Abstract
Regular patterns of turbulent and laminar fluid motion arise in plane Couette flow near the lowest Reynolds number for which turbulence can be sustained. We study these patterns using an extension of the minimal flow unit approach to simulations of channel flows pioneered by Jiménez and Moin. In our case computational domains are of minimal size in only two directions. The third direction is taken to be large. Furthermore, the long direction can be tilted at any prescribed angle to the streamwise direction. We report on different patterned states observed as a function of Reynolds number, imposed tilt, and length of the long direction. We compare our findings to observations in large aspect-ratio experiments.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barkley, D. and Tuckerman, L.S. (1999). Stability analysis of perturbed plane Couette flow. Phys. Fluids 11, 1187–1195.
Barkley, D. and Tuckerman, L.S. (2005). Computational study of turbulent laminar patterns in Couette flow. Phys. Rev. Lett. 94, 014502.
Bottin, S., Dauchot, O., Daviaud, F. and Manneville, P. (1998). Experimental evidence of streamwise vortices as finite amplitude solutions in transitional plane Couette flow. Phys. Fluids 10, 2597–2607.
Coles, D. (1965). Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.
Coles, D. and van Atta, C.W. (1966). Progress report on a digital experiment in spiral turbulence. AIAA J. 4, 1969–1971.
Cros, A. and Le Gal, P. (2002). Spatiotemporal intermittency in the torsional Couette flow between a rotating and a stationary disk. Phys. Fluids 14, 3755–3765.
Dauchot, O. and Daviaud, F. (1995). Finite-amplitude perturbation and spots growth-mechanism in plane Couette flow. Phys. Fluids 7, 335–343.
Eckhardt, B. and Faisst, H. (2005). Dynamical systems and the transition to turbulence. In Laminar Turbulent Transition and Finite Amplitude Solutions, Proceedings of the IUTAM Symposium, Bristol, UK, 9–11 August 2004, T. Mullin and R.R. Kerswell (eds), Springer, Dordrecht, pp. 35–50 (this volume).
Faisst, H. and Eckhardt, B. (2004). Sensitive dependence on initial conditions in transition to turbulence in pipe flow. J. Fluid Mech. 504, 343–352.
Hamilton, J.M., Kim, J. and Waleffe, F. (1995). Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.
Hegseth, J.J. (1996). Turbulent spots in plane Couette flow. Phys. Rev. E 54, 4915–4923.
Henderson, R.D. and Karniadakis, G.E. (1995). Unstructured spectral element methods for simulation of turbulent flows. J. Comput. Phys. 122, 191–217.
Hof, B., Juel, A. and Mullin, T. (2003). Scaling of the turbulence transition threshold in a pipe. Phys. Rev. Lett. 91, 244502.
Jiménez, J. and Moin, P. (1991). The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.
Jiménez, J., Kawahara, G., Simens, M.P. and del Alamo, J.C. (2005). The near-wall structures of turbulent wall flows. In Proceedings of the IUTAM Conference on Elementary Vortices and Coherent Structures, S. Kida (ed.), Springer, Dordrecht, forthcoming.
Lundbladh, A. and Johansson, A.V. (1991). Direct simulation of turbulent spots in plane Couette flow. J. Fluid Mech. 229, 499–516.
Prigent, A. (2001). La spirale turbulente: Motif de grande longueur d’onde dans les écoulements cisallés turbulents. PhD Thesis, University Paris-Sud.
Prigent, A. and Dauchot, O. (2005). Transition to versus from turbulence in subcritical Couette flows. In Laminar Turbulent Transition and Finite Amplitude Solutions, Proceedings of the IUTAM Symposium, Bristol, UK, 9–11 August 2004, T. Mullin and R.R. Kerswell (eds), Springer, Dordrecht, pp. 195–219 (this volume).
Prigent, A., Grégoire, G., Chaté, H., Dauchot, O. and van Saarloos, W. (2002). Large-scale finite-wavelength modulation within turbulent shear flows. Phys. Rev. Lett. 89, 014501.
Prigent, A., Grégoire, G., Chaté, H. and Dauchot, O. (2003). Long-wavelength modulation of turbulent shear flows. Physica D 174, 100–113.
Schmiegel, A. and Eckhardt, B. (1997). Fractal stability border in plane Couette flow. Phys. Rev. Lett. 79, 5250–5253.
Schmiegel, A. and Eckhardt, B. (2000). Persistent turbulence in annealed plane Couette flow. Europhys. Lett. 51, 395–400.
Toh, S. and Itano, T. (2005). Interaction between a large-scale structure and near-wall structure in channel flow. J. Fluid Mech. 524, 249–262.
Toh, S., Itano, T. and Satoh, K. (2005). Co-supporting cycle: Sustaining mechanism of large-scale structures and near-wall structures in channel flow turbulence. In Laminar Turbulent Transition and Finite Amplitude Solutions, Proceedings of the IUTAM Symposium, Bristol, UK, 9–11 August 2004, T. Mullin and R.R. Kerswell (eds), Springer, Dordrecht, pp. 71–83 (this volume).
Tuckerman, L.S. and Tuckerman, L.S. and Barkley, D. (2002). Symmetry breaking and turbulence in perturbed plane Couette flow. Theoret. Comput. Fluid Dynam. 16, 43–48.
van Atta, C.W. (1966). Exploratory measurements in spiral turbulence. J. Fluid Mech. 25, 495–512.
Waleffe, F. (2003). Homotopy of exact coherent structures in plane shear flows. Phys. Fluids 15(6), 1517–1534.
Waleffe, F. and Wang, J. (2005). Transition threshold and the self-sustaining process. In Laminar Turbulent Transition and Finite Amplitude Solutions, Proceedings of the IUTAM Symposium, Bristol, UK, 9–11 August 2004, T. Mullin and R.R. Kerswell (eds), Springer, Dordrecht, pp. 85–106 (this volume).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer
About this paper
Cite this paper
Barkley, D., Tuckerman, L.S. (2005). Turbulent-Laminar Patterns in Plane Couette Flow. In: Mullin, T., Kerswell, R. (eds) IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions. Fluid Mechanics and its Applications, vol 77. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4049-0_6
Download citation
DOI: https://doi.org/10.1007/1-4020-4049-0_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-4048-1
Online ISBN: 978-1-4020-4049-8
eBook Packages: EngineeringEngineering (R0)