Spectra and pseudospectra for pipe Poiseuille flow

Computer Methods in Applied Mechanics and Engineering

Volumn 175, Issue 3-4, 1999, Pages 413-420

  Trefethen, Anne E ^a   Trefethen, Lloyd N ^b   Schmid, Peter J ^c  

^a Numerical Algorithms Group   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LAMINAR FLOW; PERTURBATION TECHNIQUES; REYNOLDS NUMBER; SPECTRUM ANALYSIS;

POISEUILLE FLOW;

PIPE FLOW;

COMPUTATIONAL FLUID DYNAMICS; LAMINAR-TURBULENT TRANSITION; PIPE FLOW; POISEUILLE FLOW;

EID: 0033516440     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00364-8     Document Type: Article

References (26)

1. [1] J.S. Baggett, T.A. Driscoll and L.N. Trefethen, A mostly linear model of transition to turbulence, Phys. Fluids 7 (1995) 833-838.
2. [2] J.S. Baggett and L.N. Trefethen, Low-dimensional models of subcritical transition to turbulence, Phys. Fluids 9 (1997) 1043-1053.
3. [3] L. Begström, Optimal growth of small disturbances in pipe Poiseuille flow', Phys. Fluids A 5 (1993) 2710-2720.
4. [4] L. Boberg and U. Brosa, Onset of turbulence in a pipe, Z. Naturforschung 43a (1988) 697-726.
5. [5] D.M. Burridge and P.G. Drazin, Comments on 'Stability of pipe Poiseuille flow, Phys. Fluids 12 (1969) 264-265.
6. [6] K.M. Butler and B.F. Farrell, Three-dimensional optimal perturbations in viscous shear flow, Phys. Fluids A 4 (1992) 1637-1650.
7. [7] A.G. Darbyshire and T. Mullin, Transition to turbulence in constant-mass-flux pipe flow, J. Fluid Mech. 289 (1995) 83-114.
8. [8] A. Davey and P.G. Drazin, The stability of Poiseuille flow in a pipe, J. Fluid Mech. 36 (1969) 209-218.
9. [9] P.G. Drazin and W.H. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 1981).
10. [10] T. Gebhardt and S. Grossmann, Chaos transition despite linear stability, Phys. Rev. E 50 (1994) 3705-3711.
11. [11] D.S. Henningson, Bypass transition and linear growth mechanisms, in: R. Benzi, ed., Advances in Turbulence V (Kluwer, 1995).
12. [12] D.S. Hennington and S.C. Reddy, On the role of linear mechanisms in transition to turbulence, Phys. Fluids 6 (1994) 1396-1398.
13. [13] T. Herbert, Die neutrale Fläche der ebenen Poiseuille Strömung, Habilitationschrift, Universität Stuttgart, 1977.
14. [14] I. Herron, The linear stability of circular pipe flow to axisymmetric disturbances, Stab. Appl. Anal. Continuous Media 2 (1992) 293-303.
15. [15] A. Lundbladh, D.S. Henningson and S.C. Reddy, Threshold amplitudes for transition in channel flows, in: Transition, Turbulence, and Combustion, Vol. 1 (Kluwer, 1994).
16. [16] E.W. Mayer and E. Reshotko, Evidence for transient disturbance growth in a 1961 pipe-flow experiment, Phys. Fluids 9 (1997) 242-244.
17. [17] F.T.M. Nieuwstadt, A.A. Draad and G.D.C. Kuiken, Laminar-turbulent transition in pipe flow, in: S. Gavrilakis et al., eds., Advances in Turbulence VI (Kluwer, 1996) 371-374.
18. [18] P. O'Sullivan and K. Breuer, Transient growth in circular pipe flow. Part I: linear disturbances, Phys. Fluids 6 (1994) 3643-3651.
19. [19] S.C. Reddy and D.S. Henningson, Energy growth in viscous channel flows, J. Fluid Mech. 252 (1993) 209-238.
20. [20] O. Reynolds, An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels, Phil. Trans. Roy. Soc. 174 (1883) 935-982.
21. [21] H. Salwen, F.W. Cotton and C.E. Grosch, Linear stability of Poiseuille flow in a circular pipe, J. Fluid Mech. 98 (1980), 273-284.
22. [22] P.J. Schmid and D.S. Henningson, Optimal energy density growth in Hagen-Poiseuille flow, J. Fluid Mech. 277 (1994) 197-225.
23. [23] L.N. Trefethen, Pseudospectra of linear operators, SIAM Rev. 39 (1997) 383-406.
24. [24] L.N. Trefethen, A.E. Trefethen, S.C. Reddy and T.A. Driscoll, Hydrodynamic stability without eigenvalues, Science 261 (1993) 578-584.
25. [25] A. Tumin, Receptivity of pipe Poiseuille flow, J. Fluid Mech. 315 (1996) 119-137.
26. [26] O. Zikanov, On the instability of pipe Poiseuille flow, Phys. Fluids 8 (1996) 2923-2932.