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Experiments on transition in plane Couette flow

Published online by Cambridge University Press:  26 April 2006

Nils Tillmark
Affiliation:
Department of Gasdynamics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
P. Henrik Alfredsson
Affiliation:
Department of Gasdynamics, Royal Institute of Technology, S-100 44 Stockholm, Sweden

Abstract

The first flow visualization experimental results of transition in plane Couette flow are reported. The Couette flow water channel was of an infinite-belt type with counter-moving walls. The belt and channel walls were transparent making it possible to visualize the flow pattern in the streamwise-spanwise plane by utilizing fluid-suspended reflective flakes. Transition was triggered by a high-amplitude pointwise disturbance. The transitional Reynolds number, i.e. the lowest Reynolds number for which turbulence can be sustained, was determined to be 360 ± 10, based on half-channel height and half the velocity difference between the walls. For Reynolds numbers above this value a large enough amplitude of the initial disturbance gave rise to a growing turbulent spot. Its shape and spreading rate was determined for Reynolds numbers up to 1000.

Type
Research Article
Copyright
© 1992 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
Aydin, M. & Leutheusser, H. J. 1979 Novel experimental facility for the study of plane Couette flow. Rev. Sci. Instrum. 50, 1362.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Carlson, D. R., Widnall, S. E. & Peeters, M. F. 1982 A flow-visualization study of transition in plane Poiseuille flow. J. Fluid Mech. 121, 487.Google Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385.Google Scholar
Couette, M. 1890 éAtudes sur le frottement des liquids. Ann. Chim. Phys. 21, 433.Google Scholar
Davey, A. 1973 On the stability of plane Couette flow to infinitesimal disturbances. J. Fluid Mech. 57, 369.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Ellingsen, T., Gjevik, B. & Palm, E. 1970 On the non-linear stability of plane Couette flow. J. Fluid Mech. 40, 97.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
Gustavsson, L. H. 1991 Energy growth of three-dimensional disturbances in plane Poiseuille flow. J. Fluid Mech. 224, 241.Google Scholar
Gustavsson, L. H. & Hultgren, L. S. 1980 A resonance mechanism in plane Couette flow. J. Fluid Mech. 98, 149.Google Scholar
Leutheusser, H. J. & Chu, V. H. 1971 Experiments on plane Couette flow. J. Hydraul. Div. ASCE 97 (HY9), 1269.Google Scholar
Lundbladh, A. & Johansson, A. V. 1991 Direct simulation of turbulent spots in plane Couette flow. J. Fluid Mech. 229, 499.Google Scholar
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. & Kells, C. 1980 Transition to turbulence in plane Poiseuille and plane Couette flow. J. Fluid Mech. 96, 159.Google Scholar
Orszag, S. A. & Patera, A. T. 1983 Secondary instability of wall-bounded shear flow. J. Fluid Mech. 128, 347.Google Scholar
Reichardt, H. 1956 Über die Geschwindigkeitsverteilung in einer geradliningen turbulenten CouettestroUmung. Z. Angew. Math. Mech. 36, S26.Google Scholar
Reynolds, O. 1883 An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and the law of resistance in parallel channels. Phil. Trans. R. Soc. Lond. 174, 311.Google Scholar
Taylor, G. I. 1936 Fluid friction between rotating cylinders, Part I. Torque measurements. Proc. R. Soc. Lond. A 157, 546.Google Scholar
Wendt, F. 1933 Turbulente StroUmungen zwischen zwei rotierenden konaxialen Zylindern. Ing. Arch. 4, 577.Google Scholar