The dynamics of transition to turbulence in plane couette flow

Mathematics and Computation, a Contemporary View: The Abel Symposium 2006 - Proceedings of the 3rd Abel Symposium

Volumn , Issue , 2008, Pages 109-127

  Viswanath, D ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGEN-VALUE; INCOMPRESSIBLE FLUID; PLANE COUETTE FLOW; STREAM-WISE VELOCITIES; TRANSITION TO TURBULENCE; TRAVELING WAVE SOLUTION; WALL-NORMAL DIRECTION;

EIGENVALUES AND EIGENFUNCTIONS; LAMINAR FLOW; REYNOLDS NUMBER;

TURBULENCE;

EID: 84883626966     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-68850-1_6     Document Type: Conference Paper

References (21)

1. D. Acheson. Elementary Fluid Dynamics. Oxford University Press, Oxford, 1990.
2. K.H. Bech, N. Tillmark, P.H. Alfredsson, and H.I. Andersson. An investigation of turbulent plane Couette flow at low Reynolds number. Journal of Fluid Mechanics, 286: 291-325, 1995.
3. A. Cherhabili and U. Eherenstein. Finite-amplitude equilibrium states in plane Couette flow. Journal of Fluid Mechanics, 342: 159-177, 1997.
4. J.F. Gibson, J. Halcrow, and P. Cvitanovic. Visualizing the geometry of state space in plane Couette flow. Journal of Fluid Mechanics, 2008. To appear. Available at www.arxiv.org:0705.3957.
5. G. Kawahara. Laminarization of minimal plane Couette flow: going beyond the basin of attraction of turbulence. Physics of Fluids, 17:art. 041702, 2005.
6. S.J. Kline, W.C. Reynolds, F.A. Schraub, and P.W. Rundstadler. The structure of turbulent boundary layers. Journal of Fluid Mechanics, 30: 741-773, 1967.
7. G. Kreiss, A. Lundbladh, and D.S. Henningson. Bounds for threshold amplitudes in subcritical shear flows. Journal of Fluid Mechanics, 270: 175-198, 1994.
8. M. Lagha, T.M. Schneider, F. De Lillo, and B. Eckhardt. Laminar-turbulent boundary in plane Couette flow. 2007. preprint.
9. A. Lundbladh, D.S. Henningson, and S.C. Reddy. Threshold amplitudes for transition in channel flows. In M.Y. Hussaini, T.B. Gatski, and T.L. Jackson, editors, Turbulence and Combustion. Kluwer, Holland, 1994.
10. A.S. Monin and A.M. Yaglom. Statistical Fluid Mechanics. The MIT Press, Cambridge, 1971.
11. M. Nagata. Three dimensional finite amplitude solutions in plane Couette flow: bifurcation from infinity. Journal of Fluid Mechanics, 217: 519-527, 1990.
12. M. Nagata. Three-dimensional traveling-wave solutions in plane Couette flow. Physical Review E, 55: 2023-2025, 1997.
13. S.A. Orszag and L.C. Kells. Transition to turbulence in plane Poiseuille and plane Couette flow. Journal of Fluid Mechanics, 96: 159-205, 1980.
14. T.M. Schmiegel and B. Eckhardt. Fractal stability border in plane Couette flow. Physical Review letters, 79: 5250, 1997.
15. T.M. Schneider, B. Eckhardt, and J.A. Yorke. Turbulence transition and edge of chaos in pipe flow. Physical Review Letters, 99: 034502, 2007.
16. L.N. Trefethen, A.E. Trefethen, S.C. Reddy, and T.A. Driscoll. Hydrodynamic stability without eigenvalues. Science, 261: 578-584, 1993.
17. D. Viswanath. Recurrent motions within plane Couette turbulence. Journal of Fluid Mechanics, 580: 339-358, 2007.
18. F. Waleffe. Three-dimensional coherent states in plane shear flows. Physical Review Letters, 81: 4140-4143, 1998.
19. F. Waleffe. Exact coherent structures in channel flow. Journal of Fluid Mechanics, 435: 93-102, 2001.
20. F. Waleffe. Homotopy of exact coherent structures in plane shear flows. Physics of Fluids, 15: 1517-1534, 2003.
21. J. Wang, J.F. Gibson, and F Waleffe. Lower branch coherent states in shear flows: transition and control. Physical Review Letters, 98: 204501, 2007.