Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session L29: Chaos, Fractals, and Dynamical Systems I: Lagrangian Coherent Structures |
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Chair: Wenbo Tang, Arizona State University Room: 32B |
Monday, November 19, 2012 3:35PM - 3:48PM |
L29.00001: Lagrangian Coherent Structures separate dynamically distinct regions Douglas Kelley, Michael Allshouse, Nicholas Ouellette Lagrangian Coherent Structures (LCS) are special material lines that play a role in unsteady flow analogous to the stable and unstable manifolds of hyperbolic fixed points in periodic flows. Since they are material lines, fluid elements cannot cross them, and thus they separate regions of the flow field that are kinematically distinct. Using recently developed filter-space techniques that allow us to localize spectral transport processes in space, we study the Lagrangian averages of scale-to-scale energy transfer in an experimental quasi-two-dimensional flow. We find that, surprisingly, LCS appear to divide regions that are dynamically as well as kinematically distinct. We find that on the average LCS separate parts of the flow field with coherent (in a Lagrangian sense) scale-to-scale energy fluxes in different directions. [Preview Abstract] |
Monday, November 19, 2012 3:48PM - 4:01PM |
L29.00002: Particle manipulation using vibrating cilia Phanindra Tallapragada, Scott Kelly The ability to manipulate small particles suspended in fluids has many practical applications, ranging from the mechanical testing of macromolecules like DNA to the controlled abrasion of brittle surfaces for precision polishing. A natural method is non-contact manipulation of particles through boundary excitations. Particle-manipulation via a vibrating cilia to establish controlled fluid flows with desired patterns of transport is one such bioinspired method. We show experimental results on the clustering and transport of finite-sized particles in the streaming flow set up by the oscillating cilia. We further show computations to explain the effects of hyperbolic structures in the four dimensional phase space of the dynamics of finite-sized particles. [Preview Abstract] |
Monday, November 19, 2012 4:01PM - 4:14PM |
L29.00003: Passive scalar statistics and its dependence on Lagrangian coherent structures in stochastic flows Wenbo Tang, Phillip Walker, Michael Allshouse, Diego del-Castillo-Negrete In recent years, various mathematical tools have been developed to identify the organizing mixing patterns in deterministic aperiodic dynamical systems. In this talk we will discuss the dependence on different identification methods, (Lagrangian Okubo-Weiss, Finite-time Lyapunov exponents, ergodicity partition and geodesic theory), of Lagrangian statistics associated with stochastic aperiodic dynamical systems (e.g. fluid flows with subgrid-scale uncertainties). Gaussian and L\'{e}vy type noises will be considered. [Preview Abstract] |
Monday, November 19, 2012 4:14PM - 4:27PM |
L29.00004: Finite-time statistics of scalar diffusion in Lagrangian coherent structures Phillip Walker, Wenbo Tang When investigating chaotic mixing in nonlinear aperiodic dynamic systems, the domain can be frame-independently partitioned into different regions identified by Lagrangian coherent structures (LCS). We consider stochastic scalar dispersion associated with LCS and find that the statistics of various moments exhibit strong coherence in separate flow partitions. The probability density of dispersion approach self-similar profiles with anomalous exponents at intermediate time scales. Such coherence in statistics indicate that the Lagrangian topology highlight variability of diffusion. In this talk we explore such correlation between Lagrangian topology, as identified by LCS, and effective mixing. [Preview Abstract] |
Monday, November 19, 2012 4:27PM - 4:40PM |
L29.00005: Efficient and robust detection of transport barriers using the geodesic approach Michael Allshouse, Jean-Luc Thiffeault, Thomas Peacock There is an increasing number of applications where the identification of transport barriers is valuable. A recent advance in transport barrier theory has created a unified approach to detecting hyperbolic (LCS based), elliptic (KAM based), and parabolic (shear jets) transport barriers. We have developed an algorithm building on the details from this result. We present a number of modifications to the algorithm which aim to increase accuracy, reduce unnecessary calculations, and make the method suitable for practical applications. This approach is then applied to an ocean surface model to study transport barriers present during the Deepwater Horizon spill. [Preview Abstract] |
Monday, November 19, 2012 4:40PM - 4:53PM |
L29.00006: Integrated computation of Lagrangian coherent structures during DNS of unsteady and turbulent flows Justin Finn, Sourabh Apte The computation of Lagrangian coherent structures (LCS) typically involves post processing of experimentally or numerically obtained fluid velocity fields to obtain the finite time Lyapunov exponent (FTLE) via a sequence of flow maps (vector fields which describe fluid displacement patterns over a finite time interval, $t_0 \pm T$). However, this procedure can be prohibitively expensive for large-scale complex flows of engineering interest. In this work, an alternative approach involving computation of the FTLE on the fly during direct numerical simulation (DNS) of the 3D Navier-Stokes equations is developed. This incorporation of the FTLE computations into a parallel DNS solver relies on Lagrangian particle tracking to compose forward time flow maps, and an Eulerian treatment of the backward time flow map [Leung, J. Comp. Physics 2011] coupled with a semi-Lagrangian advection scheme. The time $T$ flow maps are accurately constructed from smaller sub-steps [Brunton \& Rowley, Chaos 2010], resulting in low CPU and memory requirements for computing evolving FTLE fields. Illustrative examples will be presented to demonstrate the capability of the approach including the evolution of a turbulent vortex ring and turbulent flows in complex porous media. [Preview Abstract] |
Monday, November 19, 2012 4:53PM - 5:06PM |
L29.00007: Visualization of invariant sets in incompressible fluid flows from Lagrangian data Marko Budi\v{s}i\'{c}, Igor Mezi\'{c} We analyze Lagrangian data of incompressible fluid flows to provide a coarse-grained visualization of material transport. It is often difficult to resolve features in 3D plots of trajectories. Instead, we visualize sets that are transport-invariant. In spirit, the algorithm groups trajectories that are similar \emph{on average} into invariant sets of different spatial scales. Invariant sets are represented by level-sets of flow-invariant functions, which partition the space. We construct such invariant functions by averaging a basis set, e.g., Fourier basis, along Lagrangian trajectories. Our Ergodic Quotient algorithm then combines trajectory averages to form scale-ordered invariant partitions. The lower orders visualize coarse features, e.g., dominant vortices, while higher orders resolve sub-features, e.g., secondary vortices weaving around the dominant ones. The algorithm is suitable for visualization of both numerical and experimental Lagrangian data. It has a benefit of not requiring an access to the entire space: it is possible to resolve the features even by seeding initial conditions into experimentally accessible regions and allowing for the flow to disperse the tracers. We demonstrate the algorithm on several numerical flows and explain future extensions. [Preview Abstract] |
Monday, November 19, 2012 5:06PM - 5:19PM |
L29.00008: Short- and Long- Time Transport Structures in a Three Dimensional Time Dependent Flow Rodolphe Chabreyrie, Stefan Llewellyn Smith Lagrangian transport structures for three-dimensional and time-dependent fluid flows are of great interest in numerous applications, particularly for geophysical or oceanic flows. In such flows, chaotic transport and mixing can play important environmental and ecological roles, for examples in pollution spills or plankton migration. In such flows, where simulations or observations are typically available only over a short time, understanding the difference between short-time and long-time transport structures is critical. In this talk, we use a set of classical (i.e. Poincar\'e section, Lyapunov exponent) and alternative (i.e. finite time Lyapunov exponent, Lagrangian coherent structures) tools from dynamical systems theory that analyze chaotic transport both qualitatively and quantitatively. With this set of tools we are able to reveal, identify and highlight differences between short- and long-time transport structures inside a flow composed of a primary horizontal contra-rotating vortex chain, small lateral oscillations and a weak Ekman pumping. The difference is mainly the existence of regular or extremely slowly developing chaotic regions that are only present at short time. [Preview Abstract] |
Monday, November 19, 2012 5:19PM - 5:32PM |
L29.00009: The role of filamentation and vortex merging in coastal particle accumulation and transport Cheryl Harrison, David Siegel, Satoshi Mitarai Understanding ocean transport of coastally released material is crucial for predicting planktonic and pollutant transport. Here we use a coupled particle-tracking/ocean circulation model of an upwelling current to identify important transport processes at meso- to submesoscales. Buoyant particles released over the continental shelf simulate surface following planktonic material. Particles are largely organized into filaments found between mesoscale eddies that correspond to attracting Lagrangian coherent structures (LCS), material curves that map filamentation and transport boundaries, and here correlate with temperature fronts and their associated secondary ageostrophic circulation. Filamentation and vortex merging reduce mixing, aggregating particles from many source regions and release times into small, highly dense packets. As predicted by structural stability of LCS, filaments and packets are robust to strong levels of random walk ``swimming'' perturbations, indicating these processes will be robust to a wide range of planktonic behavioral strategies. This study demonstrates that 1) coherent flow structures play an important role in pelagic transport of marine propagules, plankton and floating pollutants in the coastal ocean, and 2) dynamical systems techniques will have broad applicability in these systems. [Preview Abstract] |
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