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Origin of the peak-valley wave structure leading to wall turbulence

Published online by Cambridge University Press:  26 April 2006

Masahito Asai  and
Michio Nishioka
Masahito Asai
Affiliation:
Department of Aeronautical Engineering, University of Osaka Prefecture, Sakai, Osaka 591, Japan
Michio Nishioka
Affiliation:
Department of Aeronautical Engineering, University of Osaka Prefecture, Sakai, Osaka 591, Japan
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Abstract

A generation process for the three-dimensional wave which dominates the transition preceded by a Tollmien-Schlichting (T-S) wave is studied both experimentally and numerically in plane Poiseuille flow at a subcritical Reynolds number of 5000. In order to identify the origin of the three-dimensional wave in Nishioka et al.'s laboratory experiment, the corresponding spanwise mean-flow distortion and two-dimensional T-S wave modes are introduced into a parabolic flow as the initial disturbance conditions for a numerical simulation of temporally growing type. Through reproducing the actual wave development into the peak-valley structure, the simulation pinpoints the origin to be the slight spanwise mean-flow distortion in the experimental basic flow. Furthermore, the simulation clearly shows that the growth of the three-dimensional wave requires the vortex stretching effect due to the streamwise vortices, which appear under the experimental conditions only when the amplitude of the two-dimensional T-S wave is above the observed threshold.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 208 , November 1989 , pp. 1 - 23
Copyright
© 1989 Cambridge University Press

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References

Benney, D. J. & Lin, C. C. 1960 On the secondary motion induced by oscillations in a shear flow. Phys. Fluids 3, 656–657.Google Scholar
Craik, A. D. D. 1971 Nonlinear resonant instability in boundary layers. J. Fluid Mech. 50, 393–413.Google Scholar
Craik, A. D. D. 1985 Wave Interactions and Fluid Flows. Cambridge Monographs on Mech. and Applied Math. Cambridge University Press.
Dhanak, M. R. 1983 On certain aspects of three-dimensional instability of parallel flows. Proc. R. Soc. Lond. A 385, 53–84.Google Scholar
DiPrima, R. C. & Habetler, G. J. 1969 A completeness theorem for non-selfadjoint eigenvalue problems in hydrodynamic stability. Arch. Rat. Mech. Anal. 34, 218–227.Google Scholar
Fasel, H. & Bestek, H. 1980 Investigation of nonlinear, spatial disturbance amplification in plane Poiseuille flow. In Laminar-Turbulent Transition (ed. R. Eppler & H. Fasel), pp. 173–185. Springer.
Hama, F. R. & Nutant, J. 1963 Detailed flow-field observations in the transition process in a thick boundary layer. In Proc. 1963 Heat Transfer and Fluid Mech. Institute, Stanford University, pp. 77–93.
Herbert, Th. 1977 Finite amplitude stability of plane parallel flows. AGARD CP-224, 3.1–3.10.Google Scholar
Herbert, Th. 1984a Secondary instability of shear flow. AGARD Rep. 709.Google Scholar
Herbert, Th. 1984b Modes of secondary instability in plane Poiseuille flow. In Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi), pp. 53–58. North-Holland.
Herbert, Th. & Morkovin, M. V. 1980 Dialogue on bridging some gaps in stability and transition research. In Laminar-Turbulent Transition (ed. R. Eppler & H. Fasel), pp. 47–72. Springer.
Itoh, N. 1974 Spatial growth of finite wave disturbances in parallel and nearly parallel flows, I. The theoretical analysis and the numerical results for plane Poiseuille flow. Trans. Japan Soc. Aeron. Space Sci. 17, 160–174.Google Scholar
Itoh, N. 1980 Three-dimensional growth of finite wave disturbances in plane Poiseuille flow. Trans. Japan Soc. Aeron. Space Sci. 23, 91–103.Google Scholar
Itoh, N. 1987 Another route to the three-dimensional development of Tollmien-Schlichting waves with finite amplitude. J. Fluid Mech. 181, 1–16.Google Scholar
Kachanov, Yu. S. & Levchenko, V. Ya. 1984 The resonant interaction of disturbances at laminar-turbulent transition in a boundary layer. J. Fluid Mech. 138, 209–247.Google Scholar
Klebanoff, P. S. & Tidstrom, K. D. 1959 Evolution of amplified waves leading to transition in a boundary layer with zero pressure gradient. NASA Tech. Note D-195.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary layer instability. J. Fluid Mech. 12, 1–34.Google Scholar
Kleiser, L. 1982 Spectral simulations of laminar-turbulent transition in plane Poiseuille flow and comparison with experiments. Lecture Notes in Physics, vol. 170, pp. 280–285. Springer.
Kovasznay, L. S. G., Komoda, H. & Vasudeva, B. R. 1962 Detailed flow field in transition. In Proc. 1962 Heat Transfer and Fluid Mech. Institute, Stanford University, pp. 1–26.
Kozlov, V. V. & Ramazanov, M. P. 1983 Development of finite amplitude disturbances in a Poiseuille flow. Izv. Akad. Nauk SSSR, Mekh. Zhid. i Gaza 43–47.Google Scholar
Morkovin, M. V. 1983 Understanding transition to turbulence in shear layers. Dept Mech. Aerosp. Engng, Illinois Inst. Tech., Chicago, Rep. AFOSR-FR-83.Google Scholar
Nishioka, M. & Asai, M. 1984 Evolution of Tollmien-Schlichting waves into wall turbulence. In Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi). pp. 87–92. North-Holland.
Nishioka, M. & Asai, M. 1985a Some observations of subcritical transition in plane Poiseuille flow. J. Fluid Mech. 150, 441–450.Google Scholar
Nishioka, M. & Asai, M. 1985b Three-dimensional wave-disturbances in plane Poiseuille flow. In Laminar-Turbulent Transition (ed. V. V. Kozlov), pp. 173–182. Springer.
Nishioka, M., Asai, M. & Iida, S. 1980 An experimental investigation of the secondary instability. In Laminar-Turbulent Transition (ed. R. Eppler & H. Fasel), pp. 37–46. Springer.
Nishioka, M., Asai, M. & Iida, S. 1981 Wall phenomena in the final stage of transition to turbulence. In Transition and Turbulence (ed. R. E. Meyer), pp. 113–126. Academic.
Nishioka, M., Iida, S. & Ichikawa, Y. 1975 An experimental investigation of the stability of plane Poiseuille flow. J. Fluid Mech. 72, 731–751.Google Scholar
Nishioka, M., Iida, S. & Kanbayashi, S. 1978 An experimental investigation of the subcritical instability in plane Poiseuille flow. In Proc. 10th Turbulence Symposium, Inst. Space Aeron. Sci., Tokyo University, pp. 55–62.
Orszag, S. A. & Kells, L. C. 1980 Transition to turbulence in plane Poiseuille flow and plane Couette flow. J. Fluid Mech. 96, 159–205.Google Scholar
Orszag, S. A. & Patera, A. T. 1983 Secondary instability of wall-bounded shear flows. J. Fluid Mech. 128, 347–385.Google Scholar
Saric, W. S. & Thomas, A. S. W. 1984 Experiments on the subharmonic route to turbulence in boundary layers. In Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi), pp. 117–122. North-Holland.
Singer, B. A., Reed, H. L. & Ferziger, J. H. 1986 Investigation of the effects of initial disturbances on plane channel transition. AIAA Paper 86–0433.Google Scholar
Singer, B. A., Reed, H. L. & Ferziger, J. H. 1987 Effect of streamwise vortices on transition in plane channel flow. AIAA Paper 87–0048.Google Scholar
Stuart, J. T. 1960 On the non-linear mechanics of wave disturbances in stable and unstable parallel flows, I. The basic behaviour in plane Poiseuille flow. J. Fluid Mech. 9, 353–370.Google Scholar
Stuart, J. T. 1962 On three-dimensional non-linear effects in the stability of parallel flow. Adv. Aero. Sci. 3, 121–142.Google Scholar
Stuart, J. T. 1965 The production of intense shear layers by vortex stretching and convection. AGARD Rep. 514.Google Scholar
Stuart, J. T. 1986 Stewartson memorial lecture: Hydrodynamic stability and turbulent transition. In Numerical and Physical Aspects of Aerodynamic Flows III, pp. 23–38. Springer.
Tani, I. 1981 Three-dimensional aspects of boundary-layer transition. Proc. Indian Acad. Sci. 4, 219–238.Google Scholar