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 M29: Chaos, Fractals, and Dynamical Systems II |
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Chair: Tom Solomon, Bucknell University Room: 32B |
Tuesday, November 20, 2012 8:00AM - 8:13AM |
M29.00001: ABSTRACT WITHDRAWN |
Tuesday, November 20, 2012 8:13AM - 8:26AM |
M29.00002: Dynamical behavior of flame front instability induced by radiative heat loss Hiroshi Gotoda, Takuya Ikawa, Koshiro Maki, Takaya Miyano Exploring complexities in flame front instability leading to flame extinction is of current interest in combustion physics and nonlinear science. We investigate the dynamical properties of the flame front instability induced by radiative heat loss using nonlinear forecasting. The flame front instability represents high-dimensional chaos generated via the period-doubling cascade process, while its short-term behavior is predictable using a local nonlinear predictor based on the Sugihara-May method (G. Sugihara, R. M. May, Nature 344, 734 (1990), H. Gotoda et al., Chaos 22, 033106, (2012)). The feasibility of a new approach based on short-term prediction is also discussed in this work from the practical viewpoint of combustion systems. [Preview Abstract] |
Tuesday, November 20, 2012 8:26AM - 8:39AM |
M29.00003: The nonlinear behaviour of a ducted premixed flame Karthik Kashinath, Iain Waugh, Santosh Hemchandra, Matthew Juniper Nonlinear thermoacoustic oscillations are one of the most challenging problems in premixed gas turbine engine combustors. We investigate the nonlinear thermoacoustic behaviour of a ducted premixed flame using time domain analyses of the fully coupled thermoacoustic system. Nonlinear time series analysis tools are used to analyse the complex oscillations that the system exhibits. The system shows periodic, quasi-periodic, frequency-locked and chaotic oscillations depending on the operating condition. While such behaviour has been observed in experiments (Kabiraj et. al., Chaos 22, 023129 (2012)), this is the first attempt at modelling this system using an approach that captures the details of the flame front dynamics. The bifurcations of the system for changes in operating conditions are studied for a few different control parameters such as the flame equivalence ratio, geometry of the system and mean flow velocity. Furthermore, a route to chaos is identified in this system. [Preview Abstract] |
Tuesday, November 20, 2012 8:39AM - 8:52AM |
M29.00004: Front propagation in steady cellular flows: A large-deviation approach Alexandra Tzella, Jacques Vanneste We examine the speed of propagation of chemical fronts modelled by the Fisher--Kolmogorov--Petrovskii--Piskunov nonlinearity in steady cellular flows. A number of predictions have been previously derived assuming small molecular diffusivity (large P\'eclet number) and either very slow (small Damk\"ohler number) or very fast (large Damk\"ohler number) chemical reactions. Here, we employ the theory of large deviations to obtain a family of eigenvalue problems from whose solution the front speed is inferred. The matched-asymptotics solution of these eigenvalue problems in the limit of large P\'eclet number provides approximations for the front speed for a wide range of Damk\"ohler numbers. Two distinguished regimes are identified; in both regimes the front speed is given by a non-trivial function of the P\'eclet and Damk\"ohler numbers which we determine. Earlier results, characterised by power-law dependences on these numbers, are recovered as limiting cases. The theoretical results are illustrated by a number of numerical simulations. [Preview Abstract] |
Tuesday, November 20, 2012 8:52AM - 9:05AM |
M29.00005: Experimental studies of stationary reaction fronts in a chain of vortices Carleen Boyer, Tom Solomon We present results of experiments studying the behavior of the excitable Belousov-Zhabotinsky (BZ) reaction in a chain of alternating vortices with an imposed uniform wind. Previous experiments\footnote{M.E. Schwartz and T.H. Solomon, Phys. Rev. Lett. {\bf 100}, 028302 (2008).} have shown that fronts in this system are pinned for a wide range of imposed wind speeds, propagating neither forward against the wind nor in the downwind direction. We explain this behavior with a recent theory\footnote{J. Mahoney, D. Bargteil, M. Kingsbury, K. Mitchell and T. Solomon, Europhys. Lett. {\bf 98}, 44005 (2012).} that proposes the existence of {\em burning invariant manifolds} (BIMs) that act as local barriers to front propagation. Fronts are pinned when a BIM or a combination of BIMs spans the width of the vortex chain, blocking the reaction front. We show experimental measurements of the shape of the pinned front for a range of different wind speeds, and compare these shapes to the BIMs calculated theoretically. We also consider the dependence of the front shape on the location of the initial trigger for the front. [Preview Abstract] |
Tuesday, November 20, 2012 9:05AM - 9:18AM |
M29.00006: Burning invariant manifolds and pinning of reaction fronts in spatially-disordered fluid flows Tom Solomon, Maya Najarian We present experiments that test the ideas of {\em burning invariant manifolds} (BIMs) for propagating fronts in spatially-disordered fluid flows with an imposesd wind. The disordered flow is driven by a magnetohydrodynamic forcing technique, and there is a uniform wind imposed on the flow with the use of a translation stage. Reaction fronts are produced using the excitable Belousov-Zhabotinsky chemical reaction. For a wide range of wind speeds, a complicated stationary front forms, pinned to the underlying vortex flow, neither propagating forward against the wind nor being blown backwards. The shape of the front depends significantly on the magnitude of the imposed wind. We test the hypothesis that the shape of the stationary front is determined by a collection of overlapping BIMs that act as barriers against forward movement of the reaction front. The location of the BIMs are predicted by integrating a three-dimensional set of ordinary differential equations\footnote{J. Mahoney, D. Bargteil, M. Kingsbury, K. Mitchell and T. Solomon, Europhys. Lett. {\bf 98}, 44005 (2012).} that describes the dynamics of an element of an evolving reaction front in the fluid flow. [Preview Abstract] |
Tuesday, November 20, 2012 9:18AM - 9:31AM |
M29.00007: Pinning fronts in advection-reaction-diffusion systems: a dynamical systems approach Kevin Mitchell, John Mahoney, John Li Recent experiments have demonstrated the pinning of reaction-diffusion fronts in magnetohydrodynamically-forced vortex flows. Specifically, a magnetic stage moving beneath the fluid layer ``captures,'' and then drags, a reaction-diffusion pattern, which remains pinned to the frame of the stage. Here, we use dynamical systems techniques to explain the sequence of bifurcations that leads from an unpinned to a pinned state, as well as bifurcations that change the topological structure of the pinning fronts. We also explain how different pinning behavior can coexist within the same fluid flow, and analyze the associated basins of attraction. Our analysis is based on the recent concept of ``burning'' invariant manifolds (BIMs); BIMs extend the invariant manifolds traditionally used in passive advection to the case of reaction-diffusion systems. [Preview Abstract] |
Tuesday, November 20, 2012 9:31AM - 9:44AM |
M29.00008: An FTLE analysis for reaction-diffusion fronts in fluid flows John Mahoney, Kevin Mitchell The theory of advective transport depends heavily on the elucidation of organizing structures within the fluid. In a time-independent or time-periodic flow, one can define invariant manifolds. In a time-aperiodic flow, one often employs the finite-time-lyapunov-exponent (FTLE) and Lagrangian coherent structures. It has been recently demonstrated that fronts, e.g. reaction-diffusion fronts, propagating in time-periodic flows can also depend on such organizing invariant manifolds. In this talk, we describe an FTLE analysis for propagating fronts in two-dimensional fluid flows. In particular, we employ a dimension reduction technique to the front system so that a two-dimensional FTLE approach is feasible. [Preview Abstract] |
Tuesday, November 20, 2012 9:44AM - 9:57AM |
M29.00009: Uncertainty propagation using spectral methods and flow map composition Dirk M. Luchtenburg, Steven L. Brunton, Clarence W. Rowley Uncertainty quantification is becoming more widely used in a variety of applications: for instance, when analyzing oil spills, one wants to predict the extent of the contaminated region, but the velocity field is not known precisely. We propose an efficient method for computing the propagation of a probability density function (PDF) through the long-time, nonlinear flow map associated with an uncertain fluid velocity field. Uncertain initial conditions and parameters are both addressed. The method approximates the short-time flow map by a spectral basis and uses flow map composition to construct the long-time flow map. The short-time flow map is characterized by small stretching and folding of the associated trajectories and hence can be represented by a relatively low-order basis. The composition of these low-dimensional bases then accurately describe the uncertainty behavior for long times. We use sampling of the spectral representations to compute stochastic quanti- ties, such as the mean and variance. The method is applied to several numerical examples including the long-time advection of a distribution of particles through an uncertain velocity field. [Preview Abstract] |
Tuesday, November 20, 2012 9:57AM - 10:10AM |
M29.00010: Noise-induced complexity in active nonlinear spatially extended systems Marc Pradas, Serafim Kalliadasis, Dmitri Tseluiko, Demetrios T. Papageorgiou, Grigorios A. Pavliotis We study noise-induced phenomena on spatially extended systems (SES) that are close to the instability onset. We consider a degenerate noise that is acting on the subspace of stable modes only, and by means of a multiple scale analysis for general noisy SES we obtain an amplitude equation for the dominant mode. This then allows us to analytically investigate the noise effects on the dominant dynamics of the system. We observe that several non-trivial scenarios are possible depending on the stable modes the noise is acting on, including noise-induced critical transitions, intermittency and stabilisation when the noise is acting on the first stable mode only; or a noise filtering process, i.e. the dominant mode is not affected at all by the stochastic forcing when it is acting on the second stable mode. Our analytical findings are exemplified with a model SES, the noisy Kuramoto-Sivashinsky equation which describes, amongst many other different physical settings, the dynamics of a thin-liquid film flowing over a topographical substrate. In all cases, very good agreement between the theoretical predictions and numerical experiments is observed. [Preview Abstract] |
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