Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session A29: Nonlinear Dynamics: Coherent Structures I 
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Chair: Nicholas Ouellette, Stanford University Room: 310 
Sunday, November 22, 2015 8:00AM  8:13AM 
A29.00001: Correlating Lagrangian structures with forcing in twodimensional flow Nicholas Ouellette, Charlie Hogg, Yang Liao Lagrangian coherent structures (LCSs) are the dominant transport barriers in unsteady, aperiodic flows, and their role in organizing mixing and transport has been well documented. However, nearly all that is known about LCSs has been gleaned from passive observations: they are computed in a postprocessing step after a flow has been observed, and used to understand why the mixing and transport proceeded as it did. Here, we instead take a first step toward controlling the presence or locations of LCSs by studying the relationship between LCSs and external forcing in an experimental quasitwodimensional weakly turbulent flow. We find that the likelihood of finding a repelling LCS at a given location is positively correlated with the mean strain rate injected at that point and negatively correlated with the mean speed, and that it is not correlated with the vorticity. We also find that mean time between successive LCSs appearing at a fixed location is related to the structure of the forcing field. Finally, we demonstrate a surprising difference in our results between LCSs computed forward and backwards in time, with forwardtime (repelling) LCSs showing much more correlation with the forcing than backwardstime (attracting) LCSs. [Preview Abstract] 
Sunday, November 22, 2015 8:13AM  8:26AM 
A29.00002: A Spectral Clustering Approach to Lagrangian Vortex Detection Alireza Hadjighasem, Daniel Karrasch, Hiroshi Teramoto, George Haller One of the ubiquitous features of reallife turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent Lagrangian vortices in several two and threedimensional flows. [Preview Abstract] 
Sunday, November 22, 2015 8:26AM  8:39AM 
A29.00003: Objective Eulerian Coherent Structures and their ShortTerm Prediction Mattia Serra, George Haller We discuss a frameinvariant (objective) method for Eulerian Coherent Structure (ECS) identification in twodimensional unsteady flows. ECSs reveal a timevarying skeleton of fluid flows that instantaneously approximates the most influential material surfaces in transport and mixing. We also describe an objective nondimensional metric that quantifies the persistence of vortextype ECSs. In an application to persistent eddy detection in satellitederived ocean velocity data, we find that our ECS persistence metric significantly outperforms vortex predictions from other customary Eulerian diagnostics, such as the potential vorticity gradient and the OkuboWeiss criterion. [Preview Abstract] 
Sunday, November 22, 2015 8:39AM  8:52AM 
A29.00004: Variational approach to Lagrangian vortices in 3D unsteady flows David Oettinger, Daniel Blazevski, George Haller From a Lagrangian perspective, vortices can be viewed as material surfaces, i.e., as surfaces moving with the fluid. Lagrangian vortices are therefore directly linked to particle motion. Here, we use the objective (frameinvariant) approach of Lagrangian Coherent Structures (LCSs) to identify Lagrangian vortices as tubular, nonfilamenting material surfaces (elliptic LCSs). By introducing a dual and autonomous dynamical system, we present a new method for constructing LCSs in threedimensional unsteady flows. We illustrate the geometric significance of this approach with various examples. [Preview Abstract] 
Sunday, November 22, 2015 8:52AM  9:05AM 
A29.00005: Complexity of coherent structures computed from braids of passive particles Marko Budisic, JeanLuc Thiffeault Transport in fluids can be characterized by tracking passive particles advected by the fluid flow. When particles are distributed densely, as can be achieved in laboratory, the fluid velocity field can be reconstructed through Particle Tracking Velocimetry, enabling computation of Lyapunov exponents or other numerical analyses. When particles are sparse, as in drifter measurements of oceans, the velocity field cannot be reliably reconstructed. Nevertheless, the amount of entanglement of particle paths over time can be used to estimate the dynamical complexity of the flow by computing the FiniteTime Braiding Exponent (FTBE). The technique is based on braid dynamics and measures the rate at which particle motion stretches topological loops, i.e., the ``rubber bands'' enclosing subsets of particles. Allshouse and Thiffeault showed that minimallystretching loops correspond to the structures coherent under material transport in flows. We extend their work and couple it to the FTBE calculations in order to characterize the spatial distribution of flow complexity. Analysis is demonstrated on the Hackborn rotoroscillator model, which exhibits regions of chaotic and regular dynamics, and can be realized both numerically and experimentally. [Preview Abstract] 
Sunday, November 22, 2015 9:05AM  9:18AM 
A29.00006: Laboratory experimental investigations of braid theory using the rotoroscillator flow Margaux Filippi, S\'everine Atis, Michael Allshouse, Gustaaf Jacobs, Marko Budi\v{s}i\'{c}, JeanLuc Thiffeault, Thomas Peacock Interpreting ocean surface dynamics is crucial to many areas of oceanography, ranging from marine ecology to pollution management. Motivated by this, we investigated the braid theory method to detect transport barriers bounding coherent structures in twodimensional flows. Whereas most existing techniques rely on an extensive spatiotemporal knowledge of the flow field, we sought to identify these structures from sparse data sets involving trajectories of a few tracer particles in a twodimensional flow. We present the results from our laboratory experiments, which were based on investigations using the rotoroscillator flow, as a stepping stone towards oceanic applications. [Preview Abstract] 
Sunday, November 22, 2015 9:18AM  9:31AM 
A29.00007: Lagrangian transport near perturbed periodic lines in threedimensional unsteady flows Michel Speetjens Periodic lines formed by continuous strings of periodic points are key organizing entities in the Lagrangian flow topology of certain threedimensional (3D) timeperiodic flows. Such lines generically consist of elliptic and/or hyperbolic points and thus give rise to 3D flow topologies made up of families of concentric closed trajectories embedded in chaotic regions. Weak perturbation destroys the periodic lines and causes said trajectories to coalesce into families of concentric tubes. However, emergence of isolated periodic points near the disintegrating periodic lines and/or partitioning of the original lines into elliptic and hyperbolic segments interrupt the tube formation. This yields incomplete tubes that interact with the (chaotic) environment through their open ends, resulting in intricate and essentially 3D flow topologies These phenomena have been observed in various realistic flows yet the underlying mechanisms are to date only partially understood. This study deepens insight into the (perturbed) Lagrangian dynamics of these flows by way of a linearized representation of the equations of motion near the periodic lines. Predictions on the basis of this investigation are in full (qualitative) agreement with observed behavior in the actual flows [Preview Abstract] 
(Author Not Attending)

A29.00008: Lagrangian coherent structures as mesoscale transport barriers in atmospheric flows Shibabrat Naik, Shane Ross Coherent structures in twodimensional flows have long been studied in the context of transport in fluid dynamics. However, for geophysical systems a small vertical velocity can lead to nontrivial threedimensional motion of airborne biological populations affecting agriculture or hazardous outputs from natural disasters. The pathways and barriers in the lower atmosphere, from ground level to a kilometer altitude and over a horizontal scale of several kilometerswhich bridge the scale of, for example, local farmlands to the larger regional scaleare still unclear. This requires exploring relevant spatiotemporal scales related to advection in the space of 3D + time. In this talk, we will present the application of finitetime Lyapunov exponent based threedimensional Lagrangian coherent structures (LCS) to address questions of transport using historical data sets from satellite observations, field measurements and the Weather Research and Forecasting (WRF) model. [Preview Abstract] 
Sunday, November 22, 2015 9:44AM  9:57AM 
A29.00009: The domain dependence of chemotaxis in twodimensional turbulence Wenbo Tang, Kimberly Jones, Phillip Walker Coherent structures are ubiquitous in environmental and geophysical flows and they affect reactiondiffusion processes in profound ways. In this presentation, we show an example of the domain dependence of chemotaxis process in a twodimensional turbulent flow. The flow has coherent structures that form barriers that prohibit longrange transport of tracers. Accordingly, the uptake advantage of nutrient by motile and nonmotile species differs significantly if the process start in different locations of the flow. Interestingly, the conventional diagnostic of Finitetime Lyapunov exponents alone is not sufficient to explain the variability  methods to extract elliptic transport barriers are essential to relate to the explanation. We also offer some explanations of the observed scalar behaviors via analyses of bulk quantities. [Preview Abstract] 
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