Transport and pattern formation in pipe flow: theory / simulation

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In contrast to many other flows, the flow down a pipe of circular cross-section becomes turbulent despite linear stability of its laminar parabolic profile. In addition, at low Reynolds numbers turbulence does not fill the pipe but it occurs in the form of spatially localized patches, called puffs, surrounded by laminar flow. During the start of this century there has been great progress in the understanding of the turbulent transition process and the resulting turbulent state. This success has built first on the discovery of three-dimensional coherent structures that are (traveling wave) solutions of the Navier-Stokes equation and capture features of turbulent pipe flow. Another important aspect has been the observation that puffs are transient and that their decay statistics are as expected from chaotic repellers. In the first phase of this project we have described several bifurcations of coherent structures and identified the routes to chaotic motions. We have also identified the critical point for the onset of sustained turbulence that is connected with the spatial proliferation of turbulent patches in long pipes. In the second phase of the project the focus will be on identifying the global bifurcations, on characterizing the behaviour near the critical point, on developing methods to stabilize travelling waves numerically and experimentally and on developing reduced models of pipe flow. Throughout the second phase we will continue to closely interacting with experimentalists in Erlangen, Göttingen and Delft.