90 Laminar-turbulent pattern in plane Couette flow 83 quantitatively it leads to a downward shift of R g, R t, and it is not obvious that it is still effective in describing properties of the long term dynamics of bands, in particular pattern stability and band breaking, at a sufficiently accurate level. As a matter of fact it was shown in Fig. 1 that, within these restrictions, stable bands three, two, and even one could be observed with N y 15 in a periodic domain over time spans much larger than 10 4 time units hu. Recent results for PCF in a quasi-one-dimensional geometry 8 show that the decay of turbulence at R g is well accounted for by a continuous second order non-equilibrium phase transition in the directed percolation DP class. Knowing that spatiotemporal correlations are strongly dependent on confinement characteristics 9, it seems important to scrutinize the quasi-two-dimensional case of interest in experiments. It seems clear that under-resolved simulations need not be continued and that the indications obtained in this context have to be confirmed by fully resolved computations. The dynamics of multi-band states and the stability of one-band states while varying the domain size and its geometrical proportions since, owing to periodic boundary conditions, this controls the angle of bands should then be studied with two ideas in mind: i while decreasing R from R t, explore the putative extremum of the potential from which an envelope equation would derive, yielding a preferred wavelength and angle at given R, if any; ii examine whether the transition at R g is continuous as implied in the DP scenario, or else discontinuous with finite turbulent fraction at R g. On the one hand, criticality at R g in the continuous case is likely more difficult to ascertain in the quasi-2d case ideally requiring a finite-size scaling approach than in the quasi-1d case for which convincing results have been obtained 8. On the other hand, a discontinuous transition at R g is forcedly less sensitive to size effects due to the primary role played by extreme localized excursions toward laminar flow 7, with a variety of band configurations possible above R g, hence a finite range of turbulent fraction depending on the geometry, and no turbulence at all in the long term below R g. The main merit of our preliminary study at reduced resolution is therefore to help us better situating the problem not of the nature of turbulence but of the nature of the transition and how to describe it at the global level. Acknowledgements: The author would like to thank the members of the JSPS-CNRS collaboration TransTurb for discussions related to the work presented here, in particular G. Kawahara and M. Shimizu Osaka, T. Tsukahara Tokyo on the Japanese side, and Y. Duguet LIMSI, R. Monchaux and M. Couliou ENSTA-ParisTech on the French side. References 1 A. Prigent, G. Grégoire, H. Chaté O. Dauchot, Long wavelength modulation of turbulent shear flows, Physica D, 174, 2003 2. L S. Tuckerman, D. Barkley O. Dauchot, Instability of uniform turbulent plane Couette flow: Spectra, probability distribution functions and K Ω closure model, 7th IUTAM Symposium on Laminar-Turbulent Transition, Stockholm, Ph. Schlatter, D. Henningson, eds, pp, Springer 2009 3. P. Manneville, Turbulent patterns in wall-bounded flows: a Turing instability? Europhys Lett, 98, 2012 4. D. Barkley L S. Tuckerman Mean flow of turbulent-laminar patterns in plane Couette flow, J. Fluid Mech, 576, 2007 5. P. Manneville, Dissipative structures and weak turbulence, Academic Press 1990 6. P. Manneville J. Rolland, On modelling transitional turbulent flows using under-resolved direct numerical simulations: The case of plane Couette flow, Theor Comput. Fluid Dyn, 25, 2011 7. P. Manneville, On the decay of turbulence in plane Couette flow, Fluid Dyn Res, 43, 2011 8. G. Lemoult, L. Shi, K. Avila, S V. Jalikop, M. Avila B. Hof, Directed percolation phase transition to sustained turbulence in Couette flow. To be published in Nature Phys 2016. 9 J. Philip P. Manneville, From temporal to spatiotemporal dynamics in transitional plane Couette flow, Phys Rev. E, 83, 2011. Conférence en lhonneur de Claude Lobry, Université Gaston Berger, Saint Louis Sénégal- An Internet-based graphical programming tool for teaching power system harmonic measurement Oops! Something went wrong while submitting the form. Invariance déchelle. Des changements détats à la turbulence À ce sujet, quapporte la coopération entre les marques, leurs réseaux et les distributeurs, pourquoi est-ce un enjeu, un levier? mercredi 7 novembre, de 14h à 16h:Alignement de données pour figurer sur la liste dadresses, envoyer un message John Szczepaniak, Hardcore Gaming 101, 15 janvier 2011 Inscrivez-vous à notre newsletter afin de bénéficier de 5 sur votre première commande! On Saturday, Curatorial talk by Aliocha Imoff Kantuta Quiros, at Zurich University of the Arts On présentera une méthode de faisceau pour la minimisation de fonctions non différentiables et non convexes, puis on lappliquera à des problèmes doptimisation de lois de commande structurées issus de lindustrie aéronautique. 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