Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session EJ: Chaos and Fractals II |
Hide Abstracts |
Chair: Tom Solomon, Bucknell University Room: Salt Palace Convention Center 250 D |
Sunday, November 18, 2007 4:10PM - 4:23PM |
EJ.00001: Stretching, break-up and coarsening in a flow with chaotic advection Tom Solomon, Jeff Boehmer We present experimental studies of the behavior of drops of an immiscible impurity in time-periodic flows that exhibit chaotic mixing. Two flows are used: a blinking vortex flow and a 2D array of oscillating vortices. The immiscible impurity is a fluorescent oil that floats in a thin layer on the surface of the flow. Large oil droplets are broken up by advection, whereas small droplet coalesce. The balance between these effects results in a distribution of oil droplets and tendrils. We measure the spectrum of this distribution and investigate how this spectrum evolves in time and varies with the strength of the flow. We also investigate the time-dependent stretching and relaxation of individual droplets, relating this behavior to the time-variation of a ``Lagrangian Capillary Number'' which is based on finite-time Lyapunov exponents. [Preview Abstract] |
Sunday, November 18, 2007 4:23PM - 4:36PM |
EJ.00002: Frozen fronts in cellular flows Mollie Schwartz, Tom Solomon We present experiments showing that cellular flows often freeze the motion of chemical fronts in the presence of an opposing uniform wind. Fronts pin to the vortex structure in a chain of counter-rotating vortices for a wide range of imposed wind speeds that grows nonlinearly with the strength of the underlying vorticity. The same phenomenon is observed in a two-dimensional, spatially-disordered array of vortices, indicating that the ability to pin fronts is a general property of vortices. We further investigate the strength of the pinning with the addition of a time-periodic (oscillatory) wind, introducing chaotic advection and potential effects of mode-locking. These results demonstrate that any general theory of advection-reaction-diffusion dynamics will have to account for the tendency of cellular structures to pin fronts. [Preview Abstract] |
Sunday, November 18, 2007 4:36PM - 4:49PM |
EJ.00003: Curvature Fields, Topology, and the Dynamics of Spatiotemporal Chaos Jerry Gollub, Nicholas Ouellette Identifying the dynamically relevant degrees of freedom in a spatiotemporally chaotic flow has proved to be challenging. Here, we show a novel way to identify the time-dependent topologically special points of a flow that exhibits spatiotemporal chaos, and we suggest that they can be used to describe the flow as a whole. We produce the flow by electromagnetic forcing of a thin conducting fluid layer above a square array of disk magnets. The fluid is driven into a regime of spatiotemporal chaos. We measure the instantaneous velocities and accelerations of tracer particle trajectories using accurate particle tracking, and use them to construct the local curvature field. We show that the points of locally high curvature correspond to the hyperbolic (stagnation) points and elliptic points (regions of local rotation). The value of the Okubo-Weiss parameter allows them to be distinguished from each other. These special topological points can be accurately tracked over time. When the forcing is weak, they are pinned to the forcing magnet array, but for stronger forcing they wander over the flow domain and can be created and annihilated. Their behavior reveals a two-stage transition to spatiotemporal chaos: a gradual loss of spatial and temporal order followed by an abrupt onset of topological changes. [Preview Abstract] |
Sunday, November 18, 2007 4:49PM - 5:02PM |
EJ.00004: Simulations of the Reaction-Diffusion System demonstrating the increase in Spatial Variation of the Location of Phase Slips with increasing System Length Thomas Olsen, Yunjie Zhao, Andrew Halmstad, Richard Wiener The Reaction-Diffusion model\footnote{H. Riecke and H.-G. Paap, Europhys. Lett. \textbf{14}, 1235 (1991).} has been applied to a wide variety of pattern forming systems. It correctly predicted a period doubling cascade to chaos in Taylor-Couette flow with hourglass geometry\footnote{Richard J. Wiener \textit{et al}, Phys. Rev. E \textbf{55}, 5489 (1997).}. We have extended previous calculations to systems possessing a greater variety of lengths. We show that a modest doubling of length extends the region of phase slips (formation of Taylor Vortex pairs) from the length of one vortex pair to seven, while quadrupling only increases it to the length of eight. [Preview Abstract] |
Sunday, November 18, 2007 5:02PM - 5:15PM |
EJ.00005: The new type of intermittency at chaotic surface waves in cylindrical tanks under limited excitation Tatyana Krasnopolskaya, Alexander Shvets The problem of scenario disclosure of transition from one type steady-stated regimes to another's, in particular, from the regular regimes to chaotic is one of the most interesting in theory of dynamic systems. In space of parameters of the considered system (fluid free surface waves in cylindrical rigid tanks and process of the shaft rotation of the electromotor with a limited power, energizing spatial oscillations of a tank) the new scenario of transition such as chaos - ``chaos'' is found. This scenario belongs to type of transitions to chaos through intermittency. It is generalization of the known scenario of transition from a limit cycle to chaos through intermittency of the first type on Pomeau - Manneville. At the new scenario the role of a vanishing limit cycle of Pomeau -- Manneville's scenario plays vanishing, at a bifurcation, a chaotic attractor. A laminar phase of the detected intermittency is chaotic motion along of an originating new attractor in a neighbourhood of trajectories of a vanishing chaotic attractor. A turbulent phase is unpredictable beforehand drifts of trajectories in the remote fields of a phase space. [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. |
© 2024 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
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700