John Gibson

Phone: (603) 862-2681
Office: Mathematics & Statistics, Kingsbury Hall Rm N309 E, Durham, NH 03824
John Gibson

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.


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

Research Interests

  • Applied Mathematics
  • Computational Mathematics
  • Fluid Dynamics
  • Nonlinear Dynamics

Courses Taught

  • 527: Diff Equation w/Linear Algebra
  • 531: Mathematical Proof
  • 961: Numerical Linear Algebra
  • 999: Doctoral Research
  • IAM 950: Spatiotemp. & Turb. Dynamics
  • IAM 961: Numerical Linear Algebra
  • MATH 445: Mathematics and Apps in MATLAB
  • MATH 527: Diff Equation w/Linear Algebra
  • MATH 531: Mathematical Proof
  • MATH 747/847: Intro Nonlinear Dynamics&Chaos

Selected Publications

Brand, E., & Gibson, J. F. (2014). A doubly localized equilibrium solution of plane Couette flow. JOURNAL OF FLUID MECHANICS, 750. doi:10.1017/jfm.2014.285

Schneider, T. M., Gibson, J. F., & Burke, J. (2010). Snakes and Ladders: Localized Solutions of Plane Couette Flow. PHYSICAL REVIEW LETTERS, 104(10). doi:10.1103/PhysRevLett.104.104501

Gibson, J. F., Halcrow, J., & Cvitanovic, P. (2008). Visualizing the geometry of state space in plane Couette flow. JOURNAL OF FLUID MECHANICS, 611, 107-130. doi:10.1017/S002211200800267X