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Many people have contributed to this effort; for a literature overview, see Gibson et al. Here we cite only a few articles that cover technical aspects of this tutorial.
- M. Nagata, "Three-dimensional finite-amplitude
solutions in plane Couette flow: bifurcation from infinity," J. Fluid Mech.
217 (1990).
Calculation of a lower/upper branch pair of equilibrium solutions to plane Couette flow.
- J. M. Hamilton, J. Kim and F. Waleffe,
"Regeneration mechanisms of near-wall turbulence structures,"
J. Fluid Mech. 287 (1995).
Identification and numerical study of organized dynamics in low-Reynolds plane
Couette flow in small aspect ratio cells.
- F. Waleffe, "Homotopy of exact coherent
structures in plane shear flows," Phys. Fluids 15 (2003).
Exact numerical solutions to plane Couette flow with a variety
of boundary conditions. Waleffe lower branch and upper branch
solutions served as the starting point of our investigation.
- G. Kawahara and S. Kida, "Periodic motion
embedded in Plane Couette turbulence: regeneration cycle and burst,"
J. Fluid Mech. 449, 291 (2001). The first determination
of unstable time-periodic solutions in a fully-resolved Navier-Stokes flow.
- D. Viswanath, "Recurrent motions within plane
Couette turbulence," J. Fluid Mech. 580 (2007)
[arXiv:/physics/0604062].
A novel combination of the Newton-hookstep trust-region
minimization algorithm with the GMRES algorithm for iterative solution of
high-dimensional linear algebra problems. First computation of relative periodic orbits of plane Couette flow, using a CFD algorithm
to evaluate Navier-Stokes dynamics and close recurrences for initial guesses.
- J. F. Gibson, J. Halcrow and P. Cvitanović
"Visualizing the geometry of state space in plane Couette flow," J. Fluid Mech. (2008), to appear
[arXiv:0705.3957].
A technical exposition of the material presented in this tutorial.
-
J. Halcrow, J. F. Gibson and P. Cvitanović,
"Steady states and traveling waves
of moderate Re=400 plane Couette flow,"
in preparation.
Status as of Nov 2007, summarized by this plot.
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