Abstract
An energy transfer analysis of turbulent plane Couette flow is performed. It is found that nonlinear interaction between the [0, ±1] modes is principally responsible for maintaining the mean streamwise turbulent velocity profile. The [0, ±1] modes extract energy from the laminar flow by linear non-modal growth mechanisms and transfer it directly to the mean flow mode. The connection of this work to linear/nonlinear models of transition is discussed.
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
Baggett, J.S., Driscoll, T.A., Trefethen, L.N. (1995) A mostly linear model of transition to turbulence, Phys. Fluids 7: 833–838
Baggett, J.S., Trefethen, L.N. (1997) Low-dimensional models of subcritical transition to turbulence, Phys. Fluids 9: 1043–1053
Boberg, L., Brosa, U. (1988) Onset of turbulence in a pipe, Z. Naturforschung 43a: 697–726
Butler, K.M., Farrell, B.F. (1992) Three-dimensional optimal perturbations in viscous shear flow, Phys. Fluids A 4: 1637–1650
Drazin, P.G., Reid, W.H. (1981) Hydrodynamic Stability, Cambridge University Press, Cambridge
Ellingsen, T, Palm, E. (1975) Stability of linear flow, Phys. Fluids 18: 487–488
Farrell, B.F., Ioannou, P.J. (1994) Variance maintained by stochastic forcing of non-normal dynamical systems associated with linear stable shear flows, Phys. Rev. Lett. 72: 1188–1191
Farrell, B.F., Ioannou, P.J. (1996) Generalized stability theory I: Autonomous systems, J. Atmos. Sci. 53: 2025–2039
Farrell, B.F., Ioannou, P.J. (1998) Perturbation structure and spectra in turbulent channel flow, Theoret. Comput. Fluid Dynamics 11: 237–250
Gebhardt, T., Grossman, S. (1994) Chaos transition despite linear stability, Phys. Rev. E 50: 3705–3711
Hamilton, J. M., Kim, J., Waleffe, F. (1995) Regeneration mechanisms of near-wall turbulence structures, J. Fluid Mech. 287: 317–348
Lundbladh, A., Henningson, D.S., Johansson, A.V. (1992) An efficient spectral integration method for the solution of the Navier-Stokes equations. Technical Report FFA-TN 1992–28, Aeronautical Research Institute of Sweden, Bromma, Sweden
Schmid, P. J., Henningson, D.S. (1995) Nonlinear energy density transfer in plane Poiseuille flow. In: Benzi, R. (Ed.) Advances in Turbulence V, Kluwer, Dordrecht, The Netherlands
Trefethen, L.N., Trefethen, A.E., Reddy, S.C., Driscoll, T.A. (1993) Hydrodynamic stability without eigenvalues, Science 261: 578–584
Waleffe, F. (1997) On a self-sustaining process in shear flows, Phys. Fluids 9: 883–900
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Reddy, S.C., Ioannou, P.J. (2000). Energy Transfer Analysis of Turbulent Plane Couette Flow. In: Fasel, H.F., Saric, W.S. (eds) Laminar-Turbulent Transition. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03997-7_30
Download citation
DOI: https://doi.org/10.1007/978-3-662-03997-7_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08752-3
Online ISBN: 978-3-662-03997-7
eBook Packages: Springer Book Archive