Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session F01: Nonlinear Dynamics: Bifurcations & Chaos |
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Chair: Spencer Smith, Mt. Holyoke College Room: Georgia World Congress Center B201 |
Monday, November 19, 2018 8:00AM - 8:13AM |
F01.00001: Ensemble-based Topological Entropy Calculation in Three Dimensions Eric J Roberts, Suzanne Sindi, Spencer Smith, Kevin A Mitchell Topological entropy measures the number of distinguishable orbits in a dynamical system, thereby quantifying the complexity of chaotic dynamics. Such knowledge aids greatly in a wide variety of natural and industrial fluid systems, including the large-scale dispersion of pollutants in the Earth's atmosphere and oceans and the rapidly developing field of microfluidics. We introduce a computational geometry framework for estimating a three dimensional flow's topological entropy from the collective motion of an ensemble of system trajectories. This work is analogous to the entropy calculation from "braiding" of system trajectories in two dimensions and is a first step towards building a triangulation-based method for computing topological entropy from an ensemble of trajectory data in three dimensions and higher. In it, we consider a two-dimensional rubber sheet stretched around a collection of points in a three-dimensional flow. A 3D triangulation may be used to track point-face or edge-edge collisions and the rubber sheet may be chosen as one of the faces in the initial triangulation. As the points evolve in time, they carry the sheet along with them, stretching and folding it so that its growth reflects the flow complexity. |
Monday, November 19, 2018 8:13AM - 8:26AM |
F01.00002: System identification of a low-density jet via its noise-induced dynamics Minwoo Lee, Yuanhang Zhu, Larry K.B. Li, Vikrant Gupta Low-density jets are central to many natural and engineering processes. Under certain conditions, they can develop global oscillations at a limit cycle, behaving as a prototypical example of a self-excited hydrodynamic oscillator. In this study, we perform system identification of a low-density jet using measurements of its noise-induced dynamics in the unconditionally stable regime, prior to both the Hopf and saddle-node points. We show that this approach can enable prediction of (i) the order of nonlinearity, (ii) the locations and types of the bifurcation points (and hence the stability boundaries), and (iii) the resulting limit-cycle oscillations. The only assumption made about the system is that it obeys a Stuart-Landau equation in the vicinity of the Hopf point, thus making the method applicable to a variety of hydrodynamic systems. This study constitutes the first experimental demonstration of system identification using only the noise-induced dynamics in the unconditionally stable regime, opening up new possibilities for the prediction and analysis of the stability and nonlinear behavior of hydrodynamic systems. |
Monday, November 19, 2018 8:26AM - 8:39AM |
F01.00003: Chaotic sensitivity analysis of noise at chevron nozzle exits Nisha Chandramoorthy, Qiqi Wang, Zhong-Nan Wang The computation of sensitivities of turbulent fluid flows to input parameter perturbations is important for gradient-based multi-disciplinary design optimization, uncertainty quantification, mesh adaptation and so on. Since linearized perturbation equations are unstable in chaotic systems, conventional adjoint sensitivity analysis methods that are successful with steady RANS solutions, fail in the case of high-fidelity chaotic numerical simulations such as LES. At present, some potential candidates for sensitivity computation in chaotic systems are shadowing-based and ensemble-based methods. Ensemble-based methods exhibit poor rate of convergence and are hence impractical for eddy-resolving simulations; Shadowing-based methods are not guaranteed to converge since the computed shadowing trajectories may be rare trajectories that do not correspond to the average dynamics of the fluid system. We propose an alternative called Space-Split-Sensitivity (S3) computation that provably converges to the mean response of a chaotic system to parameter perturbations. We demonstrate that the new algorithm enables optimization of chevron nozzle geometry to reduce the noise produced by jet engines. |
Monday, November 19, 2018 8:39AM - 8:52AM |
F01.00004: Nonlinear dynamics of micro rotors and mixing of fluid in a confined domain Phanindra Tallapragada, Senbagaraman Sudarsanam We present some results on the two dimensional mixing of a fluid confined to a circular domain at low Reynolds number through the use of microrotors. The microrotors are modeled as rotlets, which are a singularity solution of the Stokes equation. The microrotors are free to move under the influence of other rotors and the image singularities which arise to satisfy the boundary conditions on the circular boundary. Two specific cases are explored, the mixing due to one rotor and the mixing due to a pair of rotors. In the former case computations show that the fluid in the domain is not mixed well, while in the latter case the fluid could be mixed well for certain initial configurations of the rotors. The two rotlet case produces a rich array of dynamics of the rotlets themselves. The boundary plays an important role, by making the dynamics of the two rotlets nonintegrable. This role of the boundary is identified as a cause of the mixing. Poincare maps, Lyapunov exponents and variance calculations are employed to quantify mixing. The stretching and folding of initially coherent blobs of fluid tracers into thin striations and consequent mixing are easily visualized. |
Monday, November 19, 2018 8:52AM - 9:05AM |
F01.00005: Dynamic behavior of flow velocity fluctuations in a H2/O2 turbulent coaxial jet Wataru Kobayashi, Hiroshi Gotoda, Yuya Ohmichi, Shingo Matsuyama We have numerically studied the dynamic behavior of flow velocity fluctuations in H2/O2 turbulent coaxial jet from a viewpoint of complex networks. The turbulence network proposed by Taira et al., [J. Fluid Mech. 795, R2 (2016).] in which weighted networks are constructed by connecting each fluid element to other fluid elements, is useful for identifying vortical interactions in a turbulent flow. The importance of the turbulence network has been shown in different physical settings by one of authors [S. Murayama et al., Phys. Rev. E. 97, 022223 (2018); K. Takagi et al., Chaos 28, 045116 (2018)]. Here we adopt the turbulent network for the vorticity field in H2/O2 turbulent coaxial jet. A clear power-low decay appears in the probability density function of vertex strength. In this presentation, we discuss a possible existence of scale-free structure in the network. |
Monday, November 19, 2018 9:05AM - 9:18AM |
F01.00006: Chaotic advection in 3D unsteady flows: not the tori way Sebastian Contreras, Michel Speetjens, Herman Clercx Theoretical and numerical studies revealed that 3D unsteady flows with invariant spheroids follow a route to chaos upon (weak) perturbation that is fundamentally different from that of the classical case of invariant tori. Weak perturbation of the invariant spheroids results in the formation of intricate coherent structures consisting of thin spheroidal shells connected by tubes via a mechanism termed "resonance-induced merger" (RIM). These structures enable a first global dispersion of tracers and constitute the precursor to unrestricted 3D chaos emerging from perturbation of systems accommodating invariant spheroids. Recent studies provided first experimental evidence of RIM yet direct validation remained outstanding. The present study conclusively demonstrates RIM and the associated coherent structures by way of experimental 3D Lagrangian studies using 3D Particle Tracking Velocimetry. |
Monday, November 19, 2018 9:18AM - 9:31AM |
F01.00007: Spirals and ribbons: frequency prediction from mean flows and a new heteroclinic orbit Yacine Bengana, Laurette Tuckerman A number of time-periodic flows, (e.g. the wake of a circular cylinder and the flow over an open cavity) have been found to have the RZIF property: a linear stability analysis carried out about the temporal mean (rather than the usual steady state) leads to an eigenvalue whose Real part is near Zero and whose Imaginary part is the nonlinear Frequency. For 2D thermosolutal convection, a Hopf bifurcation leads to traveling waves which satisfy RZIF and standing waves which do not. We have investigated this property numerically for counter-rotating Couette-Taylor flow, in which a Hopf bifurcation gives rise to branches of upwards and downwards traveling spirals and ribbons which are an equal superposition of the two. In the regime that we have studied, we find that both spirals and ribbons satisfy the RZIF property. In addition, the ribbon branch is succeeded by a heteroclinic orbit anchored by unstable axisymmetric Taylor-vortex flows with excursions into the ribbon regime. |
Monday, November 19, 2018 9:31AM - 9:44AM |
F01.00008: Complex dynamics of the vertical oscillating and stably stratified square cavity Jason Yalim, Bruno D Welfert, Juan Lopez We study numerically the behavior of a fluid flow inside the vertically oscillating and stably stratified square cavity. For a set of harmonic forcing frequencies and amplitudes, it is well known that the flow's basic state loses stability to a nontrivial internal wave mode. However, the dynamical details of how the instability occurs are not well understood. The dynamics are shown to be complicated by a family of codimension-two bifurcations near the primary locus of instability. |
Monday, November 19, 2018 9:44AM - 9:57AM |
F01.00009: Fractal Measures in Paper Marbling Spencer Smith, Michelle Wellman Paper marbling is an old art form with major traditions in Europe, Turkey (Ebru), and Japan (Suminagashi). Creating marbled paper involves floating paints on the surface of a liquid bath, potentially using tools like combs or a stylus to stir the fluid, and transferring the resulting pattern to paper. There are a wealth of fluid dynamic concepts that marblers use to create specific effects, from modifying the Reynolds number to get a range of behaviors (Stokes to weakly turbulent) to varying the paint's surface tension to get Marangoni flows. Here we view the formation of patterns through the lens of nonlinear dynamics and, in particular, chaotic passive scalar advection. Classic work by Ott et al. showed that repeated application of a chaotic area-preserving map concentrates the gradient of the scalar on a set that is generically fractal and results in specific restrictions on the fractal dimension spectrum. Through a collaboration with professional marblers, we have numerically tested these ideas on high-resolution scans of marbled paper created by the repeated action of a combing process. The beautiful patterns that emerge clearly show the fractal measures inherent in the art of paper marbling. |
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