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 R29: Chaos, Fractals, and Dynamical Systems III |
Hide Abstracts |
Chair: Nicholas Ouellette, Yale University Room: 32B |
Tuesday, November 20, 2012 1:00PM - 1:13PM |
R29.00001: Almost cyclic sets, topological chaos, and mixing in a lid-driven cavity flow Pradeep Rao, Mohsen Gheisarieha, Shane Ross, Mark Stremler Topological chaos, or chaos that is guaranteed to exist in a system due to sufficiently complex motion of a few periodic orbits, has been demonstrated for a variety of flows, with a primary focus on creeping or ideal flows. Nearly-periodic systems can by analyzed in a similar way based on the presence of ``braiding'' Almost Cyclic Sets (ACS) with similarly complex space-time trajectories. For flow in a two-dimensional lid-driven cavity, this analysis can also be accurately extended to finite Reynolds numbers using a 2D Fourier-Chebyshev spectral algorithm for the streamfunction-vorticity formulation. We investigate the connection between the occurrence of braiding ACS, exponential stretching of material lines associated with topological chaos, and the efficiency of mixing for laminar flow in a lid-driven cavity. [Preview Abstract] |
Tuesday, November 20, 2012 1:13PM - 1:26PM |
R29.00002: Acceleration feature points of unsteady shear flows Jens Kasten, Jan Reininghaus, Ingrid Hotz, Hans-Christian Hege, Bernd R. Noack, Guillaume Daviller, Pierre Comte, Marek Morzy\'nski We generalize velocity topology with centers (vortices) and saddle points in a Galilean-invariant manner. In particular, a computationally robust (derivative-free) framework for their extraction of two-dimensional unsteady flows is presented. The key enabler is the definition of feature points based on the acceleration magnitude. The extracted feature points are tracked over time resulting in corresponding trajectories. Using homological persistence and lifetime of features, a spatiotemporal importance measure for vortex core lines is introduced that enables a hierarchical filtering. As example, homological persistence is shown to discriminate between hydrodynamic and aeroacoustic flow structures. Our framework is applied to analytic examples as well as simulations of a cylinder wake, of a two-dimensional mixing layer and of a jet. [Preview Abstract] |
Tuesday, November 20, 2012 1:26PM - 1:39PM |
R29.00003: Perturbation of coherent structures in three-dimensional laminar flows: predictions versus experimental observations Fan Wu, Michel Speetjens, Dmitri Vainchtein, Ruben Trieling, Herman Clercx Coherent structures in the fluid trajectories of three-dimensional (3D) laminar flows are key to their transport properties These structures typically undergo qualitative changes upon introducing some geometric or dynamical perturbation However, insight into such response scenarios in realistic 3D flows remains limited. The present study seeks to deepen this by investigating the response of coherent structures within a 3D time-periodic lid-driven cylinder flow in its Stokes limit to various weak perturbations. Numerical predictions by a spectral flow solver are compared against experiments by 3D PTV. The computations consider perturbation by weak fluid inertia and by a slight asymmetry in flow forcing, both causing essentially the same change in coherent structures. This signifies, consistent with theory on idealized flows, a generic response to weak perturbations, irrespective of their particular nature. The experiments, instead of explicit perturbation, rely on natural departures from a perfect state as e.g. geometric imperfections and weak fluid inertia. This results in dynamics that closely agree with the numerical predictions, thus offering first experimental evidence that indeed a universal mechanism is at play in the response of 3D coherent structures to perturbations [Preview Abstract] |
Tuesday, November 20, 2012 1:39PM - 1:52PM |
R29.00004: Effect of the forcing on ``steady'' turbulent states Brice Saint-Michel, Guillaume Mancel, B\'ereng\`ere Dubrulle, \'Eric Herbert, Fran\c{c}ois Daviaud Turbulent systems are intrinsically out of equilibrium, and thus have no reason to respect the symmetries of their forcing. It is yet generally accepted that symmetries are ``statistically'' restored in turbulence. Von K\'arm\'an swirling flows, though, might display continuous transitions or hysteretic behaviour depending on the type of forcing when the impeller speed is imposed. In the latter case, turbulent steady states are found to depend on the history of the system, three states being -- at least marginally -- stable for perfectly symmetric forcing. We have recently investigated the effect of the forcing on this system. When torque is imposed to the impellers, a whole new dynamics region is accessible inside the hysteresis loop; our system becomes multistable, continuously transiting between a small number of localised states. We characterize the structures displayed by such states and examine what governs the dynamics between them. [Preview Abstract] |
Tuesday, November 20, 2012 1:52PM - 2:05PM |
R29.00005: Streamline and vorticity topology of eruption from a boundary layer induced by a 2D vortex patch Morten Andersen, Morten Brons, Mark Thompson We investigate the flow field generated by a vortex patch near a wall. Secondary vortices are created and boundary layer eruption may occur for increasing time or Reynolds number. The stream line topology and the vorticity topology are investigated and compared motivated by the work of Kudela \& Malecha, Fluid Dyn. Res. 2009. Keeping track of vortices is a widely used procedure to explain ``what is going on'' in a fluid. However, different measures may be used for identifying a vortex. We will compare two of them under simplified conditions namely in the case of two dimensional incompressible flow with constant third component of the velocity vector. In the vorticity formulation a vortex is identified as an extremum of the vorticity. In the stream function formulation, if an elliptic fixed point exists then a vortex exists. The coordinate system is moving with constant speed equal to the generating vortex speed in inviscid flow. We find that vortex creation occur by saddle - node bifurcations in the streamlines, not by pinching off as suggested by Kudela \& Malecha. Close to the creation of vortices, good agreement between the vorticity structure and the streamline topology is observed. At later stages, this may break down and streamline centers may disappear even though a vor [Preview Abstract] |
Tuesday, November 20, 2012 2:05PM - 2:18PM |
R29.00006: Bifurcations in bifurcations: a dynamical analysis of an impacting T-junction flow Kevin Chen, Clarence Rowley, Howard Stone, Daniele Vigolo, Stefan Radl Pipe bifurcations are a common flow configuration, for instance, in industrial systems and blood vessels. The impacting flow through a T-junction can cause corrosion, damage, and even aneurysms. To complement ongoing particle-laden flow physics research on this geometry, we perform a local bifurcation analysis of the steady-state Navier--Stokes solutions. We carry out numerical continuation on the Reynolds number, using a combination of linear extrapolation and the Newton-GMRES algorithm. A supercritical pitchfork (i.e., symmetry-breaking) bifurcation occurs at $Re \approx 410$, at which the pair of counter-rotating vortices in the outflow pipes becomes asymmetric. A supercritical Hopf bifurcation occurs at $Re \approx 540$, at which the asymmetric steady-state solution becomes unstable, and a stable periodic orbit grows out of this equilibrium. [Preview Abstract] |
Tuesday, November 20, 2012 2:18PM - 2:31PM |
R29.00007: Collective motion of interacting particles in spatially coherent flow Nidhi Khurana, Nicholas T. Ouellette Previous studies have shown that background flows can significantly modify the dynamics of independent active particles. In this work, we investigate how a spatially coherent turbulent-like flow modifies the collective behavior of interacting particles. We consider spherical point-like particles that interact according to a standard collective motion model. The particles move with a constant intrinsic speed but with a direction that depends on their neighbors. In addition, they are advected by a strongly fluctuating, multiscale flow field generated by kinematic simulation. By varying the relative strength of the intrinsic particle speed and the background flow, we study the effects of the complex flow field on the collective behavior of the particles. [Preview Abstract] |
Tuesday, November 20, 2012 2:31PM - 2:44PM |
R29.00008: Efficient POD-based ROMs to approximate bifurcation diagrams Filippo Terragni, Jose Manuel Vega Computing transitions and instabilities is a relevant issue in many fields, whose analysis usually involves time dependent nonlinear models. Thus, construction of bifurcation diagrams in extended systems may require huge computational resources. In dissipative problems, proper orthogonal decomposition (POD) may provide a low dimensional manifold containing the large-time dynamics of the system. In this talk, simple ideas are exploited in order to get flexible and accurate POD-based reduced order models (ROMs). The proposed method relies on the observation that POD manifolds resulting from snapshots calculated from a generic initial condition, a non-small time span, and specific values of the parameters contain the attractors for a wide range of parameter values. Appropriate POD manifolds can then be constructed with great flexibility and used to fast compute bifurcations. This is illustrated for fairly complex bifurcation diagrams (involving chaotic attractors) in the complex Ginzburg-Landau equation, in which a good set of snapshots can be calculated from either parameter values yielding simple dynamics, or rough numerical solvers, or different equations. [Preview Abstract] |
Tuesday, November 20, 2012 2:44PM - 2:57PM |
R29.00009: Identifying Oscillatory Modes Using Harmonically Averaged Equations Jay Qi, Jonathan Tu, Clarence Rowley, Rajat Mittal We present a method for analyzing dynamical systems exhibiting oscillatory behavior, using harmonic averaging. This method involves solving modified governing equations to directly obtain oscillatory modes corresponding to certain, specified frequencies. Common spectral analysis techniques post-process time-resolved data from full simulations; our approach instead leverages a priori knowledge of the system to directly compute the oscillatory modes. The method bears some similarity to a previous approach, the nonlinear frequency domain (NLFD) method, and is equivalent under certain conditions. However, because of the ability to choose arbitrary frequencies, harmonic averaging is advantageous in some cases, for instance for quasiperiodic phenomena, or when only a few frequencies are present. We demonstrate the method using a one-dimensional model problem, the Kuramoto-Sivashinsky equation, and show that the harmonic averaging method is able to accurately solve for the oscillatory modes in quasiperiodic systems. [Preview Abstract] |
Tuesday, November 20, 2012 2:57PM - 3:10PM |
R29.00010: Developing flexible but efficient software for dynamical systems analysis of fluid flow Siavash Ameli, Yogin Desai, Shawn Shadden The computation of Lagrangian coherent structures (LCS) has become a standard tool for the analysis of advective transport in unsteady flow applications. LCS identification is typically accomplished by computation of finite-time (or finite-size) Lyapunov exponent fields (FTLE), or similar measures based on the Cauchy Green deformation tensor. Sampling of such fields over the fluid domain requires the advection of large numbers of tracers, which can be computationally intensive, but presents a large degree of data parallelism. There is compelling need for software that provides a flexible interface for LCS computation from fluid flow data, while leveraging advances in parallel architectures for data processing. We will describe work on these fronts. Specifically, we discuss the use of the Visualization Toolkit (VTK) libraries as a foundation for object-oriented, polymorphic LCS computation, and how this framework can facilitate integration into powerful flow visualization software such as Paraview. We also discuss the development of CUDA-c and OpenCL GPU kernels, and multicore CPU implementation, for efficient parallel computation of the flow map. We demonstrate results of these implementations on large-scale computations involving millions of tracers on large unstructured grids. [Preview Abstract] |
Tuesday, November 20, 2012 3:10PM - 3:23PM |
R29.00011: Analysis of Fluid Flows via Spectral Properties of the Koopman Operator Igor Mezi\'c We discuss theory and applications of Koopman modes in fluid mechanics. Koopman mode decomposition is based on the fact that normal modes of linear oscillations have its natural analogue - Koopman modes - in the context of nonlinear dynamics. To pursue this analogy, one must change the representation of the system from the state-space representation to the dynamics governed by the linear Koopman operator on an infinite-dimensional space of observables. The analysis is based on spectral properties of the Koopman operator. The point spectrum corresponds to isolated frequencies of oscillation present in the fluid flow, and also to growth rates of stable and unstable modes. The continuous part of the spectrum corresponds to chaotic motion on the attractor. A theoretical method of computation of the spectrum and the associated Koopman modes is given, in terms of the Generalized Laplace Analysis. A computational alternative is given by Arnoldi-type methods, leading to the so-called Dynamic Mode Decomposition (DMD). Koopman mode theory is shown to unify and provide a rigorous background for a number of different concepts that have been advanced in fluid mechanics, including Global Mode Analysis, triple decomposition and Dynamic Mode Decomposition. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2019 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
1 Research Road, Ridge, NY 11961-2701
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700