Strong echo effect and nonlinear transient growth in shear flows

Physics of Fluids

Volumn 10, Issue 6, 1998, Pages 1398-1404

  Vanneste, J ^a,d   Morrison, P J ^b   Warn, T ^c  

^a UNIVERSITY OF TORONTO   (Canada)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c MCGILL UNIVERSITY   (Canada)

^d UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001254408     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869664     Document Type: Article

References (20)

1. W. M. F. Orr, "The stability and instability of the steady motion of a perfect liquid and a viscous liquid. Parts I and II." Proc. R. Ir. Acad. Ser. A 27, 9 (1907).
2. B. F. Farrell, "Optimal excitation of perturbations in a viscous shear flow," Phys. Fluids 31, 2093 (1988).
3. B. F. Farrell and P. J. Ioannou, "Optimal excitation of three-dimensional perturbations in viscous constant shear flows," Phys. Fluids A 5, 1390 (1993).
4. K. M. Butler and B. F. Farrell, "Three-dimensional optimal perturbations in viscous shear flow," Phys. Fluids A 4, 1637 (1992).
5. S. C. Reddy and D. S. Henningson, "Energy growth in viscous channel flows," J. Fluid Mech. 252, 209 (1993).
6. L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. B. Driscoll, "Hydrodynamics stability without eigenvalues," Science 261, 578 (1993).
7. N. J. Balmforth and P. J. Morrison, "Singular eigenfunctions for shearing fluids," Institute for Fusion Studies Report, No. 692, The University of Texas, Austin, Texas, 1995.
8. B. F. Farrell and P. J. Ioannou, "Generalized stability theory. Part I: autonomous operators," J. Atmos. Sci. 53, 2025 (1996).
9. S. Brown and K. Stewartson, "On the algebraic decay of disturbances in stratified shear flows," J. Fluid Mech. 100, 811 (1980).
10. E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics (Pergamon, New York, 1981).
11. T. G. Shepherd, "Time development of small disturbances to plane Couette flow," J. Atmos. Sci. 42, 1868 (1985).
12. E. L. Hahn, "Spin echoes," Phys. Rev. 80, 580 (1950).
13. R. W. Gould, T. M. O'Neil, and J. H. Malmberg, "Plasma wave echo," Phys. Rev. Lett. 19, 219 (1967).
14. I. D. Abella, N. A. Kurnit, and S. R. Hartmann, "Photon echoes," Phys. Rev. 141, 391 (1966).
15. T. M. O'Neil and R. W. Gould, "Temporal and spatial plasma wave echoes," Phys. Fluids 11, 134 (1968).
16. A. E. Lifshitz, "An echo effect in hydrodynamics," Sov. Phys. Dokl. 34, 783 (1989).
17. W. Thomson, "Stability of fluid motion - Rectilineal motion of viscous fluid between two parallel planes," Philos. Mag. 24, 188 (1887).
18. L. Engevik, "On the stability of plane Couette flow," Department of Applied Mathematics Bergen Norway, Pub. No. 11, 1966.
19. K. K. Tung, "Initial-value problem for Rossby waves in a shear flow with critical level," J. Fluid Mech. 133, 443 (1983).
20. P. H. Haynes, "On the instability of sheared disturbances," J. Fluid Mech. 175, 463 (1987).