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====== References ======

===== Numerical algorithms =====
  

   - L. Kleiser and U. Schuman, //Treatment of incompressibility and boundary conditions in 3-D numerical spectral simulations of plane channel flows,// in  Proc. 3rd GAMM Conf. Numerical Methods in Fluid Mechanics, ed. E. Hirsch (1980) 
   - Canuto, Hussaini, Quarteroni, and Zang,  //Spectral Methods in Fluid Dynamics//, Springer-Verlag (1998) 
   - R. Peyret, //Spectral Methods for Incompressible Flows,"// Springer-Verlag (2002) 
   - D. Viswanath, //Recurrent motions within plane Couette turbulence,// J. Fluid Mech. 580 (2007), arXiv:/physics/0604062 
   - M. Frigo and S.G. Johnson, //The Design and Implementation of FFTW3,//  Proceedings of the IEEE 93 (2) (2005) 

===== Dynamics of turbulence =====

   * 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. Nagata-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. 611 (2008), [arXiv:0705.3957]. A technical exposition of the material presented in this tutorial. [[http://www.cns.gatech.edu/~gibson/publications/GibsonJFM08.pdf|PDF]]

   * J. Halcow, J.F. Gibson, P. Cvitanović, and D. Viswanath, //Heteroclinic connections in plane Couette flow,//  J. Fluid Mech. (2009) to appear. Calculation of four heteroclinic connections between unstable equilibria of plane Couette flow. [[http://www.cns.gatech.edu/~gibson/publications/HalcrowARX08a.pdf|PDF]]

   * J. Halcrow, J.F. Gibson and P. Cvitanović, //Equilibrium and traveling waves solutions of low-Reynolds plane Couette flow,// Submitted to JFM [[http://www.cns.gatech.edu/~gibson/publications/HalcrowARX08b.pdf|PDF]]

   * T. M. Schneider, J.F. Gibson, M. Lagha, F. De Lillo, B. Eckhardt  //Laminar-turbulent boundary in plane Couette flow// Phys. Rev. E (2008)  78, 037301 [[http://www.cns.gatech.edu/~gibson/publications/SchneiderPRE08.pdf|PDF]]

   * J. Wang, J.F. Gibson, and F. Waleffe //Lower branch coherent states: transition and control// Phys. Rev. Lett. (2007) 98, 20 [[http://www.cns.gatech.edu/~gibson/publications/WangPRL07.pdf|PDF]]
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