Turbulence Transition in Shear Flows and Dynamical Systems Theory

Turbulence is allegedly “the most important unsolved problem of classical physics” (attributed to Richard Feynman). While the equations of motion are known since almost 150 years and despite the work of many physicists, in particular the transition to turbulence in linearly stable shear flows eva...

Ausführliche Beschreibung

Gespeichert in:
1. Verfasser: Kreilos, Tobias
Beteiligte: Eckhardt, Bruno (Prof. Dr.) (BetreuerIn (Doktorarbeit))
Format: Dissertation
Sprache:Englisch
Veröffentlicht: Philipps-Universität Marburg 2014
Physik
Ausgabe:http://dx.doi.org/10.17192/z2014.0356
Schlagworte:
Online Zugang:PDF-Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!

1. http://archiv.ub.uni-marburg.de/diss/z2000/0062


2. http://archiv.ub.uni-marburg.de/diss/z2007/0539


3. van Veen, L., Kida, S., and Kawahara, G. Periodic motion representing isotropic turbulence. Fluid Dynamics Research, 38(1):19–46, 2006.


4. Gibson, J. F., Halcrow, J., and Cvitanović, P. Visualizing the geometry of state space in plane Couette flow. Journal of Fluid Mechanics, 611:107–130, 2008.


5. Duguet, Y., Willis, A. P., and Kerswell, R. R. Transition in pipe flow: the saddle structure on the boundary of turbulence. Journal of Fluid Mechanics, 613:255–274, 2008.


6. Lan, Y. and Cvitanović, P. Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics. Physical Review E, 78(2):026208, 2008.


7. Pringle, C. C. T., Duguet, Y., and Kerswell, R. R. Highly symmetric travelling waves in pipe flow. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 367(1888):457–472, 2009.


8. Schneider, T. M. and Eckhardt, B. Lifetime statistics in transitional pipe flow. Phys- ical Review E, 78:46310, 2008.


9. Halcrow, J., Gibson, J. F., Cvitanović, P., and Viswanath, D. Heteroclinic connections in plane Couette flow. Journal of Fluid Mechanics, 621:365–376, 2009.


10. Gibson, J. F., Halcrow, J., and Cvitanović, P. Equilibrium and traveling-wave solu- tions of plane Couette flow. Journal of Fluid Mechanics, 638:243–266, 2009.


11. Lagha, M. and Manneville, P. Modeling transitional plane Couette flow. The Euro- pean Physical Journal B, 58:433–447, 2007.


12. Lebovitz, N. R. Shear-flow transition: the basin boundary. Nonlinearity, 22:2645, 2009.


13. Avila, M., Willis, A. P., and Hof, B. On the transient nature of localized pipe flow turbulence. Journal of Fluid Mechanics, 646:127–136, 2010.


14. Schneider, T. M., Gibson, J. F., and Burke, J. Snakes and Ladders: Localized Solutions of Plane Couette Flow. Physical Review Letters, 104(10):104501, 2010b.


15. Mellibovsky, F. and Eckhardt, B. Takens-Bogdanov bifurcation of travelling-wave solutions in pipe flow. Journal of Fluid Mechanics, 670:96–129, 2011.


16. Froehlich, S. and Cvitanović, P. Reduction of continuous symmetries of chaotic flows by the method of slices. Communications in Nonlinear Science and Numerical Simulation, 17(5):2074–2084, 2012.


17. Barkley, D. Simplifying the complexity of pipe flow. Physical Review E, 84(1):016309, 2011a.


18. Sipos, M. and Goldenfeld, N. Directed percolation describes lifetime and growth of turbulent puffs and slugs. Physical Review E, 84(3):035304, 2011.


19. Manneville, P. Spatiotemporal perspective on the decay of turbulence in wall-bounded flows. Physical Review E, 79(2):025301, 2009.


20. van Veen, L. and Kawahara, G. Homoclinic tangle on the edge of shear turbulence. Physical Review Letters, 107:114501, 2011.


21. Barkley, D. Modeling the transition to turbulence in shear flows. Journal of Physics: Conference Series, 318:032001, 2011b.


22. Mellibovsky, F. and Eckhardt, B. From travelling waves to mild chaos: a supercritical bifurcation cascade in pipe flow. Journal of Fluid Mechanics, 709:149–190, 2012.


23. Willis, A. P., Cvitanović, P., and Avila, M. Revealing the state space of turbulent pipe flow by symmetry reduction. Journal of Fluid Mechanics, 721:514–540, 2013.


24. Kreilos, T. and Eckhardt, B. Periodic orbits near onset of chaos in plane Couette flow. Chaos: An Interdisciplinary Journal of Nonlinear Science, 22(4):047505, 2012.


25. Kreilos, T., Veble, G., Schneider, T. M., and Eckhardt, B. Edge states for the turbulence transition in the asymptotic suction boundary layer. Journal of Fluid Mechanics, 726:100–122, 2013.


26. Cvitanović, P., Borrero-Echeverry, D., Carroll, K. M., Robbins, B., and Siminos, E. Cartography of high-dimensional flows: a visual guide to sections and slices. Chaos, 22:047506, 2012b.


27. Avila, M., Mellibovsky, F., Roland, N., and Hof, B. Streamwise-Localized Solutions at the Onset of Turbulence in Pipe Flow. Physical Review Letters, 110(22):224502, 2013.


28. Biau, D. Laminar-turbulent separatrix in a boundary layer flow. Physics of Fluids, 24:034107, 2012.


29. Gibson, J. F. and Brand, E. Spatially localized solutions of shear flows. 2013.


30. Itano, T., Akinaga, T., Generalis, S. C., and Sugihara-Seki, M. Transition of Planar Couette Flow at infinite Reynolds numbers. arXiv:1306.2702, 2014.


31. Riols, A., Rincon, F., Cossu, C., Lesur, G., Longaretti, P.-Y., Ogilvie, G. I., and Herault, J. Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow. Journal of Fluid Mechanics, 731:1–45, 2013.


32. Khapko, T., Duguet, Y., Kreilos, T., Schlatter, P., Eckhardt, B., and Henningson, D. S. Complexity of localised coherent structures in a boundary-layer flow. The European Physical Journal E, 37(4):32, 2014.


33. Chantry, M., Willis, A. P., and Kerswell, R. R. The genesis of streamwise-localized solutions from globally periodic travelling waves in pipe flow. 2013.


34. Kreilos, T., Khapko, T., Schlatter, P., Duguet, Y., Henningson, D. S., and Eckhardt, B. Bypass transition in boundary layers as an activated process. Manuscript in preparation, 2014b. Bibliography Kreilos, T., Zammert, S., and Eckhardt, B. Comoving frames and symmetry-related dynamics in parallel shear flows. arXiv:1309.4590, 2014c.


35. Melnikov, K., Kreilos, T., and Eckhardt, B. Long-wavelength instability of coherent structures in plane Couette flow. Physical Review E, 89(4):043008, 2014.


36. Dauchot, O. and Bertin, E. The glass transition in a nutshell: a source of inspiration to describe the subcritical transition to turbulence. arXiv:1310.6967, 2014.


37. Kreilos, T., Eckhardt, B., and Schneider, T. M. Increasing Lifetimes and the Growing Saddles of Shear Flow Turbulence. Physical Review Letters, 112(4):044503, 2014a.


38. Zammert, S. and Eckhardt, B. Periodically bursting edge states in plane Poiseuille flow. arXiv:1312.6783, 2013.


39. Tuckerman, L. S., Kreilos, T., Schrobsdorff, H., Schneider, T. M., and Gibson, J. F. Turbulent-laminar patterns in plane Poiseuille flow. arXiv:1404.1502, 2014.


40. Zammert, S. and Eckhardt, B. A Fully Localised Periodic Orbit In Plane Poiseuille Flow. arXiv:1404.2582, 2014.


41. Brand, E. and Gibson, J. F. A doubly-localized equilibrium solution of plane Couette flow. arXiv:1404.2887, 2014.


42. Madré, T. Turbulence Transition in the Asymptotic Suction Boundary Layer, Diplo- marbeit, Philipps Universität Marburg, 2011, Philipps Universität Marburg.


43. Schmiegel, A. and Eckhardt, B. Fractal stability border in plane Couette Flow. Physical Review Letters, 79:5250–5253, 1997.


44. Eckhardt, B. Periodic Orbit Theory. arXiv:chao-dyn/9303015, 1991.


45. Hof, B., Juel, A., and Mullin, T. Scaling of the Turbulence Transition Threshold in a Pipe. Physical Review Letters, 91(24):244502, 2003.


46. Schneider, T. M., Eckhardt, B., and Yorke, J. A. Turbulence transition and the edge of chaos in pipe flow. Physical Review Letters, 99:34502, 2007b.


47. Faisst, H. and Eckhardt, B. Transition from the Couette-Taylor system to the plane Couette system. Physical Review E, 61:7227–7230, 2000. Bibliography Faisst, H. and Eckhardt, B. Traveling waves in pipe flow. Physical Review Letters, 91:224502, 2003.


48. Faisst, H. and Eckhardt, B. Sensitive dependence on initial conditions in transition to turbulence in pipe flow. Journal of Fluid Mechanics, 504:343–352, 2004.


49. Barkley, D. and Tuckerman, L. S. Computational Study of Turbulent Laminar Pat- terns in Couette Flow. Physical Review Letters, 94(1):014502, 2005.


50. Vinod, N. and Govindarajan, R. The signature of laminar instabilities in the zone of transition to turbulence. Journal of Turbulence, 8:N2, 2007.


51. Viswanath, D. Recurrent motions within plane Couette turbulence. Journal of Fluid Mechanics, 580:339–358, 2007.


52. Kerswell, R. R. and Tutty, O. R. Recurrence of travelling waves in transitional pipe flow. Journal of Fluid Mechanics, 584:69–102, 2007.


53. Schneider, T. M., Eckhardt, B., and Vollmer, J. Statistical analysis of coherent structures in transitional pipe flow. Physical Review E, 75:66313, 2007a.


54. Wang, J., Gibson, J. F., and Waleffe, F. Lower Branch Coherent States in Shear Flows: Transition and Control. Physical Review Letters, 98(20):204501, 2007.


55. Cross, M. C. and Hohenberg, P. C. Pattern formation outside of equilibrium. Reviews of Modern Physics, 65:851–1112, 1993.


56. Rowley, C. W., Kevrekidis, I. G., Marsden, J. E., and Lust, K. Reduction and recon- struction for self-similar dynamical systems. Nonlinearity, 16:1257–1275, 2003.


57. Waleffe, F. Hydrodynamic stability and turbulence: beyond transients to a self- sustaining process. Studies in applied mathematics, 95(3):319–343, 1995.


58. Navier, C. L. M. H. Mémoire sur les lois du mouvement des fluides. Mémoires de l'Académie Royale des Sciences de l'Institut de France, 6:389–440, 1823.


59. Frigo, M. and Johnson, S. The Design and Implementation of FFTW3. Proceedings of the IEEE, 93(2):216–231, 2005.


60. Wedin, H. and Kerswell, R. R. Exact coherent structures in pipe flow: travelling wave solutions. Journal of Fluid Mechanics, 508:333–371, 2004.


61. Meseguer, A. and Trefethen, L. N. Linearized pipe flow to Reynolds number 10 7 . Journal of Computational Physics, 186(1):178–197, 2003.


62. Taylor, G. I. The Spectrum of Turbulence. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 164(919):476–490, 1938.


63. Rowley, C. W. and Marsden, J. E. Reconstruction equations and the Karhunen–Loève expansion for systems with symmetry. Physica D: Nonlinear Phenomena, 142(1-2): 1–19, 2000.


64. Li, Y.-T. and Yorke, J. A. Period Three Implies Chaos. The American Mathematical Monthly1 , 82(10):985–992, 1975.


65. Christiansen, F., Cvitanović, P., and Putkaradze, V. Spatiotemporal chaos in terms of unstable recurrent patterns. Nonlinearity, 10:55, 1997.


66. Jiménez, J., Kawahara, G., Simens, M. P., Nagata, M., and Shiba, M. Character- ization of near-wall turbulence in terms of equilibrium and " bursting " solutions. Physics of Fluids, 17:15105, 2005.


67. Cvitanović, P. Invariant measurement of strange sets in terms of cycles. Physical Review Letters, 61:2729–2732, 1988.


68. Viswanath, P. R. Aircraft viscous drag reduction using riblets. Progress in Aerospace Sciences, 38(6-7):571–600, 2002. Bibliography Vollmer, J., Schneider, T. M., and Eckhardt, B. Basin boundary, edge of chaos and edge state in a two-dimensional model. New Journal of Physics, 11:013040, 2009.


69. Schoppa, W. and Hussain, F. Coherent structure generation in near-wall turbulence. Journal of Fluid Mechanics, 453:57–108, 2002.


70. Waleffe, F. Homotopy of exact coherent structures in plane shear flows. Physics of Fluids, 15:1517–1534, 2003.


71. Lorenz, E. N. Deterministic Nonperiodic Flow. Journal of the Atmospheric Sciences, 20:130–141, 1963.


72. Gutzwiller, M. C. Chaos in classical and quantum mechanics. Journal of Physics A: Mathematical and Theoretical, 43:285302, 1990.


73. Guckenheimer, J. and Holmes, P. Nonlinear oscillations, dynamical systems and bifurcations of vector fields, volume 42 of Applied Mathematical Sciences. Springer- Verlag, 1983.


74. Brosa, U. Turbulence without Strange Attractor. Journal of Statistical Physics, 55


75. Eckhardt, B. and Ott, G. Periodic orbit analysis of the Lorenz attractor. Zeitschrift für Physik B, 93:259–266, 1994.


76. Sivashinsky, G. I. Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations. Acta Astronautica, 4(11-12):1177–1206, 1977.


77. Metropolis, N., Stein, M. L., and Stein, P. R. On finite limit sets for transformations on the unit interval. Journal of Combinatorial Theory, Series A, 44:25–44, 1973.


78. Chaté, H. and Manneville, P. Spatio-temporal intermittency in coupled map lattices. Physica D: Nonlinear Phenomena, 32(3):409–422, 1988b.


79. Feigenbaum, M. J. The onset spectrum of turbulence. Physics Letters A, 74(6): 375–378, 1979.


80. Lebovitz, N. R. Boundary collapse in models of shear-flow transition. Communica- tions in Nonlinear Science and Numerical Simulation, 17:2095–2100, 2012.


81. Schlatter, P., Stolz, S., and Kleiser, L. LES of transitional flows using the approximate deconvolution model. International Journal of Heat and Fluid Flow, 25(3):549–558, 2004.


82. Cvitanović, P. Recurrent flows : the clockwork behind turbulence. Journal of Fluid Mechanics, 726:1–4, 2013.


83. Toh, S. and Itano, T. A periodic-like solution in channel flow. Journal of Fluid Mechanics, 481:67–76, 2003.


84. Fransson, J. H. M. and Alfredsson, P. H. On the disturbance growth in an asymptotic suction boundary layer. Journal of Fluid Mechanics, 482:51–90, 2003.


85. Brandt, L., Schlatter, P., and Henningson, D. S. Transition in boundary layers subject to free-stream turbulence. Journal of Fluid Mechanics, 517:167–198, 2004.


86. Peixinho, J. and Mullin, T. Finite-amplitude thresholds for transition in pipe flow. Journal of Fluid Mechanics, 582:169–178, 2007.


87. Salwen, H., Cotton, F. W., and Grosch, C. E. Linear stability of Poiseuille flow in a circular pipe. Journal of Fluid Mechanics, 98(2):273–284, 1980. Bibliography Saric, W. S., Reed, H. L., and Kerschen, E. J. Boundary-Layer Receptivity to Freestream Disturbances. Annual Review of Fluid Mechanics, 34:291–319, 2002.


88. Orszag, S. A. and Kells, L. C. Transition to turbulence in plane Poiseuille and plane Couette flow. Journal of Fluid Mechanics, 96(01):159–205, 1980.


89. Zaman, K. B. M. Q. and Hussain, A. K. M. F. Taylor hypothesis and large-scale coherent structures. Journal of Fluid Mechanics, 112:379–396, 1981.


90. Spalart, P. R. and Yang, K.-S. Numerical study of ribbon-induced transition in Blasius flow. Journal of Fluid Mechanics, 178:345–365, 1987.


91. Antonia, R. A., Fulachier, L., Krishnamoorthy, L. V., Benabid, T., and Anselmet, F. Influence of wall suction on the organized motion in a turbulent boundary layer. Journal of Fluid Mechanics, 190:217–240, 1988.


92. Jiménez, J. and Moin, P. The minimal flow unit in near-wall turbulence. Journal of Fluid Mechanics, 225:213–240, 1991.


93. Lundbladh, A. and Johansson, A. V. Direct simulation of turbulent spots in plane Couette flow. Journal of Fluid Mechanics, 229:499–516, 1991.


94. Darbyshire, A. G. and Mullin, T. Transition to turbulence in constant-mass-flux pipe flow. Journal of Fluid Mechanics, 289:83–114, 1995.


95. Gutzwiller, M. C. Periodic orbits and classical quantization conditions. Journal of Mathematical Physics, 12(3):343, 1971.


96. Moehlis, J., Eckhardt, B., and Faisst, H. Fractal lifetimes in the transition to turbu- lence. Chaos: An Interdisciplinary Journal of Nonlinear Science, 14:S11, 2004a.


97. Adrian, R. J. Hairpin vortex organization in wall turbulence. Physics of Fluids, 19 (4):041301, 2007.


98. Henningson, D. S., Spalart, P., and Kim, J. Numerical simulations of turbulent spots in plane Poiseuille and boundary-layer flow. Physics of Fluids, 30(10):2914, 1987.


99. Waleffe, F. On a self-sustaining process in shear flows. Physics of Fluids, 9:883–900, 1997.


100. Cvitanović, P. and Gibson, J. F. Geometry of the turbulence in wall-bounded shear flows: periodic orbits. Physica Scripta, T142:014007, 2010.


101. Busse, F. H. Non-linear properties of thermal convection. Reports on Progress in Physics, 41(12):1929, 1978.


102. Allhoff, K. T. and Eckhardt, B. Directed percolation model for turbulence transition in shear flows. Fluid Dynamics Research, 44(3):031201, 2012.


103. Kerswell, R. R. Recent progress in understanding the transition to turbulence in a pipe. Nonlinearity, 18(6):R17–R44, 2005.


104. Eckhardt, B. Turbulence transition in pipe flow: some open questions. Nonlinearity, 21:T1, 2008.


105. Mellibovsky, F. and Meseguer, A. Critical threshold in pipe flow transition. Philo- sophical transactions. Series A, Mathematical, physical, and engineering sciences, 367(1888):545–560, 2009.


106. Gebhardt, T. and Grossmann, S. Chaos transition despite linear stability. Physical Review E, 50(5):3705–3711, 1994.


107. Willis, A. P. and Kerswell, R. R. Coherent Structures in Localized and Global Pipe Turbulence. Physical Review Letters, 100(12):124501, 2008.


108. Stavans, J., Heslot, F., and Libchaber, A. Fixed Winding Number and the Quasiperi- odic Route to Chaos in a Convective Fluid. Physical Review Letters, 55(11):1239, 1985.


109. Chaté, H. and Manneville, P. Transition to turbulence via spatio-temporal intermit- tency. Physical Review Letters, 58(2):112–115, 1987.


110. Crutchfield, J. P. and Kaneko, K. Are Attractors Relevant to Turbulence? Physical Review Letters, 60(26):2715–2719, 1988.


111. Tuckerman, L. S. and Barkley, D. Global Bifurcations to Traveling Waves in Axisym- metric Convection. Physical Review Letters, 61(4):408–411, 1988.


112. Prigent, A., Grégoire, G., Chaté, H., Dauchot, O., and van Saarloos, W. Large-Scale Finite-Wavelength Modulation within Turbulent Shear Flows. Physical Review Letters, 89(1):014501, 2002.


113. Skufca, J. D., Yorke, J. A., and Eckhardt, B. Edge of chaos in a parallel shear flow. Physical Review Letters, 96:174101, 2006.


114. Willis, A. P. and Kerswell, R. R. Critical Behavior in the Relaminarization of Local- ized Turbulence in Pipe Flow. Physical Review Letters, 98:014501, 2007.


115. Pringle, C. C. T. and Kerswell, R. R. Asymmetric, Helical, and Mirror-Symmetric Traveling Waves in Pipe Flow. Physical Review Letters, 99(7):074502, 2007.


116. Grossmann, S. The onset of shear flow turbulence. Reviews of Modern Physics, 72: 603–618, 2000.


117. Newhouse, S., Ruelle, D., and Takens, F. Occurrence of strange Axiom A attractors near quasi periodic flows on T m , m ≥ 3. Communications in Mathematical Physics, 64:35–40, 1978.


118. Itano, T. and Toh, S. The dynamics of bursting process in wall turbulence. Journal of the Physics Society of Japan, 8502(3):703–716, 2001.


119. Bottin, S., Daviaud, F., Manneville, P., and Dauchot, O. Discontinuous transition to spatiotemporal intermittency in plane Couette flow. Europhysics Letters, 43(2): 171–176, 1998.


120. Alfredsson, P. and Matsubara, M. Free-stream turbulence, streaky structures and transition in boundary layer flows. In Fluids 2000 Conference and Exhibit, Reston, Virigina, 2000. American Institute of Aeronautics and Astronautics.


121. Kline, S. J., Reynolds, W. C., Schraub, F. A., and Runstadler, P. W. The structure of turbulent boundary layers. Journal of Fluid Mechanics, 30(04):741–773, 1967.


122. Dhawan, S. and Narasimha, R. Some properties of boundary layer flow during the transition from laminar to turbulent motion. Journal of Fluid Mechanics, 3(04): 418–436, 1957.


123. Hamilton, J. M., Kim, J., and Waleffe, F. Regeneration mechanisms of near-wall turbulence structures. Journal of Fluid Mechanics, 287:317–348, 1995.


124. Townsend, A. A. The structure of turbulent shear flow. Cambridge University Press, 1980. ISBN 9780521298193.


125. Maurer, J. and Libchaber, A. Rayleigh-Bénard experiment in liquid helium ; fre- quency locking and the onset of turbulence. Journal de Physique Lettres, 40(16): 419–423, 1979.


126. Ott, E. Chaos in Dynamical Systems. Cambridge University Press, 1993. ISBN 9780521010849.


127. Cherubini, S., De Palma, P., Robinet, J.-C., and Bottaro, A. Edge states in a bound- ary layer. Physics of Fluids, 23:051705, 2011.


128. Halcrow, J. Charting the state space of plane Couette flow: Equilibria, relative equi- libria, and heteroclinic connections. PhD thesis, Georgia Institute of Technology, 2008.


129. Blasius, H. Grenzschichten in Flüssigkeiten mit kleiner Reibung. PhD thesis, Göttin- gen, 1907.


130. Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A. Spectral Methods in Fluid Dynamics. Springer Berlin Heidelberg, Berlin, Heidelberg, 1988. ISBN 978-3-540-52205-8.


131. Joslin, R. D. Aircraft laminar flow control. Annual Review of Fluid Mechanics, 30: 1–29, 1998.


132. Schlichting, H. Boundary-layer theory. Springer, 2004. ISBN 9783540662709.


133. Lai, Y.-C. and Tél, T. Transient Chaos: Complex Dynamics on Finite Time Scales. Springer, 2011. ISBN 9781441969873.


134. de Lozar, A., Mellibovsky, F., Avila, M., and Hof, B. Edge State in Pipe Flow Experiments. Physical Review Letters, 108(21):214502, 2012.


135. Kawahara, G. Laminarization of minimal plane Couette flow: Going beyond the basin of attraction of turbulence. Physics of Fluids, 17(4):041702, 2005.


136. Eckhardt, B., Faisst, H., Schmiegel, A., and Schneider, T. M. Dynamical systems and the transition to turbulence in linearly stable shear flows. Philosophical transac- tions. Series A, Mathematical, physical, and engineering sciences, 366:1297–1315, 2008.


137. Mellibovsky, F., Meseguer, A., Schneider, T. M., and Eckhardt, B. Transition in Localized Pipe Flow Turbulence. Physical Review Letters, 103(5):054502, 2009.


138. Khapko, T., Kreilos, T., Schlatter, P., Duguet, Y., Eckhardt, B., and Henningson, D. S. Localized edge states in the asymptotic suction boundary layer. Journal of Fluid Mechanics, 717:R6, 2013.


139. Schneider, T. M. and Eckhardt, B. Edge states intermediate between laminar and tur- bulent dynamics in pipe flow. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 367(1888):577–587, 2009.


140. Chaté, H. and Manneville, P. Continuous and Discontinuous Transition to Spatio- Temporal Intermittency in Two-Dimensional Coupled Map Lattices. Europhysics Letters (EPL), 6(7):591–595, 1988a.


141. Moehlis, J., Faisst, H., and Eckhardt, B. A low-dimensional model for turbulent shear flows. New Journal of Physics, 6:56, 2004b.


142. Schlatter, P. and Örlü, R. Turbulent asymptotic suction boundary layers studied by simulation. Journal of Physics: Conference Series, 318(2):022020, 2011.


143. Lai, Y.-C. and Grebogi, C. Converting transient chaos into sustained chaos by feed- back control. Physical Review E, 49(2):1094–1098, 1994.


144. Nagata, M. Three-dimensional traveling-wave solutions in plane Couette flow. Phys- ical Review E, 55:2023–2025, 1997.


145. Duriez, T., Aider, J.-L., and Wesfreid, J. Self-Sustaining Process through Streak Generation in a Flat-Plate Boundary Layer. Physical Review Letters, 103(14): 144502, 2009.


146. Waleffe, F. Three-dimensional coherent states in plane shear flows. Physical Review Letters, 81:4140–4143, 1998.


147. Abshagen, J., Lopez, J., Marques, F., and Pfister, G. Symmetry Breaking Via Global Bifurcations of Modulated Rotating Waves in Hydrodynamics. Physical Review Letters, 94(7):074501, 2005.


148. Eckmann, J. Roads to turbulence in dissipative dynamical systems. Reviews of Modern Physics, 53:643–654, 1981.


149. Adrian, R. J., Meinhart, C. D., and Tomkins, C. D. Vortex organization in the outer region of the turbulent boundary layer. Journal of Fluid Mechanics, 422:1–54, 2000.


150. Waleffe, F. Exact coherent structures in channel flow. Journal of Fluid Mechanics, 435:93–102, 2001.


151. Kawahara, G. and Kida, S. Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst. Journal of Fluid Mechanics, 449:291–300, 2001. Bibliography Kawahara, G., Uhlmann, M., and van Veen, L. The significance of simple invariant solutions in turbulent flows. Annual Review of Fluid Mechanics, 44(1):203–225, 2012.


152. Hoepffner, J., Brandt, L., and Henningson, D. S. Transient growth on boundary layer streaks. Journal of Fluid Mechanics, 537:91–100, 2005.


153. Levin, O. and Henningson, D. S. Turbulent spots in the asymptotic suction boundary layer. Journal of Fluid Mechanics, 584:397–413, 2007.


154. Del Álamo, J. C. and Jiménez, J. Estimation of turbulent convection velocities and corrections to Taylor's approximation. Journal of Fluid Mechanics, 640:5–26, 2009.


155. Klebanoff, P. S., Tidstrom, K. D., and Sargent, L. M. The three-dimensional nature of boundary-layer instability. Journal of Fluid Mechanics, 12(01):1–34, 1962.


156. Orszag, S. A. Accurate solution of the Orr–Sommerfeld stability equation. Journal of Fluid Mechanics, 50(04):689–703, 1971.


157. Wygnanski, I. J. and Champagne, F. H. On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug. Journal of Fluid Mechanics, 59 (2):281–335, 1973.


158. Blackwelder, R. F. and Eckelmann, H. Streamwise vortices associated with the burst- ing phenomenon. Journal of Fluid Mechanics, 94(03):577–594, 1979.


159. Nagata, M. Three-dimensional finite-amplitude solutions in plane Couette flow: bi- furcation from infinity. Journal of Fluid Mechanics, 217:519–527, 1990.


160. Jeong, J., Hussain, F., Schoppa, W., and Kim, J. Coherent structures near the wall in a turbulent channel flow. Journal of Fluid Mechanics, 332:185–214, 1997.


161. Schlatter, P., Brandt, L., de Lange, H. C., and Henningson, D. S. On streak break- down in bypass transition. Physics of Fluids, 20:101505, 2008.


162. Hanson, J. D., Cary, J. R., and Meiss, J. D. Algebraic decay in self-similar Markov chains. Journal of Statistical Physics, 39(3-4):327–345, 1985.


163. Bottin, S. and Chaté, H. Statistical analysis of the transition to turbulence in plane Couette flow. The European Physical Journal B -Condensed Matter and Complex Systems, 6(1):143–155, 1998.


164. Ott, E. Strange attractors and chaotic motions of dynamical systems. Reviews of Modern Physics, 53:655–671, 1981.


165. Reynolds, O. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinous and the law of resistance in parallel channels. Philosophical Transactions of the Royal Society, 174:935–982, 1883.


166. Chevalier, M., Schlatter, P., Lundbladh, A., and Henningson, D. S. A pseudo-spectral solver for incompressible boundary layer flows. Technical report, KTH Mechanics, Stockholm, Sweden, 2007.


167. Koschmieder, E. L. Bénard Cells and Taylor vortices. Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge University Press, 1993. ISBN 9780521402040.


168. Reshotko, E. Boundary-Layer Stability and Transition. Annual Review of Fluid Mechanics, 8:311–349, 1976.


169. Gibson, J. F. Channelflow: A spectral Navier-Stokes simulator in C++. Technical report, U. New Hampshire, 2012. URL Channelflow.org.


170. Cvitanović, P., Artuso, R., Mainieri, G., Tanner, G., and Vattay, G. Chaos: Classical and quantum. ChaosBook.org Niels Bohr Institute Copenhagen, 14 edition, 2012a.


171. Danforth, C. M. "Chaos in an Atmosphere Hanging on a Wall", 2013. URL http: //mpe2013.org/2013/03/17/chaos-in-an-atmosphere-hanging-on-a-wall/, Accessed 04.04.2014.


172. Robinson, S. K. Coherent motions in the turbulent boundary layer. Annual Review of Fluid Mechanics, 23(1):601–639, 1991.


173. Mariani, P., Spalart, P., and Kollmann, W. Direct simulation of a turbulent boundary layer with suction. Near-wall turbulent flows, pages 347–356, 1993.


174. Tsukahara, T., Seki, Y., Kawamura, H., and Tochio, D. DNS of Turbulent Channel Flow with Very Low Reynolds Numbers. In Proceedings of the 4th International Symposium on Turbulence and Shear Flow Phenomena, pages 935–940, 2005.


175. Moffatt, H. K. Fixed points of turbulent dynamical systems and suppression of nonlinearity. Whither Turbulence? Turbulence at the Crossroads, 357:250–257, 1990.


176. Andereck, C. D., Liu, S. S., and Swinney, H. L. Flow regimes in a circular Couette system with independently rotating cylinders. Journal of Fluid Mechanics, 164: 155–183, 1986.


177. Bayly, B. J., Orszag, S. A., and Herbert, T. Instability mechanisms in shear-flow transition. Annual Review of Fluid Mechanics, 20:359–391, 1988.


178. Fransson, J. H. M. Investigations of the asymptotic suction boundary layer. PhD thesis, KTH, Stockholm, 2001.


179. Schneider, T. M., Gibson, J. F., Lagha, M., De Lillo, F., and Eckhardt, B. Laminar- turbulent boundary in plane Couette flow. Physical Review E, 78:37301, 2008. Bibliography Schneider, T. M., De Lillo, F., Buehrle, J., Eckhardt, B., Dörnemann, T., Dörnemann, K., and Freisleben, B. Transient turbulence in plane Couette flow. Physical Review E, 81:015301(R), 2010a.


180. Poincaré, H. Les méthodes nouvelles de la mécanique céleste, volume 10. Gauthier- Villars, Paris, 1892. Bibliography Pomeau, Y. and Manneville, P. Intermittent Transition to Turbulence in Dissipative Dynamical Systems. Communications in Mathematical Physics, 74:189–197, 1980.


181. Marinc, D. Localised edge-states in plane Couette flow, Diplomarbeit, Philipps Uni- versität Marburg, 2008, Philipps Universität Marburg. Bibliography Matsubara, M. and Alfredsson, P. H. Disturbance growth in boundary layers sub- jected to free-stream turbulence. Journal of Fluid Mechanics, 430:149–168, 2001.


182. Duguet, Y., Schlatter, P., and Henningson, D. S. Localized edge states in plane Couette flow. Physics of Fluids, 21:111701, 2009. Bibliography Duguet, Y., Schlatter, P., and Henningson, D. S. Formation of turbulent patterns near the onset of transition in plane Couette flow. Journal of Fluid Mechanics, 650:119–129, 2010a.


183. Theodorsen, T. Mechanism of turbulence. In Proceedings of the Second Midwestern Conference on Fluid Mechanics, pages 1–18. Ohio State University, 1952.


184. Head, M. R. and Bandyopadhyay, P. New aspects of turbulent boundary-layer struc- ture. Journal of Fluid Mechanics, 107:297–338, 1981.


185. Strogatz, S. H. Nonlinear dynamics and chaos: With applications to physics, biology, chemistry, and engineering. 1994. ISBN 9780738204536. Bibliography Tasaka, Y., Schneider, T. M., and Mullin, T. Folded Edge of Turbulence in a Pipe. Physical Review Letters, 105(17):174502, 2010.


186. Hocking, L. M. Non-linear instability of the asymptotic suction velocity profile. Quarterly Journal of Mechanics and Applied Mathematics, 28(3):341, 1975.


187. Wygnanski, I. J., Sokolov, M., and Friedman, D. On a turbulent 'spot' in a laminar boundary layer. Journal of Fluid Mechanics, 78(04):785–819, 1976.


188. Thibert, J. J., Reneaux, J., and Schmitt, V. ONERA activities on drag reduction. In 17th ICAS Congress, Stockolm (Sweden), September 9-14, 1990.


189. Narasimha, R. On the distribution of intermittency in the transition region of a boundary layer. Journal of the Aeronautical Sciences, 24(9):711–712, 1957.


190. Jeong, J. and Hussain, F. On the identification of a vortex. Journal of Fluid Me- chanics, 285:69–94, 1995.


191. Morkovin, M. V. On the many faces of transition. In Wells, C., editor, Viscous drag reduction, pages 1–31. Springer US, 1969. ISBN 978-1-4899-5581-4. Bibliography Moxey, D. and Barkley, D. Distinct large-scale turbulent-laminar states in transitional pipe flow. Proceedings of the National Academy of Sciences of the United States of America, 107(18):8091–8096, 2010.


192. Stokes, G. G. On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids. Transactions of the Cambridge Philosoph- ical Society, 8:287–305, 1845.


193. Cvitanović, P. and Eckhardt, B. Periodic-orbit quantization of chaotic systems. Phys- ical Review Letters, 63(8):823–826, 1989. Bibliography Cvitanović, P. and Eckhardt, B. Periodic orbit expansions for classical smooth flows. Journal of Physics A: Mathematical and General, 24(5):L237–L241, 1991.


194. Schmid, P. J. and Henningson, D. S. Stability and Transition in Shear Flows. Number Bd. 142 in Applied mathematical sciences. Springer, 2001. ISBN 9780387989853.


195. Romanov, V. A. Stability of plane-parallel Couette flow. Functional Analysis and Its Applications, 7(2):137–146, 1973.


196. Clever, R. M. and Busse, F. H. Tertiary and quaternary solutions for plane Couette flow. Journal of Fluid Mechanics, 344:137–153, 1997.


197. Aubry, N., Holmes, P., Lumley, J. L., and Stone, E. The dynamics of coherent struc- tures in the wall region of a turbulent boundary layer. Journal of Fluid Mechanics, 192:115–173, 1988. Bibliography Avila, K., Moxey, D., de Lozar, A., Avila, M., Barkley, D., and Hof, B. The onset of turbulence in pipe flow. Science, 333(6039):192–196, 2011.


198. Emmons, H. W. The Laminar-Turbulent Transition in a Boundary Layer-Part I. Journal of the Aeronautical Sciences, 18(7):490–498, 1951.


199. Smale, S. Topology and mechanics. I. Inventiones Mathematicae, 10(4):305–331, 1970.


200. Fransson, J. H. M., Matsubara, M., and Alfredsson, P. H. Transition induced by free-stream turbulence. Journal of Fluid Mechanics, 527:1–25, 2005.


201. Andersson, P., Brandt, L., Bottaro, A., and Henningson, D. S. On the breakdown of boundary layer streaks. Journal of Fluid Mechanics, 428:29–60, 2001.


202. Ruelle, D. and Takens, F. On the Nature of Turbulence. Communications in Mathe- matical Physics, 20(3):167–192, 1971.


203. Schneider, T. M., Marinc, D., and Eckhardt, B. Localized edge states nucleate tur- bulence in extended plane Couette cells. Journal of Fluid Mechanics, 646:441–451, 2010c.


204. Levin, O., Davidsson, E. N., and Henningson, D. S. Transition thresholds in the asymptotic suction boundary layer. Physics of Fluids, 17:114104, 2005.


205. Narasimha, R. The laminar-turbulent transition zone in the boundary layer. Progress in Aerospace Sciences, 22(1):29–80, 1985.


206. Vinod, N. and Govindarajan, R. Pattern of Breakdown of Laminar Flow into Turbu- lent Spots. Physical Review Letters, 93(11):114501, 2004.


207. Hof, B., de Lozar, A., Kuik, D. J., and Westerweel, J. Repeller or Attractor? Selecting the Dynamical Model for the Onset of Turbulence in Pipe Flow. Physical Review Letters, 101:214501, 2008.


208. Duguet, Y., Schlatter, P., Henningson, D. S., and Eckhardt, B. Self-sustained lo- calized structures in a boundary-layer flow. Physical Review Letters, 108:044501, 2012.


209. Jiménez, J. and Moser, R. D. What are we learning from simulating wall turbulence? Philosophical transactions. Series A, Mathematical, physical, and engineering sci- ences, 365:715–732, 2007.


210. Gollub, J. P. and Swinney, H. L. Onset of Turbulence in a Rotating Fluid. Physical Review Letters, 35(14):927–930, 1975.


211. Andersson, P., Berggren, M., and Henningson, D. S. Optimal disturbances and bypass transition in boundary layers. Physics of Fluids, 11:134–150, 1999.


212. Duguet, Y., Monokrousos, A., Brandt, L., and Henningson, D. S. Minimal transition thresholds in plane Couette flow. Physics of Fluids, 25(8):084103, 2013.


213. Hopf, E. A mathematical example displaying features of turbulence. Communications on Pure and Applied Mathematics, 1(4):303–322, 1948.


214. Khapko, T. Transition to turbulence in the asymptotic suction boundary layer. Tech- nical report, Royal Institute of Technology, Department of Mechanics, Stockholm, Sweden, 2014.


215. Mullin, T. Experimental studies of transition to turbulence in a pipe. Annual Review of Fluid Mechanics, 43(1):1–24, 2011.


216. Peixinho, J. and Mullin, T. Decay of Turbulence in Pipe Flow. Physical Review Letters, 96:094501, 2006.


217. Moin, P. and Kim, J. Tackling Turbulence with Supercomputers. Scientific American, 276:62–68, 1997.


218. Kadanoff, L. P. and Tang, C. Escape from strange repellers. Proceedings of the National Academy of Sciences of the United States of America, 81(4):1276–1279, 1984.


219. Grebogi, C., Ott, E., and Yorke, J. A. Crises, sudden changes in chaotic attractors, and transient chaos. Physica D: Nonlinear Phenomena, 7(1-3):181–200, 1983. Bibliography Grebogi, C., Ott, E., and Yorke, J. A. Critical exponent of chaotic transients in nonlinear dynamical systems. Physical Review Letters, 57:1284–1287, 1986.


220. Armbruster, D., Guckenheimer, J., and Holmes, P. Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry. Physica D, 29(3):257–282, 1988.


221. Smith, T. R., Moehlis, J., and Holmes, P. Heteroclinic cycles and periodic orbits for the O(2)-equivariant 0:1:2 mode interaction. Physica D, 211(3-4):347–376, 2005.


222. Hof, B., van Doorne, C. W. H., Westerweel, J., Nieuwstadt, F. T. M., Faisst, H., Eckhardt, B., Wedin, H., Kerswell, R. R., and Waleffe, F. Experimental observation of nonlinear traveling waves in turbulent pipe flow. Science, 305:1594–1598, 2004. Bibliography Hof, B., Westerweel, J., Schneider, T. M., and Eckhardt, B. Finite lifetime of turbu- lence in shear flows. Nature, 443:59–62, 2006.


223. Duguet, Y., Willis, A. P., and Kerswell, R. R. Slug genesis in cylindrical pipe flow. Journal of Fluid Mechanics, 663:180–208, 2010b.