293 citations · 1.1k across the 15 of their papers we have counts for
15 papers
Algebraic models of plane Couette equilibria
Pratik P. Aghor, John F. Gibson
Recent computations of weakly unstable equilibria, traveling waves, and periodic orbits in transitional shear flows suggest a spatiotemporal, dynamical-systems approach to low-Reyn…
Chaotic mixing in plane Couette turbulence
John R. Elton, Predrag Cvitanović, Jonathan Halcrow +1
Lagrangian tracer particle trajectories for invariant solutions of the Navier-Stokes equations confined to the three-dimensional geometry of plane Couette flow are studied. Treatin…
Symmetry groups and invariant solutions of plane Poiseuille flow
Pratik P. Aghor, John F. Gibson
Equilibrium, traveling-wave, and periodic-orbit solutions of the Navier-Stokes equations provide a promising avenue for investigating the structure, dynamics, and statistics of tra…
The origin of localized snakes-and-ladders solutions of plane Couette flow
Matthew Salewski, John F. Gibson, Tobias M. Schneider
Spatially localized exact solutions of plane Couette flow are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming partial di…
Localized travelling waves in the asymptotic suction boundary layer
Tobias Kreilos, John F. Gibson, Tobias M. Schneider
We present two spanwise-localized travelling wave solutions in the asymptotic suction boundary layer, obtained by continuation of solutions of plane Couette flow. One of the soluti…
Homoclinic snaking in plane Couette flow: bending, skewing, and finite-size effects
John F. Gibson, Tobias M. Schneider
Invariant solutions of shear flows have recently been extended from spatially periodic solutions in minimal flow units to spatially localized solutions on extended domains. One set…