Colloquium on January 19th, 2009

Bruno Eckhardt
Universität Marburg

Turbulence transition in pipe flow and other shear flows

The phenomenology of the transition to turbulence in pipe flow was documented in a
careful stuy by Osborne Reynolds in 1883. The transition arises without a linear
instability of the base profile, goes immediately to a spatially and temporally fluctuating state and does not fill the entire pipe but remains localized. The lack of understanding of the transition is reflected well in the variation in the critical Reynolds numbers that are quoted in the literature: they range between 1000 to several thousands. Tools and ideas from dynamical systems theory suggest that the transition is connected with the appearance of three-dimensional coherent structures and their heteroclinic connections.
Studies on plane Couette flow and a boundary layer flow show that these ideas apply to a wide range of shear and boundary layer flows and open up new avenues to understanding and manipulating turbulence transitions in shear flows.

[1] Eckhardt, B., Schneider, T. M., Hof, B., and Westerweel, J. (2007).
Annu. Rev. Fluid Mech., 39:447?468.
[2] Skufca, J., Yorke, J., and Eckhardt, B. (2006). Phys. Rev. Lett., 96:174101.
[3] Schneider, T. M., Eckhardt, B., and Yorke, J. A. (2007). Phys. Rev. Lett., 99:034502.
[4] Schneider, T.M., Gibson, J.F., Lagha, M., deLillo F., and Eckhardt, B. (2008), Physical Review E 78:037301.