Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session H3: Dynamical Systems and Chaos I |
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Chair: Philip Yecko, Montclair University Room: 303 |
Monday, November 21, 2011 10:30AM - 10:43AM |
H3.00001: Set-based corral control in stochastic dynamical systems: Making almost invariant sets more invariant Eric Forgoston, Lora Billings, Philip Yecko, Ira Schwartz We consider the problem of stochastic prediction and control in a time-dependent stochastic environment, such as the ocean, where escape from an almost invariant region occurs due to random fluctuations. We determine high-probability control-actuation sets using geometric and probabilistic methods. These methods allow us to design regions of control that provide an increase in loitering time while minimizing the amount of control actuation. Our methods provide an exponential increase in loitering times with only small changes in actuation force. The result is that the control actuation makes almost invariant sets more invariant. [Preview Abstract] |
Monday, November 21, 2011 10:43AM - 10:56AM |
H3.00002: Maximum-entropy closure for a Galerkin system of incompressible shear flow Bernd R. Noack, Robert K. Niven A statistical physics closure is proposed for Galerkin models of incompressible shear flows. This closure employs a maximum entropy (MaxEnt) principle to infer the probability distribution in Galerkin state space using exact statistical balance equations as side constraints. Application to an empirical Galerkin model of the periodic cylinder wake predicts mean amplitude values and modal energy levels in good agreement with direct numerical simulation. Recipes for more complicated Galerkin systems are provided. [Preview Abstract] |
Monday, November 21, 2011 10:56AM - 11:09AM |
H3.00003: The Lagrangian description of time dependent aperiodic flows: applications in the Ocean and the Atmosphere Ana M. Mancho Geometry has been a very useful approach for studying dynamical systems. At the basis are Poincare ideas of seeking structures on the phase space that divide it into regions corresponding to trajectories with different dynamical fates. These ideas have demonstrated to be very powerful for the description of transport in purely advective flows and important applications have been found in geophysics. However realistic flows as those obtained by altimeter satellites or from numerical simulations are highly non-periodic and to deal with these flows is a challenge because traditional methods can be used only in autonomous and time periodic dynamical systems. We describe new Lagrangian tools that are applied to general time dependent flows. In particular we discuss results on oceanic datasets taken from altimeter satellites on the Kuroshio region. We also discuss an application on reanalysis data on the Antarctic polar vortex. [Preview Abstract] |
Monday, November 21, 2011 11:09AM - 11:22AM |
H3.00004: Nonlinear Dynamics Analysis of a Flapping Filament in a Flowing Soap Film Hamid Ait Abderrahmane, Michael P. Paidoussis, Mohamed Fayed, Hoi Dick Ng In this study we investigate the nonlinear dynamics of the flapping regime of a filament placed in a two-dimensional soap film flow for different filament lengths and flow speeds. The results show that the onset of flapping at very high Reynolds numbers is quasi-periodic, with the main flapping amplitude and frequency modulated by low-amplitude, low-frequency oscillation. At higher flow velocities, chaotic oscillation is observed. The transition to chaos occurs via the quasi-periodic route to chaos. A new bistability phenomenon is discovered in which the system alternates between the stretched-straight and oscillatory states, and is referred in this study to as ``switching oscillation.'' Unlike some previously reported forms of bistability, in this case the system alternates between the two states continuously, without any external perturbation. [Preview Abstract] |
Monday, November 21, 2011 11:22AM - 11:35AM |
H3.00005: Dynamic behavior of combustion instability in a lean premixed gas-turbine combustor Hiroshi Gotoda, Takaya Miyano, Shigeru Tachibana Periodic and chaotic behavior in combustion dynamics that can be observed as a result of combustion instabilities in fundamental and practical combustion systems are of importance to present-day combustion physics and nonlinear science research. We experimentally investigate the dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor from the viewpoint of nonlinear dynamics (Gotoda. H et al., Chaos, vol. 21, 013124, 2011). A nonlinear time series analysis clearly reveals that as the equivalence ratio increases, the dynamic behavior of the combustion instability undergoes a significant transition from stochastic fluctuation to periodic oscillation through low-dimensional chaotic oscillation. We also show that a nonlinear forecasting method is useful for predicting the short-term dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor, which has not been addressed in the fields of combustion science and physics. [Preview Abstract] |
Monday, November 21, 2011 11:35AM - 11:48AM |
H3.00006: Topological detection of Lagrangian coherent structures Jean-Luc Thiffeault, Michael Allshouse In many applications, particularly in geophysics, we often have fluid trajectory data from floats, but little or no information about the underlying velocity field. The standard techniques for finding transport barriers, based for example on finite-time Lyapunov exponents, are then inapplicable. However, if there are invariant regions in the flow this will be reflected by a `bunching up' of trajectories. We show that this can be detected by tools from topology. The method relies on examining a large number of topological loops, encoded symbolically. These loops wrap around the trajectories, which are viewed as topological obstacles. As the trajectories move around, they cause most loops to grow. The few loops that do not grow, or grow slowly, can be associated with coherent structures. [Preview Abstract] |
Monday, November 21, 2011 11:48AM - 12:01PM |
H3.00007: Stochasticity enhances hydrodynamic trapping of swimming particles in chaotic flow Nidhi Khurana, Nicholas T. Ouellette We use numerical methods to investigate the dynamics of swimming particles in a two-dimensional chaotic flow field. We model the swimmers as point-like spherical particles. We include stochastic motion in addition to deterministic swimming. We find that hydrodynamic trapping, which we had previously observed for deterministic swimming alone, can be significantly enhanced by the addition of noise terms. We therefore argue that a suppression of transport due to particle activity does not depend on the detailed swimmer model, but is likely a generic effect. [Preview Abstract] |
Monday, November 21, 2011 12:01PM - 12:14PM |
H3.00008: Dynamical systems characterization of the poor man's Navier--Stokes equations J.B. Polly, J.M. McDonough The Navier--Stokes (N.--S.) equations governing fluid flow consist of a system of time-dependent, multi-dimensional, non-linear partial differential equations (PDEs) which cannot be solved in real time using current, or near-term foreseeable, computing hardware. The poor man's Navier--Stokes (PMNS) equations comprise a discrete dynamical system (DDS) that is algebraic---hence, easily (and rapidly) solved---and yet which retains many (possibly all) of the temporal behaviors of the full (PDE) N.--S. system at specific spatial locations. In this investigation we outline the derivation of the PMNS equations beginning with the incompressible N.--S. equations. We then consider common techniques to understand the DDS sensitivity to initial conditions (SIC) through calculation of bifurcation diagrams, Lyapunov exponents, and fractal dimension. These techniques are studied with consideration of their ease of computation, and ability to characterize and describe system behavior. The time series generated by the DDS are used to obtain power spectral densities (PSDs) which can be used to categorize most system behaviors. Some chaotic behaviors, however, can be difficult to distinguish via PSD analysis alone; thus we investigate the ability of other methods to characterize the system response. [Preview Abstract] |
Monday, November 21, 2011 12:14PM - 12:27PM |
H3.00009: Vortex shedding patterns, their competition, and chaos in flow past inline oscillating rectangular cylinders Srikanth Toppaladoddi, Harish N. Dixit, Rao Tatavarti, Rama Govindarajan Different vortex shedding patterns arising in the flow past inline oscillating rectangular cylinders, at a Reynolds number of 200 is studied numerically in two-dimensions. The S-II mode of symmetric shedding, discovered in 2006, as well as the Couder-Basdevant mode [J. Fluid Mech. 173, 225-251 (1986)], seen in experiments earlier, are found numerically for the first time. Besides, a new mode of symmetric shedding, named here as S-III, is also reported. Chaotic flow in the wake of a circular cylinder, recently reported by Perdikaris \textit{et al}. [Phys. Fluids 21(10), 101705 (2009)] is also seen in flow past the rectangular geometries here, and we show that this is indeed due to mode competition, between antisymmetric and symmetric modes of vortex shedding, in the sense of Ciliberto \& Gollub [Phys. Rev. Lett. 52, 922 (1984)]. A global and reliable parameter has been constructed to ``quantify'' this chaos. The Lattice Boltzmann Method (LBM) has been used to solve for the flow. [Preview Abstract] |
Monday, November 21, 2011 12:27PM - 12:40PM |
H3.00010: Experiments on the morphology of icicles Antony Szu-Han Chen, Stephen W. Morris Icicles form when cool water drips from an overhanging support into air whose temperature is below freezing. Ice growth is controlled by the removal of latent heat, which is transferred into the surrounding air via a thin film of water flowing over the ice surface. Predicting the shape of an icicle is a non-trivial free-boundary growth problem. The global shape emerges from the local physics of the water film, the advection-diffusion of latent heat, and the slowly evolving surface position [1]. The ice-water interface can also become unstable to form ripple patterns on the icicle surface [2]. We conducted controlled icicle experiments [3], using a table-top icicle-growing apparatus. We used image analysis to probe the evolution of both the icicle shape and the rippling instability, and we investigated their dependence on ambient temperature, water supply rate, salinity, and surface tension. Our experiments showed that under certain conditions, icicles have self-similar global profiles, but non-uniformities such as tip splitting can sometimes occur. We also found that ripple formation is correlated to the purity of water used, and the ripples climb the icicle during growth. \\[4pt] [1] M. B. Short, et al., Phys. Fluids 18, 083101 (2006).\\[0pt] [2] K. Ueno, Phys. Fluids 19, 093602 (2007).\\[0pt] [3] A. S. Chen, et al., Phys. Rev. E 83, 026307 (2011). [Preview Abstract] |
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