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The wave structure of turbulent spots in plane Poiseuille flow

Published online by Cambridge University Press:  21 April 2006

Dan S. Henningson  and
P. Henrik Alfredsson
Dan S. Henningson
Affiliation:
Department of Mechanics, The Royal Institute of Technology, S-100 44 Stockholm, Sweden Present address: The Aeronautical Research Institute of Sweden, s-16111 Bromma, Sweden.
P. Henrik Alfredsson
Affiliation:
Department of Mechanics, The Royal Institute of Technology, S-100 44 Stockholm, Sweden
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Abstract

The wave packets located at the wingtips of turbulent spots in plane Poiseuille flow have been investigated by hot-film anemometry. The streamwise velocity disturbances associated with the waves were found to be antisymmetric with respect to the channel centreline. The amplitude of the waves had a maximum close to the wall that was about 4% of the centreline velocity. The modified velocity field outside the spot was measured and linear stability analysis of the measured velocity profiles showed that the flow field was less stable than the undisturbed flow. The phase velocity and amplitude distribution of the waves were in reasonable agreement with the theory, which together with the symmetry properties indicate that the wave packet consisted of the locally least stable Tollmien-Schlichting mode.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 178 , May 1987 , pp. 405 - 421
Copyright
© 1987 Cambridge University Press

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References

Alavyoon, F., Henningson, D. S. & Alfredsson, P. H. 1986 Turbulent spots in plane Poiseuille flow - flow visualization. Phys. Fluids 29, 1328.Google Scholar
Carlson, D. R., Widnall, S. E. & Peeters, M. F. 1982 A flow-visualization study of spots in plane Poiseuille flow. J. Fluid Mech. 121, 487.Google Scholar
Chambers, F. W. & Thomas, A. S. W. 1983 Turbulent spots, wave packets, and growth. Phys. Fluids 26, 1160.Google Scholar
Conte, S. D. 1966 The numerical solution of linear boundary value problems. SIAM Rev. 8, 309.Google Scholar
Gad-El-Hak, M., Blackwelder, R. F. & Riley, J. J. 1981 On the growth of turbulent regions in laminar boundary layers. J. Fluid Mech. 110, 73.Google Scholar
Gaster, M. 1975 A theoretical model of a wave packet in the boundary layer on a flat plate. Proc. R. Soc. Lond A 347, 271.Google Scholar
Gaster, M. & Grant, I. 1975 An experimental investigation of the formation and development of a wave packet in a laminar boundary layer. Proc. R. Soc. Lond. A 347, 253.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1961 The three-dimensional nature of boundary layer instability. J. Fluid Mech. 12, 1.Google Scholar
Landahl, M. T. 1972 Wave mechanics of breakdown. J. Fluid Mech. 56, 775.Google Scholar
Landahl, M. T. 1982 The application of kinematic wave theory to wave trains and packets with small dissipation. Phys. Fluids 25, 1512.Google Scholar
Landahl, M. T. & Mollo-Christensen, E. 1986 Turbulence and Random Phenomena in Fluid Mechanics. Cambridge University Press.
Nishioka, M., Iida, S. & Ichikawa, Y. 1975 An experimental investigation of the stability of plane Poiseuille flow. J. Fluid Mech. 72, 731.Google Scholar
Orszag, S. A. 1971 Accurate solution of the Orr-Sommerfeld stability equation. J. Fluid Mech. 50, 689.Google Scholar
Orszag, S. A. & Patera, A. T. 1983 Secondary instability of wall bounded shear flows. J. Fluid Mech. 128, 347.Google Scholar
Widnall, S. E. 1984 Growth of turbulent spots in plane Poiseuille flow. In Turbulence and chaotic phenomena in fluids (ed. T. Tatsumi), p. 93. Elsevier.
Wygnanski, I., Haritonidis, J. H. & Kaplan, R. E. 1979 On a Tollmien-Schlichting wave packet produced by a turbulent spot. J. Fluid Mech. 92, 505.Google Scholar
Wygnanski, I., Zilberman, M. & Haritonidis, J. H. 1982 On the spreading of a turbulent spot in the absence of a pressure gradient. J. Fluid Mech. 123, 69.Google Scholar