Over a century of research into the origin of turbulence in wall-bounded shear flows has resulted in a puzzling picture in which turbulence appears in a variety of different states competing with laminar background flow. At moderate flow speeds, turbulence is confined to localized patches; it is only at higher speeds that the entire flow becomes turbulent. The origin of the different states encountered during this transition, the front dynamics of the turbulent regions and the transformation to full turbulence have yet to be explained. By combining experiments, theory and computer simulations, here we uncover a bifurcation scenario that explains the transformation to fully turbulent pipe flow and describe the front dynamics of the different states encountered in the process. Key to resolving this problem is the interpretation of the flow as a bistable system with nonlinear propagation (advection) of turbulent fronts. These findings bridge the gap between our understanding of the onset of turbulence and fully turbulent flows.
We acknowledge the Deutsche Forschungsgemeinschaft (Project No. FOR 1182), and the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement 306589 for financial support. B.S. acknowledges financial support from the Chinese State Scholarship Fund under grant number 2010629145. B.S. acknowledges support from the International Max Planck Research School for the Physics of Biological and Complex Systems and the Göttingen Graduate School for Neurosciences and Molecular Biosciences. We acknowledge computing resources from GWDG (Gesellschaft für wissenschaftliche Datenverarbeitung Göttingen) and the Jülich Supercomputing Centre (grant HGU16) where the simulations were performed.
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Barkley D, Song B, Vasudevan M, Lemoult GM, Avila M, Hof B. The rise of fully turbulent flow. Nature. 2015;526(7574):550-553. doi:10.1038/nature15701
Barkley, D., Song, B., Vasudevan, M., Lemoult, G. M., Avila, M., & Hof, B. (2015). The rise of fully turbulent flow. Nature. Nature Publishing Group. https://doi.org/10.1038/nature15701
Barkley, Dwight, Baofang Song, Mukund Vasudevan, Grégoire M Lemoult, Marc Avila, and Björn Hof. “The Rise of Fully Turbulent Flow.” Nature. Nature Publishing Group, 2015. https://doi.org/10.1038/nature15701.
D. Barkley, B. Song, M. Vasudevan, G. M. Lemoult, M. Avila, and B. Hof, “The rise of fully turbulent flow,” Nature, vol. 526, no. 7574. Nature Publishing Group, pp. 550–553, 2015.
Barkley D, Song B, Vasudevan M, Lemoult GM, Avila M, Hof B. 2015. The rise of fully turbulent flow. Nature. 526(7574), 550–553.
Barkley, Dwight, et al. “The Rise of Fully Turbulent Flow.” Nature, vol. 526, no. 7574, Nature Publishing Group, 2015, pp. 550–53, doi:10.1038/nature15701.