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Evidence for the dynamical relevance of relative periodic orbits in turbulence

(Georgia Institute of Technology, 2022-08-01) Crowley, Christopher J.

Despite a long and rich history of scientific investigation, fluid turbulence remains one of the most challenging problems in science and engineering. One of the key outstanding questions concerns the role of coherent structures that describe frequently observed patterns embedded in turbulence. It has been suggested, but not proven, that coherent structures correspond to unstable, recurrent solutions of the governing equations of fluid dynamics. In this thesis, I present the first experimental evidence that three-dimensional turbulent flow mimics the spatial and temporal structure of multiple such solutions episodically but repeatedly. These results provide compelling evidence that coherent structures, grounded in the governing equations, can be harnessed to predict how turbulent flows evolve.
Investigation of spatiotemporal chaos using persistent homology

(Georgia Institute of Technology, 2022-01-04) Tregoning, Brett

Spatiotemporal chaos, especially fluid turbulence, is ubiquitous in nature but can be difficult to characterize because analytic solutions of the strongly nonlinear partial differential equations that govern the behavior are often intractable. However, the topology of structures observed in both experiments and numerical simulations of spatiotemporally chaotic flows can provide insights into the underlying dynamics. The topological properties of spatiotemporally chaotic data can be investigated using persistent homology, a technique of topological data analysis. In this thesis, persistent homology is used to investigate the dynamics of two different spatiotemporally chaotic fluid flows. First, in the Kuramoto-Sivashinsky equation, a popular "toy model" system that mimics the spatiotemporal chaos exhibited by fully turbulent fluid flows, persistent homology is used to detect and quantify shadowing of exact coherent structures (ECS). ECS are invariant solutions to the governing equations that structure the dynamics of spatiotemporal chaos. Persistent homology is found to be an advantageous tool for quantifying shadowing in the Kuramoto-Sivashinsky equation because it quotients out the system's continuous symmetry. Second, in Rayleigh-Bénard convection, persistent homology is used to detect and quantify plumes, which are observable pattern features in experiments and simulations. In simulations, plumes indicate spatial regions of the convective flow in which the leading Lyapunov vector magnitude, a fundamental quantity that characterizes the dynamics of the flow, is high. A long-term goal is to use plumes to connect dynamics in simulations, where the leading Lyapunov vector can be computed, to experiments, where this quantity cannot be observed. This thesis advances research in both of these topics and demonstrates that persistent homology is a powerful tool for analyzing topological structure associated with the dynamics of spatiotemporally chaotic flow.
Exact Coherent Structures and Data-Driven Modeling in a Two-Dimensional Fluid

(Georgia Institute of Technology, 2021-12-14) Kageorge, Logan

Turbulence is one of the most ubiquitous features of the world around us. Its signatures can be found at every scale, in the small eddies of streams to the vortex wakes of airliners, from ocean currents to the cosmic swirls of interstellar gases. Fluids like these have been studied for centuries, but while many advances have been made toward understanding the captivating patterns that they create, predicting the evolution of turbulent fluids remains one of the most notoriously difficult unsolved problems in classical physics. The Navier-Stokes equation is a deterministic, high-dimensional partial differential equation which allows us to make limited predictions about fluids under particular conditions. However, a characteristic feature of turbulence is that it is chaotic, meaning the evolution of a turbulent fluid is highly sensitive to its initial conditions. In practice these initial conditions can never be measured precisely enough to make long-term predictions tractable, and often measurements cannot be made of every physical quantity that goes into the Navier-Stokes equation. Physicists have thus turned recently to developing data-driven computational fluid models to gather statistics about recurring patterns that guide the flow's evolution, which can then be used to characterize an experimental flow. In this dissertation, two data-driven approaches are explored in the context of a shallow, driven fluid flow, an experimental approximation of two-dimensional (2D) Kolmogorov flow. The first approach provides experimental evidence for the statistical role of exact, unstable solutions of the Navier-Stokes equation known as exact coherent structures. In particular, periodic orbits are shown to play an important role in guiding the dynamics of a turbulent flow, as the fluid flow spends a large amount of time shadowing the most relevant orbits as predicted by periodic orbit theory. In the second approach, a weak formulation of the symbolic regression algorithm is used to develop a model of the 3D fluid using only a 2D approximation of the velocity field. The model can then be used to recreate the pressure and forcing fields, yielding a modified, quasi-2D Navier-Stokes equation that governs the flow and agrees with the first-principles model derived in previous studies. Finally, as fluid properties change, the variation in the coefficients of this quasi-2D model are also in agreement with predictions from previous work and provide a useful diagnostic tool for common experimental errors. The substantial progress provided by this dissertation suggests that physics-informed data-driven analysis of turbulent flows provides an important validation of existing models and theories.
Transforming the preparation of physics graduate teaching assistants

(Georgia Institute of Technology, 2019-12-02) Alicea-Munoz, Emily

Graduate Teaching Assistants (GTAs) are key partners in the education of undergraduate students. In large-enrollment intro physics classes, students spend roughly half of their in-class hours in labs and recitations under the supervision of GTAs. Since GTAs can have a large impact on their students' learning, it is important to provide them with appropriate preparation for teaching. But GTAs are also students themselves -- they have many demands on their time, and not all of them want to become professors after grad school. Therefore, it is crucial that GTA preparation not be a burden but rather be fully integrated into their professional development. The School of Physics at Georgia Tech has been offering a GTA prep course for first-year Ph.D. students since 2013. The majority of these first-time GTAs have no prior teaching experience but consider teaching to be an important part of their professional development as physicists. Through a cycle of implementation and revision, and guided by the 3P Framework we developed (Pedagogy, Physics, Professional Development), the course has evolved into a robust and comprehensive professional development program that is well-received by physics graduate students. We assessed the effectiveness of the course with a combination of surveys, pre/post tests, and student evaluations. We found that GTAs feel better prepared for teaching after going through the Orientation. GTAs consider most useful the course activities in which they can practice and get feedback on their teaching ("Microteaching", "Lab Simulation") and the lessons in which we discuss the pedagogical content knowledge necessary to teach intro physics labs and recitations ("Teaching Physics"). GTAs who participate in the GTA prep course adopt more learner-centered teaching approaches and increase their pedagogical knowledge. They also receive higher end-of-semester student evaluations than GTAs whose first teaching experience predated the establishment of the GTA prep course.
Physics communication and peer assessment in a reformed introductory mechanics classroom

(Georgia Institute of Technology, 2018-07-16) Douglas, Scott S.

We designed and implemented a set of introductory mechanics laboratory exercises featuring real-world data-gathering, computational modeling, and video lab reports with peer assessment. Our goal in developing a peer assessment system was to create a valid substitute for instructor grading which could operate at scale, and to achieve learning goals related to student scientific communication and critique. We found our peer assessment system to be an adequate replacement for instructor grading of these lab report videos, and discovered that students learned to produce more expert-like assessments as the semester progressed, as demonstrated by a substantial rise in student-expert rating agreement. Further investigation showed that this improvement in accuracy was related, at least in part, to the completeness (but not necessarily the correctness) of students' explanations of physics phenomena in their lab report videos. At the beginning of the semester, this completeness had no effect on the ratings which students would give each others' videos; at the end of the semester, explanation completeness was strongly correlated with lower student ratings. This correspondence between salutary communicative practices and peer assessment behavior indicates that our introduction of peer assessment was indeed effective at achieving communication-oriented learning goals. Students' retrospective accounts of their experiences with peer assessment also produced some themes and trends that seemed to be corroborated in our quantitative research. All this work together, both quantitative and qualitative, will serve as a basis for continued research into modeling student engagement with peer assessment in the introductory physics classroom.
Quasi-two-dimensional Kolmogorov flow: Bifurcations and exact coherent structures

(Georgia Institute of Technology, 2017-07-26) Suri, Balachandra

Fluid turbulence is nearly ubiquitous in natural and human-made systems. Despite systematic research for over hundred years, scientists are still searching for efficient ways to forecast and control the evolution of turbulent flows. The research presented in this thesis tests and extends recent ideas aimed at developing a simplified description of turbulent evolution, with the final goal being its efficient forecasting and control. The underlying methodology includes identifying ``Exact Coherent Structures'' (ECS), which are unstable, nonchaotic solutions of the Navier-Stokes equation that describes the evolution of fluid flows. While ECS are observed only fleetingly in turbulence, they display relatively simple spatiotemporal features. Hence, being more tractable to analysis than turbulence, ECS may serve as simple building blocks in developing a simplified description of turbulent evolution. The present study explores the role of ECS in turbulence generated in a shallow electrolyte layer which is driven using a horizontal electromagnetic force with a sinusoidal spatial profile. The flow in the experiment, often termed quasi-two-dimensional (Q2D) Kolmogorov Flow, is nearly horizontal. The Q2D flow is described theoretically using a strictly 2D model, which is validated by showing quantitative agreement between its numerical simulation and the experiment in the comparison of pre-turbulent flow states and the transitions between them. Analyzing the dynamics in the weakly turbulent regime, it is identified that dramatic slowing-down in the evolution of the flow is related to turbulent trajectories in the state space visiting the neighborhoods of unstable equilibrium solutions, a class of ECS. The dynamical role of ECS is validated by showing that turbulent trajectories in the neighborhood of an unstable equiliurbium depart following its unstable manifold. Hence, turbulent evolution in the neighborhood of the equilibrium can be forecast by constructing its unstable manifold, which is demonstrated using both the experiment and simulations. This study offers unambiguous experimental evidence for the dynamical role of ECS in turbulence, as well as the first ECS based forecasting of turbulent evolution.
Novel methods of dimensionality reduction applied to a two-dimensional fluid flow

(Georgia Institute of Technology, 2016-07-08) Tithof, Jeffrey

Fluid turbulence is a ubiquitous phenomenon that has been called "the greatest unsolved problem in classical physics." Despite the fact that fluid flows are governed by the deterministic Navier-Stokes equation, turbulence is notoriously difficult to predict. This difficulty largely arises because turbulence is chaotic (i.e., it exhibits extreme sensitivity to initial conditions) and has a very large number of degrees of freedom because of its continuous spatial dependence. However, a growing body of research suggests that turbulent dynamics are effectively low-dimensional, but it is not yet known how to optimally perform dimensionality reduction to capture the dynamically-relevant dimensions. In this dissertation, two dimensionality reduction methods are explored in the context of a quasi-two-dimensional (Q2D) fluid flow. This Q2D flow can be treated as effectively 2D, making the experimental and numerical aspects of the study more tractable than that of a fully three-dimensional flow. The first method involves the calculation of exact, unstable solutions of the Navier-Stokes equation, often called "exact coherent structures" (ECS). ECS exist in the same parameter regime as turbulence and play an important role in guiding the dynamics. In this work, experimental evidence for the existence and dynamical relevance of ECS is provided, as well as the first experimental demonstration of how ECS can be used to forecast weak turbulence. The second method, known as "persistent homology," provides a powerful mathematical formalism in which well-defined geometric features of a flow field are encoded in a so-called "persistence diagram." The results presented herein demonstrate how persistence diagrams can be used to characterize individual flow fields, make pairwise comparisons, and identify periodic dynamics. The substantial progress presented in this dissertation suggests that Q2D flows provide an excellent platform for testing new approaches to understanding turbulence.
Subcritical Transition to Turbulence in Taylor-Couette Flow

(Georgia Institute of Technology, 2014-12) Borrero, Daniel

Turbulence is ubiquitous in naturally-occurring and man-made flows. Despite its importance in scientific and engineering applications, the transition from smooth laminar flow to disorganized turbulent flow is poorly understood. In some cases, the transition can be understood in the context of linear stability theory, which predicts when the underlying laminar solution will become unstable as a parameter is varied. For a large class of flows, however, this approach fails spectacularly, with theory predicting that the laminar flow is stable but experiments and simulations showing the emergence of spatiotemporal complexity. In this dissertation, the direct or subcritical transition to turbulence in Taylor-Couette flow (i.e., the flow between independently rotating co-axial cylinders) is studied experimentally. Chapter 1 discusses different scenarios for the transition to turbulence and recent advances in understanding the subcritical transition within the framework of dynamical systems theory. Chapter 2 presents a comprehensive review of earlier investigations of linearly stable Taylor-Couette flow. Chapter 3 presents the first systematic study of long-lived super-transients in Taylor-Couette flow with the aim of determining the correct dynamical model for turbulent dynamics in the transitional regime. Chapter 4 presents the results of experiments regarding the stability of Taylor-Couette flow to finite-amplitude perturbations in the form of injection/suction of fluid from the test section. Chapter 5 presents numerical investigations of axisymmetric laminar states with realistic boundary conditions. Chapter 6 discusses in detail the implementation of time-resolved tomographic particle image velocimetry (PIV) in the Taylor-Couette geometry and presents preliminary tomographic PIV measurements of the growth of turbulent spots from finite-amplitude perturbations. The main results are summarized in Chapter 7.
Mechanisms of instability in Rayleigh-Bénard convection

(Georgia Institute of Technology, 2011-08-25) Perkins, Adam Christopher

In many systems, instabilities can lead to time-dependent behavior, and instabilities can act as mechanisms for sustained chaos; an understanding of the dynamical modes governing instability is thus essential for prediction and/or control in such systems. In this thesis work, we have developed an approach toward characterizing instabilities quantitatively, from experiments on the prototypical Rayleigh-Bénard convection system. We developed an experimental technique for preparing a given convection pattern using rapid optical actuation of pressurized SF6, a greenhouse gas. Real-time analysis of convection patterns was developed as part of the implementation of closed-loop control of straight roll patterns. Feedback control of the patterns via actuation was used to guide patterns to various system instabilities. Controlled, spatially localized perturbations were applied to the prepared states, which were observed to excite the dominant system modes. We extracted the spatial structure and growth rates of these modes from analysis of the pattern evolutions. The lifetimes of excitations were also measured, near a particular instability; a critical wavenumber was found from the observed dynamical slowing near the bifurcation. We will also describe preliminary results of using a state estimation algorithm (LETKF) on experimentally prepared non-periodic patterns in a cylindrical convection cell.
Evaluating and extending a novel reform of introductory mechanics

(Georgia Institute of Technology, 2011-08-03) Caballero, Marcos Daniel

The research presented in this thesis was motivated by the need to improve introductory physics courses. Introductory physics courses are generally the first courses in which students learn to create models to solve complex problems. However, many students taking introductory physics courses fail to acquire a command of the concepts, methods and tools presented in these courses. The reforms proposed by this thesis focus on altering the content of introductory courses rather than content delivery methods as most reforms do. This thesis explores how the performance on a widely used test of conceptual understanding in mechanics compares between students taking a course with updated and modified content and students taking a traditional course. Better performance by traditional students was found to stem from their additional practice on the types of items which appeared on the test. The results of this work brought into question the role of the introductory physics course for non-majors. One aspect of this new role is the teaching of new methods such as computation (the use of a computer to solve numerically, simulate and visualize physical problems). This thesis explores the potential benefits for students who learn computation as part of physics course. After students worked through a suite of computational homework problems, many were able to model a new physical situation with which they had no experience. The failure of some students to model this new situation might have stemmed from their unfavorable attitudes towards learning computation. In this thesis, we present the development of a new tool for characterizing students' attitudes. Preliminary measurements indicated significant differences between successful and unsuccessful students.