Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session D37: Transitional Flows & Chaotic Dynamics: In Honor of Bruno EckhardtInvited

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Sponsoring Units: DFD Chair: Alexander Morozov, Univ of Edinburgh Room: 605 
Monday, March 2, 2020 2:30PM  3:06PM 
D37.00001: What do we learn from the finite lifetime of turbulence? Invited Speaker: Nigel Goldenfeld In a seminal paper published in 2006, Bruno Eckhardt and coworkers presented evidence to support the remarkable speculation that turbulence in shear flows  specifically pipe flow  has a finite lifetime at all Reynolds numbers, without the divergence that would be expected if the laminar and turbulent state were not analytically connected. I discuss these findings and their later extensions in terms of extreme value statistics and finitesize scaling, and show that the finite lifetime in pipe flow does not necessarily contradict the notion that there is a sharp laminarturbulence transition in the universality class of directed percolation. 
Monday, March 2, 2020 3:06PM  3:42PM 
D37.00002: Is space time? A spatiotemporal tiling of turbulence Invited Speaker: Predrag Cvitanovic We address the long standing problem of how to describe, by means 
Monday, March 2, 2020 3:42PM  4:18PM 
D37.00003: Deep learning to discover the dimension of an inertial manifold and predict dynamics on it Invited Speaker: Michael Graham One of the senior author’s last conversations with Bruno Eckhardt concerned the connection of machine learning tools and ideas to dynamical systems and turbulence. This talk concerns one such connection. Many flow geometries, including pipe, channel and boundary layer, have a continuous translation symmetry. As a model for such systems we consider the KuramotoSivashinsky equation (KSE) in a periodic domain. We describe a method to map the dynamics onto a translationally invariant lowdimensional manifold and timeevolve them using neural networks (NN). Dimensionality reduction is achieved by phasealigning the spatial structures at each time, then putting them into an undercomplete autoencoder that maps the original dynamics onto a lowerdimensional inertial manifold where the longtime dynamics live. We infer the dimension of the manifold by tracking the autoencoder error vs. dimension—this drops by orders of magnitude once the proper dimension is reached. The spatial structure and phase are then integrated forward in time using a NN. This approach significantly outperforms Principal Components Analysis. 
Monday, March 2, 2020 4:18PM  4:54PM 
D37.00004: The onset of turbulence: from invariant solutions to a directed percolation phase transition Invited Speaker: Bjoern Hof Flows through pipes and channels exhibit an abrupt transition from ordered laminar to high dimensional turbulent flow. At the lowest Reynolds numbers where this transition can be observed the resulting flows are spatio temporally intermittent and are composed of patches of turbulence surrounded by laminar fluid. As will be shown, in direct numerical simulations individual turbulent patches (i.e. stripes and puffs) can be continued to much lower Reynolds numbers where they originate from spatially localized periodic orbit solutions. I will further discuss experimental studies of interacting turbulent patches and how the competition between the decay and the proliferation of turbulence gives rise to a phase transition to sustained turbulence. 
Monday, March 2, 2020 4:54PM  5:30PM 
D37.00005: Nonlinear invariant solutions underlying spatiotemporal patterns in thermally driven shear flows Invited Speaker: Tobias Schneider Driven wallbounded fluid flows transitioning to turbulence are spatially extended chaotic dissipative nonequilibrium systems that support a large variety of selforganized patterns with regular spatial and temporal structure. In linearly stable parallel shear flows, patterns such as longstudied spontaneously emerging turbulentlaminar oblique stripes remain only partly understood. On the contrary, thermal convection in a fluid layer between two horizontal plates kept at different temperature, exhibits patterns that can often be described via a sequence of bifurcations off a base state undergoing a linear instability. If a RayleighBénard convection cell is inclined against gravity, buoyancy forces drive hot and cold fluid up and down the incline leading to a shear flow. In this socalled inclined layer convection (ILC) system, the competition of buoyancy and shear gives rise to a large variety of complex spatiotemporal flow patterns. 
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