Optimal and robust control of streaks in pipe flow

Journal of Fluid Mechanics

Volumn 537, Issue , 2005, Pages 187-219

  Gavarini, M I ^a   Bottaro, A ^b   Nieuwstadt, F T M ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF GENOA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; FLOW CONTROL; GREEN'S FUNCTION; ITERATIVE METHODS; MATRIX ALGEBRA; NAVIER STOKES EQUATIONS; OPTIMIZATION; REYNOLDS NUMBER; WALL FLOW;

FLOW STRUCTURES; PARABOLIC APPROXIMATION;

PIPE FLOW;

PIPE FLOW;

EID: 23944513564     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112005005070     Document Type: Article

References (34)

1. Abergel, F. & Temam, R. 1990 On some control problems in fluid mechanics. Theoret. Comput. Fluid Dyn. 1, 303-325.
2. Airiau, C., Bottaro, A., Walther, S. & Legendre, D. 2003 a methodology for optimal laminar flow control: Application to the damping of Tollmien Schlichting waves in a boundary layer. Phys. Fluids 15, 1131-1145.
3. Anderson, P., Berggren, M. & Henningson, D. S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11, 134-150.
4. Bergström, L. 1993 Optimal growth of small disturbances in pipe Poiseuille flow. Phys. Fluids A 5, 2710-2720.
5. Bewley, T. R. & Liu, S. 1998 Optimal and robust control and estimation of linear paths to transition. J. Fluid Mech. 365, 305-349.
6. Bewley, T. R., Temam, R. & Ziane, M. 2000 A general framework for robust control in fluid mechanics. Physica D 138, 360-392.
7. Boberg, L. & Brosa, U. 1988 Onset of turbulence in a pipe. Z. Naturforsch. 43a, 697-726.
8. Butler, K. M. & Farrell, B. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4, 1637-1650.
9. Cathalifaud, P. & Bewley, T. 2004a A noncausal framework for model-based feedback control of spatially developing perturbations in boundary-layer flow systems. Part i: Formulation. Syst. Control Lett. 51, 1-13.
10. Cathalifaud, P. & Bewley, T. 2004b A noncausal framework for model-based feedback control of spatially developing perturbations in boundary-layer flow systems. Part ii: Numerical simulations using state feedback. Syst. Control Lett. 51, 15-22.
11. Cathalifaud, P. & Luchini P. 2000 Algebraic growth in boundary layers: optimal control by blowing and suction at the wall. Eur. J. Mech. Fluids B 19, 469-490.
12. Corbett, P. & Bottaro, A. 2001a Optimal control of nonmodal disturbances in boundary layers. Theoret. Comput. Fluid Dyn. 15, 65-81.
13. Corbett, P. & Bottaro, A. 2001b Optimal linear growth in swept boundary layers. J. Fluid Mech. 435, 1-23.
14. Eggels, J. G. M., Unger, F., Weiss, M. H., Westerweel, J., Adrian, R. J., Friedrich, R. & Nieuwstadt, F. T. M. 1994 Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J. Fluid Mech. 268, 175-209.
15. Farrell, B. 1988 Optimal excitation of perturbations in viscous shear flow. Phys. Fluids 31, 2093-2102.
16. Gavarini, M. I., Bottaro, A. & Nieuwstadt, F. T. M. 2004 The initial stage of transition in pipe flow: role of optimal base-flow distortions. J. Fluid Mech. 517, 131-165.
17. Gill, A. E. 1965 A mechanism for instability of plane Couette flow and of Poiseuille flow in a pipe. J. Fluid Mech. 21, 503-511.
18. Gunzburger, M. D. 1997 Introduction into mathematical aspects of flow control and optimization. In Inverse design and optimization methods, pp. 1-20, von Kármán Institute for Fluid Dynamics Lecture Series Number 1997-05. Von Karman Institute, Brussels.
19. Gad-El Hak, M. 2000 Flow Control. Passive, Active, and Reactive Flow Management. Cambridge University Press.
20. Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flow. J. Fluid Mech. 98, 243-251.
21. Luchini, P. 1996 Reynolds-number-independent instability of the boundary layer over a flat surface. J. Fluid Mech. 327, 101-115.
22. Luchini, P. 2000 Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289-309.
23. Luchini, P. & Bottaro, A. 1998 Görtler vortices: a backward-in-time approach to the receptivity problem. J. Fluid Mech. 363, 1-23.
24. Meseguer, A. 2003 Streak breakdown instability in pipe Poiseuille flow. Phys. Fluids 15, 1203-1213.
25. Milling, R. 1981 Tollmien-Schlichting wave cancellation. Phys. Fluids 24, 979-981.
26. Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1992 Numerical Recipes in C, 2nd edn. Cambridge University Press, Cambridge.
27. Reshotko, E. & Tumin, A. 2001 Spatial theory of optimal disturbances in a circular pipe flow. Phys. Fluids 13, 991-996.
28. Schmid, P. J. & Henningson D. S. 1994 Optimal energy density growth in Hagen-Poiscuille flow. J. Fluid Mech. 277, 197-225.
29. Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.
30. Thomas, A. 1983 The control of boundary layer transition using a wave superposition principle. J. Fluid Mech. 137, 233-250.
31. Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578-584.
32. Zhou, K. & Doyle, J. 1998 Essentials of Robust Control. Prentice-Hall, Englewood Cliffs, NJ.
33. Zikanov, O. Y. 1996 On the instability of pipe Poiseuille flow. Phys. Fluids 8, 2923-2932.
34. Zuccher, S., Luchini, P. & Bottaro, A. 2004 Algebraic growth in a Blasius boundary layer: optimal and robust control by mean suction in the nonlinear regime. J. Fluid Mech. 513, 135-160.