Abstract
Investigations of the mechanisms underlying bypass transition are presented, and it is shown that a linear growth mechanism is required for energy growth. In shear flows such a mechanism is identified in the rapid transient growth of streaks produced by the three-dimensional lift-up effect. A number of transition scenarios utilizing this transient growth are discussed: Streak growth and breakdown, oblique transition and transition from localized disturbances. It is also demonstrated that the transition scenarios utilizing transient growth give the lowest threshold energies for initial disturbances causing transition.
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References
L. Bergström. Optimal growth of small disturbances in pipe poiseuille flow. Phys. Fluids A, 5:2710–2720, 1993.
S. Berlin, A. Lundbladh, and D. S. Henningson. Spatial simulations of oblique transition. Phys. Fluids, 1994. (Accepted).
L. Boberg and U. Brosa. Onset of turbulence in a pipe. Z. Naturforsch., 43a:697–726, 1988.
K. S. Breuer and J. H. Haritonidis. The evolution of a localized disturbance in a laminar boundary layer. Part I: Weak disturbances. J. Fluid Mech., 220:569–594, 1990.
K. S. Breuer and T. Kuraishi. Transient growth in two- and three-dimensional boundary layers. Phys. Fluids, 6:1983–1993, 1994.
K. M. Butler and B. F. Farrell. Three-dimensional optimal perturbations in viscous shear flow.Phys. Fluids A, 4:1637–1650, 1992.
C. L. Chang and M. R. Malik. Non-parallel stability of compressible boundary layers. AIAA Paper 93–2912, 1993.
T. Ellingsen and E. Palm. Stability of linear flow. Phys. Fluids, 18:487–488, 1975.
P. A. Elofsson and P. H. Alfredsson. An experimental investigation of interacting oblique waves in plane poiseuille flow. Bull. Am. Phys. Soc., 38:2221, 1993.
B. F. Farrell. Optimal excitation of perturbations in viscous shear flow. Phys. Fluids, 31:2093–2102, 1988.
B. F. Farrell. The initial growth of disturbances in a baroclinic flow. J. Atmos. Sci., 46:1193, 1989.
B. F. Farrell and P. J. Ioannou. Optimal excitation of three dimensional perturbations in viscous constant shear flow. Phys. Fluids A, 5:1390–1400, 1993.
B. F. Farrell and A. M. Moore. An adjoint method for obtaining the most rapidly growing perturbations to oceanic flows. J. Phys. Ocean., 22:338, 1992.
H. Fasel and A. Thumm. Direct numerical simulation of three-dimensional breakdown in supersonic boundary layer transition. Bull. Am. Phys. Soc., 36:2701, 1991.
R. J. Gathmann, M. Si-Ameur, and F. Mathey. Numerical simulations of three-dimensional natural transition in the compressible confined shear layer. Phys. Fluids A, 5:2946–2968, 1993.
L. H. Gustavsson. Energy growth of three-dimensional disturbances in plane Poiseuille flow. J. Fluid Mech., 224:241–260, 1991.
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.
D. S. Henningson and S. C. Reddy. On the role of linear mechanisms in transition to turbulence. Phys. Fluids, 6:1396–1398, 1994.
R. D. Joslin, C. L. Streett, and C. L. Chang. Spatial direct numerical simulations of boundary-layer transition mechanisms: Validation of PSE theory. Theoret. Comput. Fluid Dyn., 4:271–288, 1993.
B. G. B. Klingmann. On transition due to three-dimensional disturbances in plane Poiseuille flow. J. Fluid Mech., 240:167–195, 1992.
G. Kreiss, A. Lundbladh, and D. S. Henningson. Bounds for threshold amplitudes in subcritical shear flows. J. Fluid Mech., 270:175–198, 1994.
M. T. Landahl. Wave breakdown and turbulence. SIAM J. Appl. Math., 28:735–756, 1975.
M. T. Landahl. A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech., 98:243–251, 1980.
A. Lundbladh. Simulation of Bypass Transition to Turbulence. PhD. Thesis from the Royal Institute of Technology, Stockholm, Sweden, 1993.
A. Lundbladh, D. S. Henningson, and S. C. Reddy. Threshold amplitudes for transition in channel flows. Proceedings from the 1993 ICASE/NASA Langley Workshop on the Transition to Turbulence, 1993.
M. V. Morkovin. The many faces of transition. In C. S. Wells, editor, Viscous Drag Reduction. Plenum Press, 1969.
P. J. Olsson and D. S. Henningson. Optimal disturbances in watertable flow. Technical Report TRITA-MEK 1993:11, Royal Institute of Techmology, Stockholm, 1993.
S. A. Orszag and A. T. Patera. Secondary instability of wall-bounded shear flows. J. Fluid Mech., 128:347–385, 1983.
S. C. Reddy and D. S. Henningson. Energy growth in viscous channel flows. J. Fluid Mech., 252:209–238, 1993.
N. D. Sandham, N. A. Adams, and L. Kleiser. Direct simulation of breakdown to turbulence following oblique instability waves in a supersonic boundary layer. First ERCOFTAC workshop on direct and large eddy simulation, Guildford, England, march 28–30., 1994.
P. J. Schmid and D. S. Henningson. A new mechanism for rapid transition involving a pair of oblique waves. Phys. Fluids A, 4:1986–1989, 1992.
P. J. Schmid and D. S. Henningson. Optimal energy density growth in Hagen-Poiseuille flow. J. Fluid Mech., 1994. (To Appear).
P. J. Schmid and H. K. Kytömaa. Transient and asymptotic stability of granular flow. J. Fluid Mech., 264:255–275, 1994.
P. J. Schmid, A. Lundbladh, and D. S. Henningson. Spatial evolution of disturbances in plane Poiseuille flow. Proceedings from the 1993 ICASE/NASA Langley Workshop on the Transition to Turbulence, 1993.
L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll. Hydrodynamic stability without eigenvalues. Science, 261:578–584, 1993.
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Henningson, D. (1995). Bypass Transition and Linear Growth Mechanisms. In: Benzi, R. (eds) Advances in Turbulence V. Fluid Mechanics and Its Applications, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0457-9_36
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DOI: https://doi.org/10.1007/978-94-011-0457-9_36
Publisher Name: Springer, Dordrecht
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