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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.
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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.
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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.
-
J. F. Gibson, J. Halcrow and P. Cvitanović,
"Visualizing the geometry of state space in plane Couette flow,"
J. Fluid Mech. 611, 107 (2008)
[arXiv:0705.3957].
A technical exposition of the material presented in this tutorial.
-
J. F. Gibson, J. Halcrow and P. Cvitanović,
"Equilibrium and traveling-wave solutions of plane Couette flow,"
J. Fluid Mech. 638, 243 (2009)
[arXiv:0808.3375].
-
J. Halcrow, J.F. Gibson, P. Cvitanović and D. Viswanath,
"Heteroclinic connections in plane Couette flow;"
J. Fluid Mech. 621, 365 (2009);
[arXiv:0808.1865].
-
T. Itano and S.C. Generalis,
"Hairpin vortex solution in planar Couette flow:
A tapestry of knotted vortices;" Phys. Rev. Lett. 102, 114501 (2009).
Independent discovery of the EQ8 solution.
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