Positions

Research Areas research areas

Overview

  • My primary research interest is understanding turbulence through dynamical systems theory. The key idea is to compute unstable invariant solutions of the Navier-Stokes equations (steady states, traveling waves, and periodic orbits) and describe turbulent dynamics as a chaotic walk between these unstable solutions along the low-dimensional network of their unstable manifolds. Additional interests include numerical methods, scientific computing, open-source software, the Julia programming language, and open education.
  • Publications

    Academic Article

    Year Title
    2017 Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number.Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.  375:20160092-20160092. 2017
    2016 Homoclinic snaking in plane Couette flow: bending, skewing and finite-size effectsJournal of Fluid Mechanics.  794:530-551. 2016
    2016 Localized travelling waves in the asymptotic suction boundary layerJournal of Fluid Mechanics.  795. 2016
    2014 Turbulent-laminar patterns in plane Poiseuille flowPhysics of Fluids.  26:114103-114103. 2014
    2014 A doubly localized equilibrium solution of plane Couette flowJournal of Fluid Mechanics.  750. 2014
    2014 Spanwise-localized solutions of planar shear flowsJournal of Fluid Mechanics.  745:25-61. 2014
    2010 Unstable periodic orbits and heteroclinic connections in plane Couette flowPhysica Scripta.  142. 2010
    2010 Snakes and ladders: localized solutions of plane Couette flow.Physical Review Letters.  104:104501. 2010
    2009 Equilibrium and travelling-wave solutions of plane Couette flowJournal of Fluid Mechanics.  638:243-266. 2009
    2009 Heteroclinic connections in plane Couette flowJournal of Fluid Mechanics.  621:365-376. 2009
    2008 Visualizing the geometry of state space in plane Couette flowJournal of Fluid Mechanics.  611:107-130. 2008
    2008 Laminar-turbulent boundary in plane Couette flow.Physical review. E.  78:037301. 2008
    2007 Lower Branch Coherent States in Shear Flows: Transition and ControlPhysical Review Letters.  98. 2007
    1997 Lagrangian and Eulerian view of the bursting periodPhysics of Fluids.  9:433-437. 1997
    1992 AN ANALYTIC APPROACH TO PRACTICAL STATE-SPACE RECONSTRUCTIONPhysica D: Nonlinear Phenomena.  57:1-30. 1992
    1991 State space reconstruction in the presence of noisePhysica D: Nonlinear Phenomena.  51:52-98. 1991

    Conference Proceeding

    Year Title
    2010 Geometry of the turbulence in wall-bounded shear flows: periodic orbitsPhysica Scripta. 014007-014007. 2010
    2009 Geometry of state space in plane Couette flowSpringer proceedings in physics. 75-78. 2009

    Teaching Activities

  • Diff Equation w/Linear Algebra Taught course 2018
  • Mathematics and Apps in MATLAB Taught course 2018
  • Intro to Numerical Methods I Taught course 2017
  • Numerical Linear Algebra Taught course 2017
  • Intro to Numerical Methods I Taught course 2016
  • Numerical Linear Algebra Taught course 2016
  • Mathematics and Apps in MATLAB Taught course 2016
  • Spatiotemp. & Turb. Dynamics Taught course 2016
  • Adv Rsrch Exp/Mathematics Taught course 2015
  • Diff Equation w/Linear Algebra Taught course 2015
  • Numerical Linear Algebra Taught course 2015
  • Diff Equation w/Linear Algebra Taught course 2015
  • Mathematics and Apps in MATLAB Taught course 2015
  • Mathematics and Apps in MATLAB Taught course 2014
  • Numerical Linear Algebra Taught course 2014
  • Diff Equation w/Linear Algebra Taught course 2014
  • Spatiotemp. & Turb. Dynamics Taught course 2014
  • Education And Training

  • B.A. Liberal Arts, St. John's College
  • Ph.D. Theoretical & Applied Mechanics, Cornell University
  • Full Name

  • John Gibson
  • Mailing Address

  • University of New Hampshire

    Mathematics and Statistics

    33 Academic Way

    Durham, New Hampshire  03824

    USA