-2021, ISSN: 1364-5021

Journal article

Gibbon JD, 2009, Estimating intermittency in three-dimensional Navier-Stokes turbulence, JOURNAL OF FLUID MECHANICS, Vol: 625, Pages: 125-133, ISSN: 0022-1120

Journal article

Eshraghi H, Gibbon JD, 2008, Quaternions and ideal flows - art. no. 344004, Meeting held in Honor of Darryl D Holm on Geometry and Analysis in Physical Systems, Pages: 44004-44004

Conference paper

Gibbon JD, 2008, The three-dimensional Euler equations: Where do we stand?, PHYSICA D-NONLINEAR PHENOMENA, Vol: 237, Pages: 1894-1904, ISSN: 0167-2789

Journal article

Gibbon JD, Bustamante M, Kerr RM, 2008, The three-dimensional Euler equations: singular or non-singular?, NONLINEARITY, Vol: 21, Pages: T123-T129, ISSN: 0951-7715

Journal article

Gibbon JD, Holm DD, 2008, Estimates for the LANS-α, Leray-α and Bardina Models in Terms of a Navier-Stokes Reynolds Number, INDIANA UNIVERSITY MATHEMATICS JOURNAL, Vol: 57, Pages: 2761-2773, ISSN: 0022-2518

Journal article

Gibbon JD, 2007, Orthonormal quaternion frames, Lagrangian evolution equations, and the three-dimensional Euler equations, Workshop on Mathematical Hydrodynamics, Publisher: TURPION LTD, Pages: 535-560, ISSN: 0036-0279

Conference paper

Gibbon JD, Holm DD, 2007, Lagrangian analysis of alignment dynamics for isentropic compressible magnetohydrodynamics, New Journal of Physics, Vol: 9, ISSN: 1367-2630

After a review of the isentropic compressible magnetohydrodynamics (ICMHD) equations, a quaternionic framework for studying the alignment dynamics of a general fluid flow is explained and applied to the ICMHD equations.

Journal article

Gibbon JD, Holm DD, 2007, Lagrangian particle paths and ortho-normal quaternion frames, NONLINEARITY, Vol: 20, Pages: 1745-1759, ISSN: 0951-7715

Journal article

Gibbon JD, Pavliotis GA, 2007, Estimates for the two-dimensional Navier-Stokes equations in terms of the Reynolds number, JOURNAL OF MATHEMATICAL PHYSICS, Vol: 48, ISSN: 0022-2488

Journal article

Gibbon JD, Holm DD, 2006, Length-scale estimates for the LANS-α equations in terms of the Reynolds number, PHYSICA D-NONLINEAR PHENOMENA, Vol: 220, Pages: 69-78, ISSN: 0167-2789

Journal article

Calzavarini E, Doering CR, Gibbon JD, Lohse D, Tanabe A, Toschi Fet al., 2006, Exponentially growing solutions in homogeneous Rayleigh-Benard convection, PHYSICAL REVIEW E, Vol: 73, ISSN: 1539-3755

Journal article

Gibbon JD, Holm DD, Kerr RM, Roulstone Iet al., 2006, Quaternions and particle dynamics in the Euler fluid equations, Nonlinearity, Vol: 19, Pages: 1969-1983, ISSN: 0951-7715

Journal article

Gibbon JD, Titi ES, 2005, Cluster formation in complex multi-scale systems, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 461, Pages: 3089-3097, ISSN: 1364-5021

Journal article

Gibbon JD, Doering CR, 2005, Intermittency and regularity issues in 3D Navier-Stokes turbulence, ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, Vol: 177, Pages: 115-150, ISSN: 0003-9527

Journal article

Thiffeault JL, Doering CR, Gibbon JD, 2004, A bound on mixing efficiency for the advection-diffusion equation, JOURNAL OF FLUID MECHANICS, Vol: 521, Pages: 105-114, ISSN: 0022-1120

Journal article

Gibbon JD, Ohkitani K, 2004, Evidence for singularity formation in a class of stretched solutions of the equations for ideal MHD, Fluid Mechanics and its Applications, Vol: 71, Pages: 295-304, ISSN: 0926-5112

A class of stretched solutions of the equations for incompressible, ideal 3D-MHD are studied using Elsasser variables V ± = U ± B. This class takes the form V± = (v±, v 3±) where v ± = and v ±=(x,y,t) and v 3±{x,y,z,t) = zγ ±(x,y,t) + β ±(x,y,t). The chosen domain is of a tubular form which is infinite in the z-direction with periodic cross-section. This follows a previous study by the authors on this same class of solutions for the 3D Euler equations. In both cases the systems are of infinite energy. Strong numerical evidence for a finite time singularity in the Euler case was subsequently confirmed by a rigorous analytical proof by Constantin. In the MHD case, pseudo-spectral computations of the 2D partial differential equations for γ ±, v ± and β ± valid on the cross-sectional domain provide evidence for a finite time blow-up in both the fluid and magnetic variables although an analytical proof for the existence of this singularity remains elusive. © 2002 Kluwer Academic Publishers.

Journal article

Gibbon JD, Moore DR, Stuart JT, 2003, Exact, infinite energy, blow-up solutions of the three-dimensional Euler equations, NONLINEARITY, Vol: 16, Pages: 1823-1831, ISSN: 0951-7715

Journal article

Gibbon JD, Doering CR, 2003, Intermittency in solutions of the three-dimensional Navier-Stokes equations, JOURNAL OF FLUID MECHANICS, Vol: 478, Pages: 227-235, ISSN: 0022-1120

Journal article

Gibbon JD, 2002, A quaternionic structure in the three-dimensional Euler and ideal magneto-hydrodynamics equations, PHYSICA D-NONLINEAR PHENOMENA, Vol: 166, Pages: 17-28, ISSN: 0167-2789

Journal article

Doering CR, Gibbon JD, 2002, Bounds on moments of the energy spectrum for weak solutions of the three-dimensional Navier-Stokes equations, PHYSICA D-NONLINEAR PHENOMENA, Vol: 165, Pages: 163-175, ISSN: 0167-2789

Journal article

Gibbon JD, Ohkitani K, 2001, Singularity formation in a class of stretched solutions of the equations for ideal magneto-hydrodynamics, NONLINEARITY, Vol: 14, Pages: 1239-1264, ISSN: 0951-7715

Journal article

Gibbon JD, Galanti B, Kerr RM, 2001, Stretching and compression of vorticity in the 3D Euler equations, Symposium on Vortex Dynamics and Turbulence Structure, Publisher: CAMBRIDGE UNIV PRESS, Pages: 23-34

Conference paper

Gibbon JD, Galanti B, Kerr J, 2000, Stretching & compression of vorticity in the 3D Euler equations, Turbulence structure and vortex dynamics, Editors: Hunt, Vassilicos, Cambridge, Publisher: Cambridge University Press, Pages: 22-34

Book chapter

Ohkitani K, Gibbon JD, 2000, Numerical study of singularity formation in a class of Euler and Navier-Stokes flows, Physics of Fluids, Vol: 12, Pages: 3181-3194, ISSN: 1070-6631

Journal article

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