Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session G35: Chaos, Fractals, and Dynamical Systems I: Coherent Structures |
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Chair: Shawn Shadden, University of California, Berkeley Room: 406 |
Monday, November 25, 2013 8:00AM - 8:13AM |
G35.00001: Lagrangian Coherent Structures and their application to ocean transport Thomas Peacock, Michael Allshouse The approach of Lagrangian Coherent Structures (LCSs) holds great promise for improved understanding of flow transport in the ocean, with potentially significant application to scenarios such as improved decision making strategies for pollution events. We present some improved methodology for identifying, refining and classifying LCSs in data sets and assess the utility of the approach through a number of case studies. [Preview Abstract] |
Monday, November 25, 2013 8:13AM - 8:26AM |
G35.00002: Coherent structures in reacting flows John Mahoney, Kevin Mitchell Our goal is to characterize the nature of reacting flows by identifying important ``coherent'' structures. We follow the recent work by Haller, Beron-Vera, and Farazmand which formalized the the notion of lagrangian coherent structures (LCSs) in fluid flows. In this theory, LCSs were derived from the Cauchy-Green strain tensor. We adapt this perspective to analogously define coherent structures in \emph{reacting} flows. By this we mean a fluid flow with a reaction front propagating through it such that the propagation does not affect the underlying flow. A reaction front might be chemical (Belousov-Zhabotinsky, flame front, etc.) or some other type of front (electromagnetic, acoustic, etc.). While the recently developed theory of burning invariant manifolds (BIMs) describes barriers to front propagation in time-periodic flows, this current work provides an important complement by extending to the aperiodic setting. [Preview Abstract] |
Monday, November 25, 2013 8:26AM - 8:39AM |
G35.00003: An extension of shear and strain LCS concepts to higher dimensions Siavash Ameli, Shawn C. Shadden A framework is presented for the extension of strain and shear barrier concepts to $R^n$. The concept of shear barrier was introduced by Haller \& Beron-Vera [Physica D 241 2012] in $R^2$. The framework presented herein also generalizes to normally hyperbolic, or strain LCS, as introduced by Haller [Physica D 240 2011]. We use a projection operator approach to define Lagrangian shear strain and Lagrangian normal strain vector fields from the Cauchy-Green strain tensor. These Lagrangian strain vector fields are the basis for defining maximal shear LCS, and maximal and minimal strain LCS. Criteria for shear and strain LCS are natural analogs, helping to unify these concepts. [Preview Abstract] |
Monday, November 25, 2013 8:39AM - 8:52AM |
G35.00004: Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems Ana M. Mancho, Stephen Wiggins, Jezabel Curbelo, Carolina Mendoza Lagrangian descriptors are a recent technique which reveals geometrical structures in phase space and which are valid for aperiodically time dependent dynamical systems. We discuss a general methodology for constructing them and we discuss a ``heuristic argument'' that explains why this method is successful. We support this argument by explicit calculations on a benchmark problem. Several other benchmark examples are considered that allow us to assess the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (``time averages''). In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. [Preview Abstract] |
Monday, November 25, 2013 8:52AM - 9:05AM |
G35.00005: Experimental Three Dimensional Lagrangian Coherent Structures of Inertial Particles in Flows Samuel Raben, Shane Ross, Pavlos Vlachos Finite Time Lyapunov Exponents (FTLE) are a powerful and increasingly popular tool for describing mixing and transport in both turbulent and laminar flow fields. FTLEs provide a measure of the exponential rate of divergence or convergence of Lagrangian particle trajectories and can be used both experimentally and numerically to describe a flow field, which may have a high degree of spatiotemporal complexity. While primarily used to describe single-phase flow behavior some works have attempted to account for inertial particles by modeling the particles' motion through simulations. This procedure can provide insight, but does not provide direct information about the true observable inertial particle trajectories. This work provides a method to more directly determine FTLEs from experimental data for inertial particles through the use of particle tracking velocimetry (PTV) without any a-priori assumptions about particle motion. We show, in a turbulent 3D flow field, how FTLE for various particles sizes can be computed with out numerical integration and how separating the particles effects the resulting FLTE field. This work can provide future insight into multiphase flow research and the study of inertial particle motion. [Preview Abstract] |
Monday, November 25, 2013 9:05AM - 9:18AM |
G35.00006: Inertial particle dynamics: Coherent structures in the presence of the Basset--Boussinesq memory term Mohammad Farazmand, George Haller We present an equivalent formulation of the Maxey--Riley equation in the presence of the Basset--Boussinesq memory term. A physical advantage of this formulation is that it reveals drag- and pressure-type forces within the memory term. The computational advantage of the new form is that it turns the Maxey--Riley equation from an implicit differential equation into an explicit one, enabling the use of classic numerical schemes in its solution. We further simplify the Maxey--Riley equation for small particles by deriving its reduction to its attractor. The reduced equation obtained in this fashion reveals that the memory term is asymptotically of the order of $\mbox{St}^{3/2}$, with $\mbox{St}$ being the Stokes number. This explains recent numerical findings on the relative importance of the Basset--Boussinesq term. Finally, we compute inertial Lagrangian coherent structures (ILCS) for vortex shedding behind a cylinder. The reduced ILCS closely capture the full inertial dynamics while providing significant savings in computational cost and complexity. [Preview Abstract] |
Monday, November 25, 2013 9:18AM - 9:31AM |
G35.00007: Experimental and Numerical Study of Transition to Turbulence in a Kolmogorov-Like Flow Balachandra Suri, Jeffrey Tithof, Radford Mitchell Jr., Roman Grigoriev, Michael Schatz Recent theoretical advances suggest that turbulence can be characterized using exact unstable solutions of the Navier Stokes equations, called Exact Coherent Structures (ECS). Due to their experimental accessibility and theoretical tractability, two-dimensional flows provide an ideal setting for the exploration of turbulence from a dynamical systems perspective. In our talk, we present a combined numerical and experimental study of electromagnetically driven flows in a shallow layer of electrolyte. Our experimental results include the sequence of bifurcations the flow undergoes en route to becoming weakly turbulent. We discuss the effects of boundaries on the flow structure. On the numerical front, we present results from a 2D DNS, comparing them with the experiment. Also, in the weakly turbulent simulation of the flow, we search for exact coherent structures and present a few we have identified. [Preview Abstract] |
Monday, November 25, 2013 9:31AM - 9:44AM |
G35.00008: Characterizing the dynamics of unsteady planar flows through the topology of coherent-structure-based trajectories Mark Stremler, Pradeep Rao, Shane Ross There has been significant development in the identification of coherent structures associated with Lagrangian transport. Methods include Lagrangian Coherent Structures (LCS), which identifies transport barriers with minimal flux between regions, and Almost Invariant Sets (AIS) or the related Finite-Time Coherent Sets (FTCS), which identify the coherent regions that are separated by transport barriers. These methods are valuable tools for identifying key features of complex spatio-temporal transport at given instants in time. Understanding how the time-dependent interaction of these structures relates to the global characteristics of transport in the system has proven a more difficult task. We present evidence that space-time trajectories embedded in coherent structures, which we identify via AIS or FTCS, can be used to describe the global structure of transport in the flow. For sufficiently complex flows, these trajectories `braid' about one another, and the topology of this braid can be directly correlated with chaos in the system. We investigate the connection between the occurrence of braiding AIS/FTCS trajectories and the exponential stretching of material lines associated with chaos in several example flows, including lid-driven cavity flow and the double gyre flow. [Preview Abstract] |
Monday, November 25, 2013 9:44AM - 9:57AM |
G35.00009: ABSTRACT WITHDRAWN |
Monday, November 25, 2013 9:57AM - 10:10AM |
G35.00010: Thermal coherent sets and heat transfer in chaotic laminar flows Shibabrat Naik, Piyush Grover The relation between the chaotic nature of the advection flow field and heat transfer in laminar flow heat exchangers is known to be subtle. We use the Perron-Frobenius transfer operator approach to analyze thermal transport in a coiled tube with 3D laminar flow and Dirichlet thermal boundary condition. The usual advection-only transfer operator is combined with a finite-difference diffusion operator via an operator-splitting technique. We compute various coherent sets of this approximate advection-diffusion operator. These coherent sets correspond to the important ``thermal structures'' which govern the heat transfer in this problem. This analysis gives an insight into the effect of chaotic advection field on the heat transfer performance of such devices. We study the dependence of heat transfer enhancement factor on Peclet number.This transfer operator based analysis could lead to systematic geometric optimization of micrometer sized heat exchangers. [Preview Abstract] |
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