Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-13T01:31:33.193Z Has data issue: false hasContentIssue false

An investigation of turbulent plane Couette flow at low Reynolds numbers

Published online by Cambridge University Press:  26 April 2006

Knut H. Bech
Affiliation:
Faculty of Mechanical Engineering, The Norwegian Institute of Technology, N-7034 Trondheim, Norway
Nils Tillmark
Affiliation:
Department of Mechanics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
P. Henrik Alfredsson
Affiliation:
Department of Mechanics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Helge I. Andersson
Affiliation:
Faculty of Mechanical Engineering, The Norwegian Institute of Technology, N-7034 Trondheim, Norway

Abstract

The turbulent structure in plane Couette flow at low Reynolds numbers is studied using data obtained both from numerical simulation and physical experiments. It is shown that the near-wall turbulence structure is quite similar to what has earlier been found in plane Poiseuille flow; however, there are also some large differences especially regarding Reynolds stress production. The commonly held view that the maximum in Reynolds stress close to the wall in Poiseuille and boundary layer flows is due to the turbulence-generating events must be modified as plane Couette flow does not exhibit such a maximum, although the near-wall coherent structures are quite similar. For two-dimensional mean flow, turbulence production occurs only for the streamwise fluctuations, and the present study shows the importance of the pressure—strain redistribution in connection with the near-wall coherent events.

Type
Research Article
Copyright
© 1995 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alfredsson, P. H. & Johansson, A. V. 1984 Time scales in turbulent channel flow. Phys. Fluids 27, 1974.Google Scholar
Andersson, H. I. & Kristoffersen, R. 1992 Statistics of numerically generated turbulence. Acta Appl.Math. 26, 293.Google Scholar
Aydin, E. M. & Leutheusser, H. J. 1979 Novel experimental facility for the study of plane Couette flow. Rev. Sci. Instrum. 50 ((11), 1362.Google Scholar
Aydin, E. M. & Leutheusser, H. J. 1987 Experimental investigation of turbulent plane-Couette flow. ASME Forum on Turbulent Flows, FED vol. 51, p. 51.
Aydin, E. M. & Leutheusser, H. J. 1991 Plane-Couette flow between smooth and rough walls. Exps Fluids 11, 302.Google Scholar
Bech, K. H. & Andersson, H. I. 1994 Very-large-scale structures in DNS. In Direct and Large-Eddy Simulation I. (ed. P. R. Voke, L. Kleiser & J.-P. Chollet), p. 13. Kluwer.
Blackwelder, R. F. & Kaplan, R. E. 1976 On the wall structure of the turbulent boundary layer. J. Fluid Mech. 76, 89.Google Scholar
Brooke, J. W. & Hanratty, T. J. 1993 Origin of turbulence-producing eddies in a channel flow. Phys. Fluids A 5, 1011.Google Scholar
Clever, R. M. & Busse, F. H. 1992 Three-dimensional convection in a horizontal fluid layer subjected to a constant shear. J. Fluid Mech. 234, 511.Google Scholar
El Telbany, M. M. M. & Reynolds, A. J. 1982 The structure of turbulent plane Couette flow. Trans. ASME I: J. Fluids Engng 104, 367.Google Scholar
Gavrilakis, S. 1992 Numerical simulation of low-Reynolds number turbulent flow through a straight square duct. J. Fluid Mech. 244, 101.Google Scholar
Gavrilakis, S., Tsai, H. M., Voke, P. R. & Leslie, D. C. 1986 Large-eddy simulation of low Reynolds number channel flow by spectral and finite difference methods. Not. Numer. Fluid Mech. 15, 105.Google Scholar
Guezennec, Y. G., Piomelli, U. & Kim, J. 1989 On the shape and dynamics of wall structures in turbulent channel flow. Phys. Fluids A 1, 764.Google Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1993 Regeneration of near-wall turbulence structures. 9th Symposium on Turbulent Shear Flows, Kyoto, paper 11-5.
Johansson, A. V. & Alfredsson, P. H. 1982 On the structure of turbulent channel flow. J. Fluid Mech. 122, 295.Google Scholar
Johansson, A. V. & Alfredsson, P. H. 1983 Effects of spatial resolution on measurements of wall-bounded turbulent shear flows. J. Fluid Mech. 137, 409.Google Scholar
Johansson, A. V., Alfredsson, P. H. & Kim, J. 1991 Evolution and dynamics of shear-layer structures in near-wall turbulence. J. Fluid Mech. 224, 579 (referred to herein as JAK).Google Scholar
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1971 The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50, 133.Google Scholar
Kim, J. & Hussain, F. 1993 Propagation velocity of perturbations in turbulent channel flow. Phys. Fluids A 5, 695.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741.Google Scholar
Kristoffersen, R. & Andersson, H. I. 1993 Direct numerical simulations of low Reynolds number turbulent flow in a rotating channel. J. Fluid Mech. 256, 163.Google Scholar
Kristoffersen, R., Bech, K. H. & Andersson, H. I. 1993 Numerical study of turbulent plane Couette flow at low Reynolds number. Appl. Sci. Res. 51, 337.Google Scholar
Lee, M. J. & Kim, J. 1991 The structure of turbulence in a simulated plane Couette flow. 8th Symposium on Turbulent Shear Flows, Munich, paper 5-3.
Miyake, Y., Kajishima, T. & Obana, S. 1987 Direct numerical simulation of plane Couette flow at a transitional Reynolds number. JSME Intl J. 30, 57.Google Scholar
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341.Google Scholar
Nagata, M. 1990 Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity. J. Fluid Mech. 217, 519.Google Scholar
Nishino, K. & Kasagi, N. 1991 The structure of turbulence in a simulated plane Couette flow. 8th Symposium on Turbulent Shear Flows, Munich, paper 28-3.
Papavassiliou, D. V. & Hanratty, T. J. 1994 Secondary flow and residual turbulence in plane Couette flow. Submitted to Phys. Fluids.
Reichardt, H. 1956 Über die Geschwindigkeitsverteilung in einer geradlinigen turbulenten Couetteströmung. Z. Angew. Math. Mech. 36, 26.Google Scholar
Reichardt, H. 1959 Gesetzmässigkeiten der geradlinigen turbulenten Couetteströmung. Mitt. Max-Planck-Institut für Strömungsforschung, no. 22. Göttingen.
Robertson, J. M. 1959 On turbulent plane-Couette flow. Proc. 6th Midwestern Conf. on Fluid Mech. University of Texas, Austin, p. 169.
Robertson, J. M. & Johnson, H. F. 1970 Turbulence structure in plane Couette flow. J. Engng Mech. Div. ASCE 96, 1171.Google Scholar
Robinson, S. 1991 Coherent motions in the turbulent boundary layer. Ann. Rev. Fluid Mech. 23, 601.Google Scholar
Schewe, G. 1983 On the structure and resolution of wall-pressure fluctuations associated with turbulent boundary layer flow. J. Fluid Mech. 187, 61.Google Scholar
Shah, D. A. & Antonia, R. A. 1989 Scaling of the “bursting” period in turbulent boundary layer and duct flows. Phys. Fluids A 1, 318.Google Scholar
Tillmark, N. & Alfredsson, P. H. 1991 An experimental study of transition in plane Couette flow. In Advances in Turbulence 3 (ed. A.V. Johansson & P.H. Alfredsson), p. 235. Springer.
Tillmark, N. & Alfredsson, P. H. 1992 Experiments on transition in plane Couette flow. J. Fluid Mech. 235, 89.Google Scholar
Tillmark, N. & Alfredsson, P. H. 1993 Turbulence in plane Couette flow. Appl. Sci. Res. 51, 237.Google Scholar
Tillmark, N. & Alfredsson, P. H. 1994 Structures in turbulent plane Couette flow obtained from correlation measurements. 5th European Turbulence Conference, Siena.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.