Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session L1: Nonlinear Dynamics: Coherent Structures IINonlinear Shear layer
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Chair: Philip Yecko, Cooper Union Room: 401 |
Monday, November 20, 2017 4:05PM - 4:18PM |
L1.00001: Material Barriers to Diffusive Mixing George Haller, Daniel Karrasch Transport barriers, as zero-flux surfaces, are ill-defined in purely advective mixing in which the flux of any passive scalar is zero through all material surfaces. For this reason, Lagrangian Coherent Structures (LCSs) have been argued to play the role of mixing barriers as most repelling, attracting or shearing material lines. These three kinematic concepts, however, can also be defined in different ways, both within rigorous mathematical treatments and within the realm of heuristic diagnostics. This has lead to a an ever-growing number of different LCS methods, each generally identifying different objects as transport barriers. In this talk, we examine which of these methods have actual relevance for diffusive transport barriers. The latter barriers are arguably the practically relevant inhibitors in the mixing of physically relevant tracers, such as temperature, salinity, vorticity or potential vorticity. We demonstrate the role of the most effective diffusion barriers in analytical examples and observational data. [Preview Abstract] |
Monday, November 20, 2017 4:18PM - 4:31PM |
L1.00002: Discovering Coherent Structures Using Local Causal States Adam Rupe, James P. Crutchfield, Karthik Kashinath, Mr. Prabhat Coherent structures were introduced in the study of fluid dynamics and were initially defined as regions characterized by high levels of coherent vorticity, i.e. regions where instantaneously space and phase correlated vorticity are high. In a more general spatiotemporal setting, coherent structures can be seen as localized broken symmetries which persist in time. Building off the computational mechanics framework, which integrates tools from computation and information theory to capture pattern and structure in nonlinear dynamical systems, we introduce a theory of coherent structures, in the more general sense. Central to computational mechanics is the causal equivalence relation, and a local spatiotemporal generalization of it is used to construct the local causal states, which are utilized to uncover a system's spatiotemporal symmetries. Coherent structures are then identified as persistent, localized deviations from these symmetries. We illustrate how novel patterns and structures can be discovered in cellular automata and outline the path from them to laminar, transitional and turbulent flows. [Preview Abstract] |
Monday, November 20, 2017 4:31PM - 4:44PM |
L1.00003: Identification of individual coherent sets associated with flow trajectories using Coherent Structure Coloring Kristy Schlueter-Kuck, John Dabiri In recent years, there has been a proliferation of techniques that aim to characterize fluid flow kinematics on the basis of Lagrangian trajectories of collections of tracer particles. Most of these techniques depend on presence of tracer particles that are initially closely-spaced, in order to compute local gradients of their trajectories. In many applications, the requirement of close tracer spacing cannot be satisfied, especially when the tracers are naturally occurring and their distribution is dictated by the underlying flow. Moreover, current methods often focus on determination of the boundaries of coherent sets, whereas in practice it is often valuable to identify the complete set of trajectories that are coherent with an individual trajectory of interest. We extend the concept of Coherent Structure Coloring to achieve identification of the coherent set associated with individual Lagrangian trajectories. This algorithm is proven successful in identifying coherent structures of varying complexities in canonical unsteady flows. Importantly, although the method is demonstrated here in the context of fluid flow kinematics, the generality of the approach allows for its potential application to other unsupervised clustering problems in dynamical systems. [Preview Abstract] |
Monday, November 20, 2017 4:44PM - 4:57PM |
L1.00004: Lagrangian Coherent Structures and the Onset of Jet Stream in Magnetized Plasma Driven by Drift Waves Ibere Caldas, Rafael Suigh We investigate the transport of particles on the edge of a magnetically confined plasma with a resonant and a perturbing drift wave. Chaotic transport appears in the phase space and the transport can be anomalous or diffusive and is driven by Lagrangian Coherent Structures (LCSs). To show the observed relationship between the observed transport and LCSs, we present maps of Poincar\`{e}, finite-time Lyapunov exponent diagrams. For a specific combination of parameters a jet stream appear and the transport of the chaotic region becomes asymmetric, in contrast to the symmetrical transport observed when there are no jet streams. [Preview Abstract] |
Monday, November 20, 2017 4:57PM - 5:10PM |
L1.00005: Finite-size Lagrangian coherent particle structures in thermocapillary liquid bridges Francesco Romano, Hendrik Kuhlmann A surprisingly rapid accumulation of small but finite-size particles taking curious shapes is observed in travelling hydrothermal waves in liquid bridges. The phenomenon has been termed particle accumulation structure (PAS) and belongs to the wider class of Lagrangian coherent structures. In PAS, particles are transferred from chaotic to regular regions of the flow by way of collision with the boundaries. Lubrication forces cause a dissipation of kinetic energy of the particle and give rise to particle motion attractors in the incompressible flow. Since the mechanism relies solely on the particle size, PAS is nothing but a finite-size Lagrangian coherent structure. Different theoretical models are investigated to find a minimum model for the simulation of Lagrangian finite-size coherent structures. Corresponding numerical simulations compare very well with experiments on SL-I and SL-II PAS. [Preview Abstract] |
Monday, November 20, 2017 5:10PM - 5:23PM |
L1.00006: Experimental search for Exact Coherent Structures in turbulent small aspect ratio Taylor-Couette flow Christopher J. Crowley, Michael Krygier, Roman O. Grigoriev, Michael F. Schatz Recent theoretical and experimental work suggests that the dynamics of turbulent flows are guided by unstable nonchaotic solutions to the Navier-Stokes equations. These solutions, known as exact coherent structures (ECS), play a key role in a fundamentally deterministic description of turbulence. In order to quantitatively demonstrate that actual turbulence in 3D flows is guided by ECS, high resolution, 3D-3C experimental measurements of the velocity need to be compared to solutions from direct numerical simulation of the Navier-Stokes equations. In this talk, we will present experimental measurements of fully time resolved, velocity measurements in a volume of turbulence in a counter-rotating, small aspect ratio Taylor-Couette flow. [Preview Abstract] |
Monday, November 20, 2017 5:23PM - 5:36PM |
L1.00007: Numerical investigation of exact coherent structures in turbulent small-aspect-ratio Taylor-Couette flow Michael Krygier, Christopher J. Crowley, Michael F. Schatz, Roman O. Grigoriev As suggested by recent theoretical and experimental studies, fluid turbulence can be described as a walk between neighborhoods of unstable nonchaotic solutions of the Navier-Stokes equation known as exact coherent structures (ECS). Finding ECS in an experimentally-accessible setting is the first step toward rigorous testing of the dynamical role of ECS in 3D turbulence. We found several ECS (both relative periodic orbits and relative equilibria) in a weakly turbulent regime of small-aspect-ratio Taylor-Couette flow with counter-rotating cylinders. This talk will discuss how the geometry of these solutions guides the evolution of turbulent flow in the simulations. [Preview Abstract] |
Monday, November 20, 2017 5:36PM - 5:49PM |
L1.00008: How hairpin vortices emerge from exact invariant solutions Tobias M. Schneider, Mirko Farano, Pietro De Palma, Jean-Christoph Robinet, Stefania Cherubini Hairpin vortices are among the most commonly observed flow structures in wall-bounded shear flows. However, within the dynamical system approach to turbulence, those structures have not yet been described. They are not captured by known exact invariant solutions of the Navier-Stokes equations nor have other state-space structures supporting hairpins been identified. We show that hairpin structures are observed along an optimally growing trajectory leaving a well known exact traveling wave solution of plane Poiseuille flow. The perturbation triggering hairpins does not correspond to an unstable mode of the exact traveling wave but lies in the stable manifold where non-normality causes strong transient amplification. [Preview Abstract] |
Monday, November 20, 2017 5:49PM - 6:02PM |
L1.00009: Dynamical Connections in a Turbulent Fluid: Experiment and Simulation Logan Kageorge, Balachandra Suri, Jeff Tithof, Roman Grigoriev, Michael Schatz Embedded in the state space of a turbulent flow there exist invariant solutions to the Navier-Stokes equation called Exact Coherent Structures (ECS). Recent studies have demonstrated that the geometry of the ECS locally describes the evolution of the turbulent flow\footnote{B. Suri, \textbf{Phy. Rev. Lett.} 118, 114501, 2017}. Theory suggests that global connections may serve to guide the flow from the neighborhood of one ECS to that of another. We present here a numerical model of a Kolmogorov-like two-dimensional flow in which such connections have been calculated. Moreover, we present an experimental quasi-two-dimensional realization of this flow in which these connections prove dynamically relevant. [Preview Abstract] |
Monday, November 20, 2017 6:02PM - 6:15PM |
L1.00010: An adjoint-based method for identifying invariant solutions and dynamical connections in weakly turbulent flows. Ravi Kumar Pallantla, BalaChandra Suri, Logan Kageorge, Michael Schatz, Roman Grigoriev In the past decade, numerical and experimental investigations in a variety of fluid flows have demonstrated that chaos/turbulence is guided by unstable, non-chaotic solutions. However, numerically computing these solutions using the traditional Newton-based methods is expensive and, for sufficiently large problems, may become intractable even with matrix-free methods. In this talk, we present an adjoint-based approach that overcomes some of these difficulties. We demonstrate the method by applying it to find equilibria, periodic orbits, and heteroclinic connections in an experimentally accessible Kolmogorov-like 2D flow with physical no-slip boundary conditions. [Preview Abstract] |
Monday, November 20, 2017 6:15PM - 6:28PM |
L1.00011: Application of fuzzy C-means clustering to geophysical transport Michael Allshouse Lagrangian techniques have been used to identify the underlying structures of time varying flows. The fuzzy C-means trajectory clustering is one such approach, which is based on the partitioning of trajectories into sets that remain close in Euclidean space throughout the interval of study. We apply this method first to an analytic geophysical system to determine a procedure that produces robust clusters and to determine characteristics of systems suitable for fuzzy C-means analysis. One challenge of the method is the initial seeding dependence of clustering results, which requires multiple implementations to confirm robustness. Direct comparison with the spectral clustering method demonstrates the limitations of applying the fuzzy C-means method to systems with a large number of coherent structures. We then apply our procedure to a geophysical fluid dynamics numerical simulation to visualize the dominant mechanism of transport. [Preview Abstract] |
Monday, November 20, 2017 6:28PM - 6:41PM |
L1.00012: Targeted detection of an oceanic Lagrangian transport structure Margaux Filippi, Alireza Hadjighasem, Matt Rayson, Greg Ivey, James Gilmour, Thomas Peacock To investigate the application of concepts regarding Lagrangian transport structures to oceanic flows, a field experiment was conducted at Scott Reef, a coral-reef atoll system off Western Australia. Surface velocity fields output by a numerical ocean model of the region and subsequent FTLE processing of the data revealed the existence of a pronounced Lagrangian transport structure forming at a critical time of the tidal cycle. This transport feature defined a clear, transient boundary between two bodies of water: one that remained within the atoll’s lagoon and one that was expelled via the channel. To demonstrate the actual occurrence of this feature in a field experiment, sparse arrays of surface drifters were released around the predicted time and location. The patterns of these drifter trajectories validate the predictions from our analysis. The results are a demonstration of the reliability and utility of Lagrangian processing methods for natural flows, with application, in this case, to coral reef connectivity. The specific Lagrangian feature we detected is perhaps ubiquitous to tidally-driven channel flows. [Preview Abstract] |
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