Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session EW: Mini-Symposium: Lagrangian Coherent Structures in Fluid Flows |
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Chair: John Dabiri, California Institute of Technology Room: 004 |
Sunday, November 23, 2008 4:10PM - 4:32PM |
EW.00001: Lagrangian Coherent Structures: Introduction and Applications Invited Speaker: Lagrangian Coherent Structures (LCS) are distinguished material surfaces that organize the global mixing and transport of fluid particles. While these surfaces define a skeleton that governs all mixing events even in turbulent flows, LCS remain hidden to traditional coherent structure detecting methods based on vorticity, pressure, streamlines, or other frame-dependent quantities. Here we review the mathematical foundations of LCS and discuss how they can be located in an objective (frame-independent) way in complex flows. We also highlight applications to experimental and numerical flow data analysis. Examples include two-dimensional rotating turbulence, hairpin vortices in three-dimensional numerical simulations, passive ocean pollution control and atmospheric clear-air turbulence detection. Some of these examples will be discussed in more detail in later talks within this minisymposium. [Preview Abstract] |
Sunday, November 23, 2008 4:32PM - 4:54PM |
EW.00002: Lagrangian Coherent Structures in Blood Flow Invited Speaker: Knowledge of fluid transport is particularly compelling in understanding the function of cardiovascular processes. Transport of chemicals, cells, and compounds in the vascular system is influenced by local flow structures in large vessels. Local flow features can also induce cell-signaling pathways and biologic response critical to maintaining health or disease progression. Complex vessel geometry, the pulsatile pumping of blood, and low Reynolds number turbulence leads to complex flow features in large vessels. However, we are gaining the ability to study transport in large vessels with unprecedented detail, which is in part allowing us to broaden the ``shear-centric'' view of hemodynamics. In this talk we will describe the application of computational fluid mechanics and the computation of Lagrangian coherent structures (LCS) to study transport in various cardiovascular applications. We will discuss some of the challenges of this work and some results of computing LCS in several regions of the vascular system. In collaboration with Charles Taylor, Stanford University. [Preview Abstract] |
Sunday, November 23, 2008 4:54PM - 5:16PM |
EW.00003: Lagrangian Coherent Structures in Three-Dimensional Fluid Flows Invited Speaker: We use Finite-Time Lyapunov Exponents (FTLE) to identify Lagrangian Coherent Structures in several three-dimensional flows, including a single isolated hairpin vortex, and a fully developed turbulent flow. These results are compared with commonly used Eulerian criteria for coherent vortices. Despite additional computational cost, the FTLE method has several advantages over Eulerian methods, including greater detail and the ability to define structure boundaries without relying on a preselected threshold. We also describe an application involving transport of charged particles in a toroidal magnetic field, which illustrates some limitations of the standard FTLE method when applied to a compressible medium. In collaboration with Melissa Green and Peter Norgaard, Princeton University. [Preview Abstract] |
Sunday, November 23, 2008 5:16PM - 5:38PM |
EW.00004: Lobe Dynamics in Hurricanes Invited Speaker: The classical theory of \textit{lobe dynamics} describes transport across a homoclinic trajectory in the flow of a periodically perturbed dynamical system. The flow during a single period of the perturbation defines a discrete flow map called the Poincar\'e map. Hyperbolic fixed points of the Poincar\'e map exhibit stable and unstable manifolds whose intersections define lobes and the \textit{homoclinic tangle} of chaotic dynamics. This elegant theory exists only for two-dimensional flows with periodic or quasi-periodic time-dependence. We demonstrate that Lagrangian Coherent Structures (LCS) provide an effective method for visualizing lobe dynamics in continuous flows with arbitrary time-dependence in both two and three dimensions. This method applied to reanalysis flow data for hurricanes indicates that transport in the synoptic scale flow is dominated by lobe dynamics. Furthermore, visualization of the LCS near the eyewall reveals the Lagrangian transport structures responsible for the process of eyewall replacement, a process that has been widely identified in the hurricane forecasting community as the principal mechanism for fluctuations in hurricane intensity. In collaboration with Jerrold Marsden, Caltech. [Preview Abstract] |
Sunday, November 23, 2008 5:38PM - 6:00PM |
EW.00005: Lagrangian Coherent Structures and the Kinematic Theory of Unsteady Separation Invited Speaker: The problem of determining where unsteady fluid flow separates from a no-slip boundary is long-standing and challenging. Despite some landmark advances, a practical criterion remains elusive. Recent theoretical developments in Lagrangian Coherent Structures, however, have a suggested a new approach to the problem. We review these ideas, and present the results of a combined experimental and numerical study of unsteady flow separation for a canonical flow geometry. Experimentally-detected material spikes are directly compared to separation profiles predicted from numerical shear-stress and pressure data. For steady, periodic, quasi-periodic and random forcing, fixed separation is observed, and experimental observations and theoretical predictions are in close agreement. The transition from fixed to moving separation is also reported, and methods for dealing with this scenario are discussed. In collaboration with Matthew Weldon, Gustaff Jacobs, San Diego State University; and George Haller, Morgan Stanley. [Preview Abstract] |
Sunday, November 23, 2008 6:00PM - 6:22PM |
EW.00006: The ``upstream wake'' of swimming and flying animals revealed by Lagrangian coherent structures Invited Speaker: The interaction between swimming and flying animals and their fluid environments generates downstream wake structures such as vortices. In most studies, the upstream flow in front of the animal is neglected. In this study, we use Lagrangian coherent structures (LCS) to demonstrate the existence of upstream fluid structures even though the upstream flow is quiescent or possesses a uniform incoming velocity. Using a computational model, the flow generated by a swimmer (an oscillating flexible plate) is simulated and an LCS analysis is applied to the flow to identify the upstream fluid structures from the forward finite-time Lyapunov exponent (FTLE) field. These upstream structures show the exact portion of fluid that is going to interact with the swimmer. A mass flow rate is then defined based on the upstream structures and a metric for propulsive efficiency is established using the mass flow rate and the kinematics of the swimmer. We propose that the unsteady mass flow rate defined by the `upstream wake' can be used as a metric to measure and objectively compare the efficiency of locomotion in water and air. In collaboration with Jifeng Peng, Graduate Aeronautics Laboratories and Bioengineering. [Preview Abstract] |
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