On the mechanism of optimal disturbances: The role of a pair of nearly parallel modes

Physics of Fluids

Volumn 15, Issue 7, 2003, Pages 1961-1972

  Ben Dov, Guy ^a   Levinski, Vladimir ^a   Cohen, Jacob ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

JETS; PIPE FLOW; RESONANCE; REYNOLDS NUMBER;

OPTIMAL DISTURBANCES;

SHEAR FLOW;

PIPE FLOW; REYNOLDS NUMBER; SHEAR FLOW; TURBULENCE;

EID: 0041825212     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1576763     Document Type: Article

References (35)

1. T. Elingsen and E. Palm, "Stability of linear flow," Phys. Fluids 18, 487 (1975).
2. M. T. Landahl, "A note on an algebriac instability of inviscid parallel shear flows," J. Fluid Mech. 98, 243 (1980).
3. D. J. Benney and L. H. Gustavsson, "A new mechanism for linear and nonlinear hydrodynamic instability," Stud. Appl. Math. 64, 185 (1981).
4. L. S. Hultgren and L. H. Gustavsson, "Algebriac growth of disturbances in a laminar boundary layer," Phys. Fluids 24, 1000 (1981).
5. L. H. Gustavsson, "Energy growth of three-dimensional disturbance in plane Poiseuille flow," J. Fluid Mech. 224, 241 (1991).
6. D. S. Henningson, "An eigenfunction expansion of localized disturbances," in Advances in Turbulence 3 (Springer-Verlag, Berlin, 1991), pp. 162-169.
7. P. L. O'Sullivan and K. S. Breuer, "Transient growth in circular pipe flow. 1. Linear disturbances," Phys. Fluids 6, 3643 (1994).
8. D. S. Henningson, L. H. Gustavsson, and K. S. Breuer, "Localized disturbances in parallel shear flows," Appl. Sci. Res. 53, 51 (1994).
9. K. M. Butler and B. F. Farrell, "Three-dimensional optimal perturbations in viscous shear flow," Phys. Fluids A 4, 1637 (1992).
10. S. C. Reddy and D. S. Henningson, "Energy growth in viscous channel flow," J. Fluid Mech. 252, 209 (1993).
11. P. Andersson, M. Berggren, and D. S. Henningson, "Optimal disturbances and bypass transition in boundary layers," Phys. Fluids 11, 134 (1999).
12. P. Luchini, "Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations," J. Fluid Mech. 404, 289 (2000).
13. P. Corbett and A. Buttaro, "Optimal perturbations for boundary layers subjected to streamwise pressure gradient," Phys . Fluids 12, 120 (2000).
14. A. Tumin and E. Reshotko, "Spatial theory of optimal disturbances in boundary layers," Phys. Fluids 13, 2097 (2001).
15. P. J. Schmid and D. S. Henningson, "Optimal energy density growth in Hagen-Poiseuille flow," J. Fluid Mech. 277, 197 (1994).
16. L. Bergström, "Nonlinear behaviour of transiently amplified disturbances in pipe Poiseuille flow," Eur. J. Mech. B/Fluids 14, 719 (1995).
17. L. Bergström, "Self-sustained amplification of disturbances in pipe Poiseuille flow," Eur. J. Mech. B/Fluids 18, 635 (1999).
18. L. Bergström, "Optimal growth of small disturbances in pipe Poiseuille flow," Phys. Fluids A 5, 2710 (1993).
19. E. Reshotko and A. Tumin, "Spatial theory of optimal disturbances in a circular pipe flow," Phys. Fluids 13, 991 (2001).
20. G. K. Batchelor and A. E. Gill, "Analysis of the stability of axisymmetric jets," J. Fluid Mech. 14, 529 (1962).
21. L. Bergström, "Initial algebriac growth of small angular dependent disturbances in pipe Poiseuille flow," Stud. Appl. Math. 87, 61 (1992).
22. M. R. Khorrami, M. R. Malik, and R. L. Ash, "Application of spectral collocation techniques to the stability of swirling flows," J. Comput. Phys. 81, 206 (1989).
23. J. A. C. Weideman and S. C. Reddy, A matlab differentiation matrix suite, August 1998. Available at http://osu.orst.edu-weidemaj/differ.html.
24. T. B. Benjamin, "Fluid flow with flexible boundaries," in Proceedings of the 11th International Congress on Applied Mathematics, Vol. 109, edited by H. Gortler (Springer, Berlin, 1964).
25. V. Levinski, D. E. Levy, and J. Cohen, "Effects of wall compliance on the hydrodynamic stability and transition delay of a wall-jet flow," Fluid Dyn. Res. 29, 115 (2001).
26. D. M. Bushnell, J. N. Hefner, and R. L. Ash, "Effect of compliant wall motion on turbulent boundary layers," Phys. Fluids 20, S31 (1977).
27. T. B. Benjamin, "Effects of a flexible boundary on hydrodynamic stability," J. Fluid Mech. 9, 513 (1960).
28. P. Mele, M. Morganti, M. F. Scibilia, and A. Lasek, "Behavior of wall jet in laminar-to-turbulent transition," AIAA J. 24, 938 (1986).
29. J. Cohen, M. Amitay, and B. Bayly, "Lamina-turbulent transition of wall-jet flows subjected to blowing and suction," Phys. Fluids A 4, 283 (1992).
30. D. H. Chun and W. H. Schwarz, "Stability of the plane incompressible viscous wall jet subjected to small disturbances," Phys. Fluids 10, 911 (1967).
31. N. I. Akatnov, "Development of two-dimensional laminar incompressible jet near a rigid wall," Proc. Leningrad Polytech. Inst. 5, 24 (1953).
32. M. B. Glauert, "The wall-jet" J. Fluid Mech. 1, 625 (1956).
33. M. R. Malik, "Numerical methods for hypersonic boundary layer stability," J. Comput. Phys. 86, 376 (1990).
34. A. Tumin and L. Aizatulin, "Instability and receptivity of laminar wall jets," Theor. Comput, Fluid Dyn. 9, 33 (1997).
35. G. Ben-Dov, V. Levinski, and J. Cohen, "Optimal disturbances in Hagen-Poiseuille flow with superimposed rigid rotation," in Proceedings of the 42nd Israel Annual Conference on Aerospace Sciences, February 2002.