Weakly nonlinear analysis of a localized disturbance in Poiseuille flow

Studies in Applied Mathematics

Volumn 105, Issue 2, 2000, Pages 121-141

  Ponziani, D ^a   Casciola, C M ^b   Zirilli, F ^b   Piva, R ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

LOCALISED; NONLINEAR EFFECT; NONLINEAR FEATURES; PERTURBATION ANALYSIS; PERTURBATION EXPANSIONS; POISEUILLE FLOW; SECOND ORDERS; TRANSITION TO TURBULENCE; WALL BOUNDED FLOWS; WEAKLY NON-LINEAR;

NONLINEAR ANALYSIS;

EID: 0040792267     PISSN: 00222526     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9590.00145     Document Type: Article

References (24)

1. P. G. DRAZIN and W. H. REID, Hydrodynamic Stability, Cambridge University Press, Cambridge, UK, 1981.
2. J. T. STUART, The production of intense shear layers by vortex stretching and convection, Agard Rept. 514:1-31 (1965).
3. T. ELLINGSEN and E. PALM, Stability of linear flow, Phys. Fluids 18:487 (1975).
4. M. T. LANDHAL, A note on an algebraic instability of inviscid parallel shear flows, J. Fluid Mech. 98:243 (1980).
5. L. N. TREFETHEN, A. E. TREFETHEN, S. C. REDDY, and T. A. DRISCOL, Hydrodynamic stability without eigenvalues, Science 261:578-584 (1993).
6. S. C. REDDY, P. J. SCHMID, and D. S. HENNINGSON, Pseudospectra of the Orr-Sommerfeld operator, SIAM J. Appl. Math. 53:15-47 (1993).
7. K. M. BUTLER and B. F. FARREL, Three-dimensional optimal perturbations in viscous shear flows, Phys. Fluids A 4(8):1637-1650 (1992).
8. S. REDDY, P. SCHMID, J. S. BAGGETT, and D. HENNINGSON, On the stability of streamwise streaks and transition thresholds in plane channel flows, J. Fluid. Mech. 365:269-303 (1998).
9. P. J. SCHMID and D. S. HENNINGSON, A new mechanism for rapid transiiton involving a pair of oblique waves, Phys. Fluids A 4(9):1986-1989 (1992).
10. D. S. HENNINGSON and P. J. SCHIMD, Vector eigenfunction expansions for plane channel flows, Stud. Appl. Math. 87:15-43 (1992).
11. M. GASTER, A theoretical model of a wave packet in the boundary layer on a flat plate, Proc. R. Soc. Lond. 347:271-289 (1975).
12. W. O. CRIMINALE, T. L. JACKSON, D. G. LASSEIGNE, and R. D. JOSLIN, Perturbation dynamics in viscous channel flows, J. Fluid. Mech. 339:55-75 (1997).
13. S. A. ORSZAG, Accurate solution of the Orr-Sommerfeld stability equation, J. Fluid Mech. 50:689 (1971).
14. A. NAYFEH, Perturbation Methods, John Wiley and Sons, Inc., New York, 1973.
15. J. KEVORKIAN and J. D. COLE, Perturbation Methods in Applied Mathematics, Springer, New York, 1985.
16. D. PONZIANI, C. M. CASCIOLA, and F. ZIRILLI, Nonlinear effects and transition to turbulence in a wall-bounded flow, IV Congresso Nazionale SIMAI98, Giardinin Naxos, 1998.
17. R. C. DIPRIMA and G. J. HABETLER, A completeness theorem for nonselfadjoint eigen-value problems in hydrodynamic stability, Arch. Rat. Mech. Anal. 32:218-227 (1969).
18. C. CANUTO, M. H. HUSSIANI, A. QUARTERONI, and T. A. ZANG, Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin, 1987.
19. P. R. SPALART, R. D. MOSER, and M. M. ROGERS, Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions, J. Comp. Phys. 96:297-324 (1991).
20. D. S. HENNINGSON, A. LUNDBLADH, and A. V. JOHANSSON, A mechanism for bypass transition from localized disturbances in wall-bounded shear flows, J. Fluid Mech. 250:169-207 (1993).
21. V. V. KOSLOV, and M. P. RAMAZANOV, Development of finite-amplitude disturbances in Poiseuille flow, J. Fluid Mech. 147:149-157 (1984).
22. M. GASTER and I. GRANT, An experimental investigation of the formation and development of a wave packet in a laminar boundary layer, Proc. R. Soc. Lond. 347:253-269 (1975).
23. C. M. CASCIOLA, A. OLIVIERI, and R. PIVA, Transient response to harmonic excitations in Poiseuille flows, Third European Fluid Mechanics Conferences, Gottingen, 1997.
24. W. O. CRIMINALE, and P. G. DRAZIN, The evolution of linearized perturbations of parallel flows, Stud. Appl. Math. 83:123-157 (1990). UNIVERSITÁ DI ROMA