A. Prigent, G. Grégoire, H. Chaté, and O. Dauchot, Long-wavelength modulation of turbulent shear flows, Physica D: Nonlinear Phenomena, vol.174, issue.1-4, pp.100-113, 2002.
DOI : 10.1016/S0167-2789(02)00685-1
URL : https://hal.archives-ouvertes.fr/hal-01422415

J. Rolland and P. Manneville, Ginzburg???Landau description of laminar-turbulent oblique band formation in transitional plane Couette flow, The European Physical Journal B, vol.142, issue.4, pp.529-544, 2011.
DOI : 10.1140/epjb/e2011-10730-1
URL : https://hal.archives-ouvertes.fr/hal-00997977

D. Barkley and L. S. Tuckerman, Mean flow of turbulent???laminar patterns in plane Couette flow, Journal of Fluid Mechanics, vol.576, pp.109-137, 2007.
DOI : 10.1017/S002211200600454X

L. S. Tuckerman and D. Barkley, Patterns and dynamics in transitional plane Couette flow, Physics of Fluids, vol.23, issue.4, p.41301, 2011.
DOI : 10.1063/1.3580263

H. Adia, T. Tsukahara, and Y. Kawaguchi, Development of a turbulent spot into a stripe pattern in plane Poiseuille flow, 2011.

K. Avila, D. Moxey, A. De-lozar, M. Avila, D. Barkley et al., The Onset of Turbulence in Pipe Flow, Science, vol.333, issue.6039, pp.192-196, 2011.
DOI : 10.1126/science.1203223

Y. Duguet, A. Willis, and R. , Slug genesis in cylindrical pipe flow, Journal of Fluid Mechanics, vol.75, pp.180-208, 2010.
DOI : 10.1063/1.1804549
URL : https://hal.archives-ouvertes.fr/hal-01021118

M. Shimizu and S. Kida, A driving mechanism of a turbulent puff in pipe flow, Fluid Dynamics Research, vol.41, issue.4, p.45501, 2009.
DOI : 10.1088/0169-5983/41/4/045501

F. Waleffe, On a self-sustaining process in shear flows, Physics of Fluids, vol.9, issue.4, pp.883-900, 1996.
DOI : 10.1063/1.869185

W. Schoppa and F. Hussain, Coherent structure generation in near-wall turbulence, Journal of Fluid Mechanics, vol.453, pp.57-108, 2002.
DOI : 10.1017/S002211200100667X

D. Barkley, Simplifying the complexity of pipe flow, Physical Review E, vol.84, issue.1, p.16309, 2011.
DOI : 10.1103/PhysRevE.84.016309

D. Barkley, Modeling the transition to turbulence in shear flows, Journal of Physics: Conference Series, vol.318, issue.3, p.32001, 2011.
DOI : 10.1088/1742-6596/318/3/032001

Y. Duguet and P. Schlatter, Oblique Laminar-Turbulent Interfaces in Plane Shear Flows, Physical Review Letters, vol.110, issue.3, p.34502, 2013.
DOI : 10.1103/PhysRevLett.110.034502

B. Hof, A. De-lozar, M. Avila, X. Tu, and T. M. Schneider, Eliminating turbulence in spatially intermittent flows Science, pp.1491-1494, 2010.

J. Rolland, Turbulent spot growth in plane Couette flow: statistical study and formation of spanwise vorticity, Fluid Dynamics Research, vol.46, issue.1, p.15512, 2014.
DOI : 10.1088/0169-5983/46/1/015512
URL : https://hal.archives-ouvertes.fr/hal-00995136

J. Rolland and P. Manneville, Turbulent pattern formation in plane Couette flow: modelling and investigation of mechanisms, Journal of Physics: Conference Series, vol.318, issue.3, p.32034, 2011.
DOI : 10.1088/1742-6596/318/3/032034
URL : https://hal.archives-ouvertes.fr/hal-01025978

P. Manneville, On the decay of turbulence in plane Couette flow, Fluid Dynamics Research, vol.43, issue.6, p.65501, 2011.
DOI : 10.1088/0169-5983/43/6/065501
URL : https://hal.archives-ouvertes.fr/hal-01025564

D. Coles, Transition in circular Couette flow, Ch. Van Atta, pp.385-425, 1965.
DOI : 10.1007/BF02084936

J. Philip and P. Manneville, From temporal to spatiotemporal dynamics in transitional plane Couette flow, Physical Review E, vol.83, issue.3, p.36308, 2011.
DOI : 10.1103/PhysRevE.83.036308
URL : https://hal.archives-ouvertes.fr/hal-00997976

J. Gibson, J. Halcrow, and P. Cvitanovi´ccvitanovi´c, Visualizing the geometry of state space in plane Couette flow, Journal of Fluid Mechanics, vol.301, pp.107-130, 2008.
DOI : 10.1103/PhysRevLett.79.5250

P. Manneville and J. Rolland, On modelling transitional turbulent flows using under-resolved direct numerical simulations: the case of plane Couette flow, Theor. Comput Fluid Dyn, pp.407-420, 2010.

Y. Duguet, P. Schlatter, and D. S. Henningson, Formation of turbulent patterns near the onset of transition in plane Couette flow, Journal of Fluid Mechanics, vol.2, pp.119-129, 2010.
DOI : 10.1103/PhysRevLett.69.2511

L. Shi, M. Avila, and B. Hof, Scale Invariance at the Onset of Turbulence in Couette Flow, Physical Review Letters, vol.110, issue.20, p.204502, 2013.
DOI : 10.1103/PhysRevLett.110.204502

J. Jiménez and P. , The minimal flow unit in near-wall turbulence, Journal of Fluid Mechanics, vol.204, issue.-1, pp.213-240, 1991.
DOI : 10.1017/S0022112069000115

J. M. Hamilton, J. Kim, and F. Waleffe, Regeneration mechanisms of near-wall turbulence structures, Journal of Fluid Mechanics, vol.169, issue.-1, pp.317-348, 1995.
DOI : 10.1063/1.868327

J. Rolland, A short wavelength instability in oblique bands of transitional plane Couette flow, part 2: modelling and stability analysis, 2014.

R. S. Schechter and D. M. Himmelblau, Local Potential and System Stability, Local potential and system stability, pp.1431-1437, 1965.
DOI : 10.1063/1.1761437

P. Manneville, Spatiotemporal perspective on the decay of turbulence in wall-bounded flows, Physical Review E, vol.79, issue.2, p.25301, 2009.
DOI : 10.1103/PhysRevE.79.025301
URL : https://hal.archives-ouvertes.fr/hal-01002601

. Here, corresponds to a spatial average over the whole flow, . xi , the average over a coordinate x i

R. J. Adrian, Particle-Imaging Techniques for Experimental Fluid Mechanics, Annual Review of Fluid Mechanics, vol.23, issue.1, pp.261-304, 1991.
DOI : 10.1146/annurev.fl.23.010191.001401

D. Samanta, A. De-lozar, and B. Hof, Experimental investigation of laminar turbulent intermittency in pipe flow, Journal of Fluid Mechanics, vol.174, pp.193-204, 2011.
DOI : 10.1017/S0022112010003435

Y. Duguet, O. Le-ma??trema??tre, and P. Schlatter, Stochastic and deterministic motion of a laminar-turbulent interface in a shear flow Phys, Rev. E, vol.84, p.66315, 2011.