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Secondary flow in weakly rotating turbulent plane Couette flow

  • Knut H. Bech (a1) and Helge I. Andersson (a1)


As in the laminar case, the turbulent plane Couette flow is unstable (stable) with respect to roll cell instabilities when the weak background angular velocity Ωk is antiparallel (parallel) to the spanwise mean flow vorticity (-dU/dy)k. The critical value of the rotation number Ro, based on 2Ω and dU/dy of the corresponding laminar flow, was estimated as 0.0002 at a low Reynolds number with fully developed turbulence. Direct numerical simulations were performed for Ro = ±0.01 and compared with earlier results for non-rotating Couette flow. At the low rotation rates considered, both senses of rotation damped the turbulence and the number of near-wall turbulence-generating events was reduced. The destabilized flow was more energetic, but less three-dimensional, than the non-rotating flow. In the destabilized case, the two-dimensional roll cells extracted a comparable amount of kinetic energy from the mean flow as did the turbulence, thereby decreasing the turbulent kinetic energy. The turbulence anisotropy was practically unaffected by weak spanwise rotation, while the secondary flow was highly anisotropic due to its inability to contract and expand in the streamwise direction.



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Alfredsson, P. H. & Persson, H. 1989 Instabilities in channel flow with system rotation. J. Fluid Mech. 202, 543.
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.
Bech, K. H. & Andersson, H. I. 1996 Growth and decay of longitudinal roll cells in rotating turbulent plane Couette flow. In Proc. 6th European Turbulence Conference, Lausanne (to be published by Kluwer).
Bech, K. H., Tillmark, N., Alfredsson, P. H. & Andersson, H. I. 1995 An investigation of turbulent plane Couette flow at low Reynolds numbers. J. Fluid Mech. 286, 291.
Bidokhti, A. A. & Tritton, D. J. 1992 The structure of a turbulent free shear layer in a rotating fluid. J. Fluid Mech. 241, 469.
Bradshaw, P. 1987 Turbulent secondary flows. Ann. Rev. Fluid Mech. 19, 53.
Cambon, C., Benoit, J.-P., Shao, L. & Jacquin, L. 1994 Stability analysis and large-eddy simulation of rotating turbulence with organized eddies. J. Fluid Mech. 278, 175.
Gavrilakis, S. 1992 Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct. J. Fluid Mech. 244, 101.
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. Notes on Numerical Fluid Mechanics 15, 105.
Greenspan, H.P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Johnston, J. P., Halleen, R. M. & Lezius, D. K. 1972 Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow. J. Fluid Mech. 56, 533.
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.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133.
Kristoffersen, R. & Andersson, H. I. 1993 Direct simulations of low-Reynolds-number turbulent flow in a rotating channel. J. Fluid Mech. 256, 163.
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.
Lee, M. J. & Kim, J. 1991 The structure of turbulence in a simulated plane Couette flow. In Proc. 8th Symp. on Turbulent Shear Flows, Munich.
Lezius, D. K. & Johnston, J. P. 1976 Roll-cell instabilities in rotating laminar and turbulent channel flows. J. Fluid Mech. 77, 153.
Lumley, J. L. 1978 Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123.
Metais, O., Yanase, S., Flores, C., Bartello, P. & Lesieur, M. 1992 Reorganization of coherent vortices in shear layers under the action of solid-body rotation. In Turbulent Shear Flows VIII, p. 415. Springer.
Moser, R. D. & Moin, P. 1987 The effect of curvature in wall-bounded turbulent flows. J. Fluid Mech. 175, 479.
Papavassiliou, D. V. 1993 Direct numerical simulation of plane Couette flow. MS thesis, University of Illinois, Urbana-Champaign.
Smith, G. P. & Townsend, A. A. 1982 Turbulent Couette flow between concentric cylinders at large Taylor numbers. J. Fluid Mech. 123, 187.
Speziale, C. G. & Wilson, M. B. 1989 Numerical study of plane Couette flow in a rotating framework. Acta Mech. 77, 261.
Watmuff, J. H., Witt, H. T. & Joubert, P. N. 1985 Developing turbulent boundary layers with system rotation. J. Fluid Mech. 50, 133.
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