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The rich structure of transition in a shear flow

Published online by Cambridge University Press:  07 April 2010

T. MULLIN
T. MULLIN*
Affiliation:
Manchester Centre for Nonlinear Dynamics, University of Manchester, Manchester M13 9PL, UK
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Abstract

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Significant advances have been made in applying ideas from nonlinear dynamical systems theory to flows which exhibit sequences of bifurcations in the transition to turbulence. Moreover, the recent discoveries of finite-amplitude states in linearly stable flows holds great promise for a breakthrough in our understanding transition in shear flows. Tsukahara, Tillmark & Alfredsson (J. Fluid Mech., 2010, this issue, vol. 648, pp. 5–33) study a novel variant of a classical shear flow by adding global rotation. The competition between the induced body force and shear-induced instabilities leads to the discovery of a rich and beautiful tapestry of transition sequences.

Type
Focus on Fluids
Information
Journal of Fluid Mechanics , Volume 648 , 10 April 2010 , pp. 1 - 4
Copyright
Copyright © Cambridge University Press 2010

References

Benjamin, T. B. & Mullin, T. 1982 Notes on the multiplicity of flows in the Taylor experiment. J. Fluid Mech. 121, 219–230.CrossRefGoogle Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.CrossRefGoogle Scholar
Emmons, H. W. 1951 The laminar-turbulent transition in a boundary layer. Part 1. J. Aeronaut. Sci. 18, 490–498.CrossRefGoogle Scholar
Faisst, H. & Eckhardt, B. 2003 Travelling waves in pipe flow. Phys. Rev. Lett. 91, 224502.CrossRefGoogle ScholarPubMed
Moncaux, R., Ravelet, F., Dubrulle, B., Chiffaudel, A. & Daviaud, F. 2006 Properties of steady states in turbulent axisymmetric flows. Phys. Rev. Lett. 96, 124502.CrossRefGoogle Scholar
Mullin, T., Cliffe, K. A. & Pfister, G. 1987 Unusual time-dependent phenomena in Taylor–Couette flow at moderately low Reynolds numbers. Phys. Rev. Lett. 58, 2212–2215.CrossRefGoogle ScholarPubMed
Nagata, M. 1990 Three-dimensional finite-amplitude solutions in plane Couette flow; bifurcation from infinity. J. Fluid Mech. 217, 519–527.CrossRefGoogle Scholar
Nagata, M. 1998 Tertiary solutions and their stability in rotating plane Couette flow. J. Fluid Mech. 358, 357–378.CrossRefGoogle Scholar
Prigent, A. & Dauchot, O. 2005 Transition to versus from turbulence in subcritical Couette flows. In IUTAM Symposium on Laminar Turbulent Transition and Finite Amplitude Solutions (ed. Mullin, T. & erswell, R. R.), Fluid Mechanics and its Applications, vol. 77, pp. 173–183. Springer.Google Scholar
Romanov, V. A. 1973 Stability of plane-parallel Couette flow. Funct. Anal. Appl. 7, 137–146.CrossRefGoogle Scholar
Stevens, R. J. A. M., Zhong, J., Clercx, H. J. H., Ahlers, G. & Lohse, D. 2009 Transitions between turbulent states in rotating Raleigh–Benard convection. Phys. Rev. Lett. 103, 024503.CrossRefGoogle ScholarPubMed
Tsukahara, T., Tillmark, N. & Alfredsson, P. H. 2010 Flow regimes in a plane Couette flow with system rotation. J. Fluid Mech. 648, 5–33.CrossRefGoogle Scholar
Waleffe, F. 2001 Exact coherent structures in channel flow. J. Fluid Mech. 435, 93–102.CrossRefGoogle Scholar
Wedin, H. & Kerswell, R. R. 2004 Exact coherent structures in pipe flow: travelling wave solutions. J. Fluid Mech. 508, 333–371.CrossRefGoogle Scholar
Willis, A. P. & Kerswell, R. R. 2008 Coherent structures in localized and global pipe turbulence. Phys. Rev. Lett. 100, 124501.CrossRefGoogle ScholarPubMed