Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session M1: Nonlinear Dynamics: GeneralNonlinear
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Chair: Kevin Mitchell, University of California, Merced Room: 401 |
Tuesday, November 21, 2017 8:00AM - 8:13AM |
M1.00001: Stirring inertia in time-dependent low Reynolds number flows Philip Yecko, Dirk Martin (Mark) Luchtenburg, Eric Forgoston, Lora Billings Diagnosis of a kinematic flow and its transport using Lagrangian coherent structures (LCS) based on finite-time Lyapunov exponents (FTLE) neglects dynamical effects, such as pressure, as well as dynamically important constraints, such as potential vorticity conservation. Chaotic advection, on the other hand, often neglects inertial effects, which are prominent in LCS. We present results for very low Reynolds number laboratory flows, including a Stokes double gyre, vertically sheared strain and a four roll mill. Images of tracer (dye) and FTLE fields computed from particle image velocimetry (PIV) reveal complementary sets of flow structures, giving a more complete picture of transport in these flows. We confirm by computing FTLE of an exact time-dependent Stokes flow solution and present implications of these findings for inertial object transport in flows. [Preview Abstract] |
Tuesday, November 21, 2017 8:13AM - 8:26AM |
M1.00002: Optimal bounds and extremal trajectories for time averages in dynamical systems Ian Tobasco, David Goluskin, Charles Doering For systems governed by differential equations it is natural to seek extremal solution trajectories, maximizing or minimizing the long-time average of a given quantity of interest. A priori bounds on optima can be proved by constructing auxiliary functions satisfying certain point-wise inequalities, the verification of which does not require solving the underlying equations. We prove that for any bounded autonomous ODE, the problems of finding extremal trajectories on the one hand and optimal auxiliary functions on the other are strongly dual in the sense of convex duality. As a result, auxiliary functions provide arbitrarily sharp bounds on optimal time averages. Furthermore, nearly optimal auxiliary functions provide volumes in phase space where maximal and nearly maximal trajectories must lie. For polynomial systems, such functions can be constructed by semidefinite programming. We illustrate these ideas using the Lorenz system, producing explicit volumes in phase space where extremal trajectories are guaranteed to reside. [Preview Abstract] |
Tuesday, November 21, 2017 8:26AM - 8:39AM |
M1.00003: Phase transitions in colloidal fluids: Kinetically or thermodynamically controlled? Miguel A. Duran-Olivencia, Peter Yatsyshin, James F. Lutsko, Serafim Kalliadasis In recent years, a flurry of experimental observations suggests that most phase transitions occur in a multistage manner and via intermediate phases. These precursors to the final phase are commonly understood as the local minima of the free energy of the system. Inherently, the classical paradigm of nucleation has no capacity to describe neither the origin nor the role played by these precursors in the nucleation pathway. Here we present a systematic theoretical framework capable of describing the precursor phases in a self-consistent way. We demonstrate that nucleation precursors can appear even in situations involving a single free-energy barrier. This contradicts previous phenomenological approaches, which always characterise intermediate phases as the minima of a complex free-energy landscape. We show that a kinetically-induced mechanism temporarily stabilises an intermediate phase, which thus is not the result of a local minimum of the free energy but a consequence of the entropic cost of cluster formation. Moreover, the appearance of precursors does not seem to influence the overall nucleation time, which is governed by the free-energy barrier. The mechanism uncovered in this study can be used to explain recently reported experimental findings in crystallisation. [Preview Abstract] |
Tuesday, November 21, 2017 8:39AM - 8:52AM |
M1.00004: Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation Serafim Kalliadasis, Susana Gomes, Demetrios Papageorgiou, Greg Pavliotis, Marc Pradas We present a novel methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The original equation is split into a linear stochastic and a nonlinear deterministic equation so that we can apply linear feedback control methods. Our control strategy is then based on two steps: first, stabilize the zero solution of the deterministic part and, second, control the roughness of the stochastic linear equation. We consider both periodic controls and point actuated ones, observing in all cases that the second moment of the solution evolves in time according to a power-law until it saturates at the desired controlled value. Furthermore, our control framework allows us to force the interfaces to have a prescribed shape. We observe from our numerical experiments that our results are valid for different types of nonlinearity (in particular, the Burgers and KPZ ones) as well as white and coloured noise. [Preview Abstract] |
Tuesday, November 21, 2017 8:52AM - 9:05AM |
M1.00005: Vortex network community based reduced-order force model Muralikrishnan Gopalakrishnan Meena, Aditya Nair, Kunihiko Taira We characterize the vortical wake interactions by utilizing network theory and cluster-based approaches, and develop a data-inspired unsteady force model. In the present work, the vortical interaction network is defined by nodes representing vortical elements and the edges quantified by induced velocity measures amongst the vortices. The full vorticity field is reduced to a finite number of vortical clusters based on network community detection algorithm, which serves as a basis for a skeleton network that captures the essence of the wake dynamics. We use this reduced representation of the wake to develop a data-inspired reduced-order force model that can predict unsteady fluid forces on the body. The overall formulation is demonstrated for laminar flows around canonical bluff body wake and stalled flow over an airfoil. We also show the robustness of the present network-based model against noisy data, which motivates applications towards turbulent flows and experimental measurements. [Preview Abstract] |
Tuesday, November 21, 2017 9:05AM - 9:18AM |
M1.00006: Data-driven discovery of Koopman eigenfunctions using deep learning Bethany Lusch, Steven L. Brunton, J. Nathan Kutz Koopman operator theory transforms any autonomous non-linear dynamical system into an infinite-dimensional linear system. Since linear systems are well-understood, a mapping of non-linear dynamics to linear dynamics provides a powerful approach to understanding and controlling fluid flows. However, finding the correct change of variables remains an open challenge. We present a strategy to discover an approximate mapping using deep learning. Our neural networks find this change of variables, its inverse, and a finite-dimensional linear dynamical system defined on the new variables. Our method is completely data-driven and only requires measurements of the system, i.e. it does not require derivatives or knowledge of the governing equations. We find a minimal set of approximate Koopman eigenfunctions that are sufficient to reconstruct and advance the system to future states. We demonstrate the method on several dynamical systems. [Preview Abstract] |
Tuesday, November 21, 2017 9:18AM - 9:31AM |
M1.00007: Convolutional Neural Networks for Wake Flow Predictions Tharindu Miyanawala, Rajeev Jaiman We present a Convolutional Neural Network (CNN) based deep-learning technique to predict the wake flow characteristics at a low Reynolds number for different bluff body shapes. The discrete convolution process with non-linear rectification approximates the mapping between the bluff body shape and the wake flow characteristics. The CNN is fed by an Euclidean distance function as the input and target data generated by full order Navier-Stokes (NS) computations for primitive bluff body shapes. The CNN is designed to predict the key flow dynamic parameters such as the Strouhal number, force coefficients and mean velocity and pressure fields. The CNN processes are iteratively trained using a gradient descent method. The CNN is then used to predict the flow characteristics of different geometries and the results are found to be consistent with the NS-based computations. A convergence study is performed to identify the effective dimensions of the CNN e.g. the convolution kernel size, number of kernels and convolution layers. The CNN prediction has a speed-up nearly two-orders of magnitude with less than 5\% error compared to the full-order results. This technique provides a good trade-off between the speed versus accuracy to predict the wake flow characteristics for interactive design. [Preview Abstract] |
Tuesday, November 21, 2017 9:31AM - 9:44AM |
M1.00008: Arbitrary Lagrangian Eulerian framework for efficient projection-based reduction of convection dominated nonlinear flows Rambod Mojgani, Maciej Balajewicz One of the main hurdles in projection-based model reduction techniques is the efficient approximation of convective features, specially moving shocks and sharp gradients. These features typically require a very large number of reduced basis to reach the desired precision. In this talk, we introduce details of a new Arbitrary Lagrangian Eulerian (ALE) reduction framework that significantly out-performs traditional approaches. At the heart of this method is an optimization problem to solve for a low-rank grid deformation. That is, we seek global basis functions for both the state of the system and the positions of the computational grid in the parameter space. This proposed method is general in that it is not limited to a single wave speed or direction. This method is successfully applied to the reduction of several hyperbolic and parametric elliptic partial differential equations. [Preview Abstract] |
Tuesday, November 21, 2017 9:44AM - 9:57AM |
M1.00009: Experimental Evidence of Amplitude Death in Coupled Candle Flame Oscillators Krishna Manoj, Samadhan A. Pawar, R. I. Sujith Mutual coupling causes synchronization in coupled limit cycle oscillators by locking their phases to a common value. A pair of candle flame oscillators, each consisting of 3 or more candles and capable of exhibiting self-sustained oscillations, produce synchronized behaviour in their flame dynamics upon coupling. Previous studies on synchronization of candle flame oscillators report the existence of only two modes of oscillations, in-phase and anti-phase, as a consequence of variation in inter-flame distance between the oscillators. Here, we provide experimental evidence on the presence of an ‘amplitude death’ (AD) state between the previously known states of in-phase and anti-phase oscillations. With increase in number of candles in an oscillator, we observe a considerable reduction in the AD zone. Eventually, we reach a point of phase-flip bifurcation, wherein the oscillators show sharp transition from a state of in-phase to anti-phase oscillations without showing an intermediate state of AD. We also report similar results in a pair of candle flame oscillators, where the number of candles in each oscillator is different. Based on our experimental results, we speculate on the major role of time delay coupling in inducing synchronization behaviour in candle flame oscillators. [Preview Abstract] |
(Author Not Attending)
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M1.00010: Physical experiments and analysis on the generation and evolution of tsunami-induced turbulent coherent structures Nikos Kalligeris, Patrick Lynett Numerous historical accounts describe the formation of "whirpools" inside ports and harbors during tsunami events, causing port operation disruptions. Videos from the Japan 2011 tsunami revealed complex nearshore flow patters, resulting from the interaction of tsunami-induced currents with the man-made coastline, and the generation of large eddies (or turbulent coherent structures) in numerous ports and harbors near the earthquake epicenter. The aim of this work is to study the generation and evolution of tsunami-induced turbulent coherent structures (TCS) in a well-controlled environment using realistic scaling. A physical configuration is created in the image of a port entrance at a scale of 1:27 and a small-amplitude, long period wave creates a transient flow through the asymmetric harbor channel. A separated region forms, which coupled with the transient flow, leads to the formation of a stable monopolar TCS. The surface flow is examined through mono- and stereo-PTV techniques to extract surface velocity vectors. Surface velocity maps and vortex flow profiles are used to study the experimental TCS generation and evolution, and characterize the TCS structure. Analytical tools are used to describe the TCS growth rate and kinetic energy decay. [Preview Abstract] |
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