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.
Courses Taught
- IAM 550: Intro to Engineering Computing
- IAM 961: Numerical Linear Algebra
- IAM 999: Doctoral Research
- MATH 527: Diff Equation w/Linear Algebra
- MATH 531: Mathematical Proof
- MATH 747/847: Intro Nonlinear Dynamics&Chaos
- MATH 753/853: Intro to Numerical Methods I
- TECH 411: Innovation Scholars I
Research Interests
- Applied Mathematics
- Computational Mathematics
- Fluid Dynamics
- Nonlinear Dynamics
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
