Recurrent Flows: The Clockwork Behind Turbulence

Coordinators: ​Predrag Cvitanović, Bruno Eckhardt, John Gibson, and Mike Graham

Scientific Advisors: Eberhard Bodenschatz and Eckart Meiburg

The transition to turbulence in pipe flow has remained one of the outstanding puzzles in fluid mechanics since its description by Osborne Reynolds in 1883. There is no linear instability, the turbulent state is immediately complex, and it is not persistent but transient. Moreover, the flow in the transitional regime is spatially and temporally highly intermittent, and very sensitive to perturbations. Given the difficulties in predicting the transition to turbulence in such simple geometries, it is not surprising that a predictive theory of turbulence has been considered a major outstanding problem of physics.

The 1990's discoveries of unstable steady and travelling solutions of the 3-D Navier-Stokes equations, and the subsequent detection of glimpses of them in experiments, promises a solution to many of these issues. Moreover, there are intriguing observations of large-scale coherent structures at higher Reynolds numbers, that could also be related to the presence of such exact solutions. It is now clear that these unstable coherent structures are key to the appearance of turbulence and its spatial and temporal properties.

The purpose of the program is to take stock of these achievements and the open experimental and theoretical issues, in particular the connections between the dynamical description, the theory of pattern formation, and the statistical description of the spatio-temporal dynamics of transitionally turbulent flows. On the other hand, the identification of recurrent coherent structures (“recurrent flows”) and their interconnections requires development of new computational tools. We will also extend the scope of the recurrent flow framework to spatially inhomogeneous flows such as boundary layers, bluff bodies and wings. There, spatial development plays an important role, and one has to look for recurrent flows in spatially expanding systems.