The effects of non-normality and nonlinearity of the Navier-Stokes operator on the dynamics of a large laminar separation bubble

Physics of Fluids

Volumn 22, Issue 1, 2010, Pages 1-15

  Cherubini, S ^a   Robinet, J Ch ^b   De Palma, P ^a  

^a POLITECNICO DI BARI   (Italy)

^b DYNFLUID LABORATORY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; LAMINAR FLOW; MATHEMATICAL OPERATORS; NUMERICAL MODELS; REYNOLDS NUMBER; SENSITIVITY ANALYSIS;

FINITE-AMPLITUDE PERTURBATIONS; LAMINAR SEPARATION BUBBLE; LINEAR SENSITIVITY ANALYSIS; LOW FREQUENCY OSCILLATIONS; PHYSICAL INTERPRETATION; SMALL AMPLITUDE PERTURBATIONS; SUBCRITICAL REYNOLDS NUMBERS; TRANSIENT AMPLIFICATION;

NAVIER STOKES EQUATIONS;

EID: 77951049181     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.862466     Document Type: Article

References (36)

1. Schmid P. Henningson D. Stability and Transition in Shear Flows 2001, and, (Springer, New York).
2. Schmid P.J. Nonmodal stability theory. Annu. Rev. Fluid Mech. 2007, 39:129. ARVFA3, 0066-4189, 10.1146/annurev.fluid.38.050304.092139
3. Rist U. Maucher U. Direct numerical simulation of 2-d and 3-d instability waves in a laminar separation bubble. 1994, 361. AGARD-CP.551
4. Barkley D. Gomes G.M. Henderson R.D. Three-dimensional instability in flow over a backward-facing step. J. Fluid Mech. 2002, 473:167. JFLSA7, 0022-1120, 10.1017/S002211200200232X
5. Beaudoin J.-F. Cadot O. Aider J.-L. Wesfreid J.E. Three-dimensional stationary flow over a backward-facing step. Eur. J. Mech. B/Fluids 2004, 23:147. EJBFEV, 0997-7546, 10.1016/j.euromechflu.2003.09.010,
6. Blackburn H. Barkley D. Sherwin S. Convective instability and transient growth in flow over a backward-facing step. J. Fluid Mech. 2008, 603:271. JFLSA7, 0022-1120, 10.1017/S0022112008001109
7. Marino L. Luchini P. Adjoint analysis of the flow over a forward-facing step. Theor. Comput. Fluid Dyn. 2009, 23:37. TCFDEP, 0935-4964, 10.1007/s00162-008-0090-5
8. Ehrenstein U. Gallaire F. Global low-frequency oscillations in a separating boundary-layer flow. J. Fluid Mech. 2008, 614:315. JFLSA7, 0022-1120, 10.1017/S0022112008003285
9. Gallaire F. Marquillie M. Ehrenstein U. Three-dimensional transverse instabilities in detached boundary-layers. J. Fluid Mech. 2007, 571:221. JFLSA7, 0022-1120, 10.1017/S0022112006002898
10. Marquillie M. Ehrenstein U. On the onset of nonlinear oscillations in a separating boundary-layer flow. J. Fluid Mech. 2003, 490:169. JFLSA7, 0022-1120, 10.1017/S0022112003005287
11. Williams P.T. Baker A.J. Numerical simulations of laminar flow over a 3D backward-facing step. Int. J. Numer. Methods Fluids 1997, 24:1159. IJNFDW, 0271-2091, 10.1002/(SICI)1097-0363(19970615)24:11<1159::AID-FLD534>3.0.CO;2-R
12. Theofilis V. Hein S. Dallmann U. On the origins of unsteadiness and three dimensionality in a laminar separation bubble. Philos. Trans. R. Soc. London, Ser. A 2000, 358:3229. PTRMAD, 0962-8428, 10.1098/rsta.2000.0706
13. Cherry N. Hillier R. Latour M. Unsteady measurements in a separated and reattaching flow. J. Fluid Mech. 1984, 144:13. JFLSA7, 0022-1120, 10.1017/S002211208400149X
14. Pauley L. Moin P. Reynolds W. The structure of two-dimensional separation. J. Fluid Mech. 1990, 220:397. JFLSA7, 0022-1120, 10.1017/S0022112090003317
15. Alizard F. Cherubini S. Robinet J.C. Sensitivity and optimal forcing response in separated boundary layer flows. Phys. Fluids 2009, 21:064108. PHFLE6, 1070-6631, 10.1063/1.3153908
16. Marquet O. Sipp D. Chomaz J.-.M. Jacquin L. Amplifier and resonator dynamics of a low-Reynolds-number recirculation bubble in a global framework. J. Fluid Mech. 2008, 605:429. JFLSA7, 0022-1120, 10.1017/S0022112008000323
17. Dovgal A.V. Kozlov V.V. Michalke A. Laminar boundary layer separation: Instability and associated phenomena. Prog. Aerosp. Sci. 1994, 30:61. PAESD6, 0376-0421, 10.1016/0376-0421(94)90003-5
18. Schmid P.J. Henningson D.S. On the stability of a falling liquid curtain. J. Fluid Mech. 2002, 463:163. JFLSA7, 0022-1120, 10.1017/S002211200200873X
19. Akervik E. Ehrenstein U. Gallaire F. Henningson D.S. Global two-dimensional stability measures of the flat plate boundary-layer flow. Eur. J. Mech. B/Fluids 2008, 27:501. EJBFEV, 0997-7546, 10.1016/j.euromechflu.2007.09.004,
20. Alizard F. Robinet J.-C. Spatially convective global modes in a boundary layer. Phys. Fluids 2007, 19:114105. PHFLE6, 1070-6631, 10.1063/1.2804958
21. Ehrenstein U. Gallaire F. On two dimensional temporal modes in spatially evolving open flows: The flat-plate boundary layer. J. Fluid Mech. 2005, 536:209. JFLSA7, 0022-1120, 10.1017/S0022112005005112
22. Verzicco R. Orlandi P. A finite-difference scheme for the three-dimensional incompressible flows in cylindrical coordinates. J. Comput. Phys. 1996, 123:402. JCTPAH, 0021-9991, 10.1006/jcph.1996.0033
23. Chu P. Fan C. A three point sixth-order non uniform combined compact difference scheme. J. Comput. Phys. 1999, 148:663. JCTPAH, 0021-9991, 10.1006/jcph.1998.6141
24. Tuckerman L.S. Barkley D. Bifurcation analysis for timesteppers. Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems 2000, 119:543-466. (Springer, New York, ), Vol., pp.
25. Na Y. Moin P. The structure of wall-pressure fluctuations in turbulent boundary layers with adverse pressure gradient and separation. J. Fluid Mech. 1998, 377:347. JFLSA7, 0022-1120, 10.1017/S0022112098003218
26. Åkervik E. Brandt L. Henningson D.S. Hoepffner J. Marxen O. Schlatter P. Steady solutions of the Navier-Stokes equations by selective frequency damping. Phys. Fluids 2006, 18:068102. PHFLE6, 1070-6631, 10.1063/1.2211705,
27. Lehoucq R. Sorensen D. Yang C. ARPACK Users' Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods 1997, (SIAM, Philadelphia, ).
28. Åkervik E. Hoepffner J. Ehrenstein U. Henningson D.S. Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes. J. Fluid Mech. 2007, 579:305. JFLSA7, 0022-1120, 10.1017/S0022112007005496
29. Häggmark C.P. Bakchinov A.A. Alfreddson P.H. Experiments on a two-dimensional laminar separation bubble. Philos. Trans. R. Soc. London, Ser. A 2000, 358:3193. PTRMAD, 0962-8428, 10.1098/rsta.2000.0704
30. Watmuff J.H. Evolution of a wave packet into vortex loops in a laminar separation bubble. J. Fluid Mech. 1999, 397:119. JFLSA7, 0022-1120, 10.1017/S0022112099006138
31. Marxen O. Lang M. Rist U. Wagner S. A combined experimental/numerical study of unsteady phenomena in a laminar separation bubble. Flow, Turbul. Combust. 2003, 71:133. FTCOF9, 1386-6184, 10.1023/B:APPL.0000014928.69394.50
32. Cossu C. Chomaz J. Global measure of local convective instabilities. Phys. Rev. Lett. 1997, 78:4387. PRLTAO, 0031-9007, 10.1103/PhysRevLett.78.4387
33. Kaiktsis L. Karniadakis G.E. Orszag S.A. Unsteadiness and convective instabilities in two-dimensional flow over a backward-facing step. J. Fluid Mech. 1996, 321:157. JFLSA7, 0022-1120, 10.1017/S0022112096007689
34. Trefethen L.N. Embree M. Spectra and Pseudospectra: The Behaviour of Nonnormal Matrices and Operators 2005, (Princeton University Press, Princeton, NJ).
35. Dallmann U. Herberg T. Gebing H. Su W.-H. Zhang H.-Q. Flow field diagnostics-Topological flow changes and spatio-temporal flow structure. 1995, , AIAA Paper No. 95-0791
36. Dovgal A. Sorokin A. Wave packets of controlled velocity perturbations at laminar flow separation. Proceedings of the VII IUTAM Symposium on Laminar-Turbulent Transition 2009, 18IUTAM Bookseries (Springer, New York)