Theses and Dissertations from UMD
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Item I: SUFFICIENT CONDITIONS FOR LOCAL SCALING LAWS IN 3-D TURBULENCE II: WELL-POSEDNESS FOR NONLINEAR STOCHASTIC KINETIC EQUATIONS(2023) Papathanasiou, Stavros; Bedrossian, Jacob; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Incompressible fluids at high Reynolds number quickly transition to turbulence. This implies that precise predictions for many flows in the physical world are extremely difficult - if not outright impossible. The field of statistical fluid mechanics aims to mitigate this difficulty by studying averaged quantities associated with turbulent flows. In the mathematical physics literature, turbulent flow is often described in the language of stochastic partial differential equations. The appropriate models are stochastic perturbations of well-known deterministic equations of fluid mechanics, so that the apparent randomness of turbulent flow is modeled via the tools of stochastic analysis. In the first part of this dissertation, this point of view of stochastic fluid mechanics is employed. We focus on the three dimensional case, with the goal of obtaining a conditional theorem for Kolmogorov's celebrated 4/5 law to hold in the presence of boundaries. The dimensionality enforces the use of a weak notion of solution to our model, in particular we work with families of \say{stationary martingale solutions} to the stochastic Navier-Stokes equations parametrized by the inverse Reynolds number. The main result of the first part of this dissertation provides a sufficient condition for a local version of the 4/5 law in the limit of infinite Reynolds number. In the second part of the dissertation, the focus is shifted to kinetic theory. Kinetic equations have played a prominent role in statistical mechanics since the 19th century; typically, the kinetic viewpoint represents an intermediate step of coarse-graining between the particle level, governed by Newtonian or Hamiltonian mechanics, and the hydrodynamic level, governed by continuum or fluid mechanics. The solution of a kinetic equation represents the normalized phase-space density of a large number of particles which might be interacting and potentially diffusing. The evolution of the density of an ensemble of particles interacting electrostatically is modeled by the Vlasov-Poisson equation. Thermal noise on the particles is modeled by the inclusion of a kinetic Fokker-Planck term. To incorporate the effect of macroscopic fluctuating force fields into kinetic modeling, we perturb the Vlasov-Poisson-Fokker-Planck equation by a stochastic kinetic transport term. We modify and exploit a popular scheme of stochastic fluid mechanics relying on the Gy\"ongy-Krylov lemma and construct local strong solutions to the stochastic Vlasov-Poisson-Fokker-Planck equation.Item A NEW HOPE: CAN WE PREDICT GEODYNAMO DYNAMICS?(2022) Perevalov, Artur; Lathrop, Daniel; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The Earth’s magnetic field is hugely important, as it protects the surface of the planet from cosmic radiation and charged particles coming from the Sun and enables navigation for many living species. However, how it is generated and why it changes its value and configuration in time is poorly understood. The leading theory for the generation of the Earth’s magnetic field is the geodynamo: an electrically conductive fluid in the Earth’s core creates and maintains a magnetic field over an astronomical time scale.To probe this theory experimentally, the Three Meter Experiment—a 3 meter diameter spherical-Couette apparatus—was built to model the Earth's core. The experiment consists of two rotating concentric spheres with liquid sodium between them. The rotating spheres generate fluid motion and reproduce the dynamics similar to those that occur in the planet's core. The previous generation of the experiment was not able to generate a self-sustaining magnetic field. However, numerical studies suggest that increasing the roughness of the liquid to the solid boundary should allow enable entering the dynamo regime. To test this, we first built a scaled-down model of the Three Meter sodium experiment. This was a 40-cm water experiment to examine the increase in helicity of the flow from installing baffles on the inner sphere. We then drained 12 tons of liquid sodium from the Three Meter experiment, cleaned, fixed, and upgraded it with baffles to increase surface roughness. We then re-filled the Three Meter experiment with sodium and performed several experiments. Here, we present the results of studying the torque scaling in the experiment. We show that the experiment's highest Reynolds number is limited by the maximum torque and power in the driving motors. We further investigate the magnetic data from various experiments and show that we are likely on the edge of the dynamo action. We present observation of traveling magneto-Coriolis modes and analyze their dynamics in different conditions. These structures are important for understanding some changes in celestial objects' magnetic fields and their mechanical properties. We also present a software tool developed to mimic the observed behavior of this magnetohydrodynamic experiment. This gives us a proper tool to predict the near future of dynamos, and allows us take a deeper look into its internal structure.Item Effect of Cooling on Hypersonic Boundary-Layer Stability(2022) Paquin, Laura; Laurence, Stuart J; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The prediction of boundary-layer transition on hypersonic vehicles has long been considered a primary design concern due to extreme levels of heating and dynamic pressure loading this transition induces. While it has been predicted that the temperature gradient between the vehicle and the local freestream can drastically alter boundary-layer stability, experimental research on the topic over the past fifty years has provided conflicting results. This study investigates the relationship between the wall-to-edge temperature ratio and boundary-layer stability on a slender cone. Campaigns in two wind-tunnel facilities were conducted: one set within the HyperTERP reflected-shock tunnel at the University of Maryland, and one set at the high-enthalpy T5 reflected-shock tunnel at the California Institute of Technology. Both sets of campaigns employed non-intrusive, optical diagnostics to analyze the structures and spectral content within the boundary layer. In the first part of the study, performed in HyperTERP, an experimental methodology was developed to vary the wall temperature of the model using active cooling and passive thermal management. This allowed the wall temperature ratio to be varied at the same nominal test condition (and thus freestream disturbance environment), and three thermal conditions were established for analysis. Simultaneous schlieren and temperature-sensitive-paint (TSP) imaging were performed. Calibrated schlieren images quantified the unsteady density gradients associated with second-mode instabilities, and TSP contours provided insight into the thermal footprint of mean boundary-layer structures. It was found that, overall, cooling shrunk the boundary-layer thickness, increased second-mode disturbance frequencies, and increased the amplification rate of these instabilities. At nonzero angles of attack, cooling appeared to increase the azimuthal extent of flow separation on the leeward side of the cone. In the second part of the study, performed in T5, the disturbance structures and spectral content of laminar and transitional boundary layers were characterized under high-enthalpy conditions. Schlieren images indicated that, at these extremely low wall-to-edge temperature ratios, second-mode waves were confined very close to the wall in the laminar case. During the breakdown to turbulence, structures radiating out of the boundary layer and into the freestream were discovered. A texture-based methodology was used to characterize the Mach angles associated with these structures, and a wall-normal spectral analysis indicated a potential mechanism by which energy was transferred from the near-wall region to the freestream. The study presents some of the first simultaneous imaging of the flow structures and associated thermal footprint of boundary-layer transition within an impulse facility. The work also presents the first time-resolved, full-field visualizations of the second-mode dominated breakdown to turbulence at high enthalpy. Thus, the study imparts significant insight into the mechanics of boundary-layer transition at conditions representative of true hypervelocity flight.Item DYNAMICS OF CAPSULES IN COMPLEX MICROFLUIDIC DEVICES(2018) Koolivand, Abdollah; Dimitrakopoulos, Panagiotis; Chemical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The dynamics of micro-capsules has attracted a lot of attention in the last decade due to their vast applications in different industrial sectors such as cosmetic products, food industry, chemical processes, reaction systems, cell modeling, drug delivery, and medical processes. Additionally, biological cells such as red blood cells can be modeled as capsules. Understanding the rheological behavior of these cells provides great physical insight for early diagnosis of relevant diseases. The main objective of this research is to investigate the effects of physical and geometrical parameters on the hydrodynamics of simple and multiple capsules in complex mi- crofluidic devices. For this purpose, we have developed the mathematical formulation needed for modeling multiple capsules with or without complex internal structures. The developed framework provides an enormous flexibility in problem definition, and facilitates the investigation of the hydrodynamics of a wide class of capsules in microfluidic channels and vascular capillaries. We first study the deformation of a spherical capsule in a T-junction channel. It is shown that an initially spherical capsule develops a bean shape at low flow rates and an inverse kayak shape at high flow rates. Based on the non-trivial deformation of the capsule, a new methodology for the determination of membrane moduli is proposed. For an accurate determination of the membrane moduli, it is paramount to measure the capsule dimensions precisely, which is easier in the proposed device owning to the stagnation-point flow of the T-junction. To determine the membrane moduli, one needs to do a single experiment for different flow rates, and compare the experimental measurements of the capsule steady-state dimensions with the provided computational data. We then consider the flow dynamics of non-spherical capsules and investi- gate the effects spheroidity and initial orientation on the steady-state shape. It is found that a non-spherical capsule, placed with a non-zero initial orientation angle along the centerline of a microchannel, does not practically rotate during deforma- tion. Thus, precise instrumentation is required for proper alignment of the capsule which influences the deformation and steady-state shape. This behavior may explain possible inconsistencies between measured (experimental) and calculated (compu- tational) shapes. We then study the lateral migration of capsules with different size in a mi- crofluidic channel with a trapezoidal cross-section. Owing to the emergence of 3D printing technology, fabrication of a channel with trapezoidal cross-section is fea- sible. Based on our computational data, we proposed an optimized geometry that could be utilized for separation of capsules or cells with different size. The main advantage of the proposed geometry is its inexpensive fabrication cost without the need for incorporating complicated inner structures, which automatically eliminates the risk of channel clogging. Moreover, the simple structure of the trapezoidal mi- crochannel allows an easy scale out through parallelization and reduction of the cell sorting time. In addition, we investigate the complex behavior of two (equal or unequal sized) capsules flowing in a square microfluidic channel. Capsules merging process controls the on-demand drug release and reaction. Thus, we identified the hydro- dynamic conditions that facilitates or hinders the merging of the capsules. The merging process is commonly accompanied by the drainage of existing liquid film between two particles. We observed that the capsules merging in most cases is ac- companied by the formation of dimple surfaces, and thus a simplified flat lubrication surface assumption which is widely-used in the theoretical studies might not be an ideal choice for modeling the film drainage time in merging process.Item The Structure of the Blue Whirl: A Soot-Free Reacting Vortex Phenomenon(2017) Hariharan, Sriram Bharath; Gollner, Michael J; Oran, Elaine S; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Recent experiments have led to the discovery of the blue whirl, a small, stable flame that evolves from a fire whirl, and burns typically sooty hydrocarbons without producing soot. The distinct physical structure of the flame is investigated through digital imaging techniques, which suggest that the transition and shape of the flame may be influenced by vortex breakdown. The thermal structure of the blue whirl reveals a peak temperature around 2000 K, and that most of the combustion occurs in a relatively small, visibly bright vortex ring. The formation of the flame is shown to occur over a variety of surfaces, including water and flat metal, all of which indicate that the formation of the blue whirl is strongly influenced by the flow structure over the incoming boundary layer. Finally, a schematic structure of the blue whirl is proposed, based on the measurements presented here and previous literature on fire whirls and vortex breakdown.Item Magnetic and Acoustic Investigations of Turbulent Spherical Couette Flow(2016) Adams, Matthew Michael; Lathrop, Daniel P; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Title of dissertation: MAGNETIC AND ACOUSTIC INVESTIGATIONS OF TURBULENT SPHERICAL COUETTE FLOW Matthew M. Adams, Doctor of Philosophy, 2016 Dissertation directed by: Professor Daniel Lathrop Department of Physics This dissertation describes experiments in spherical Couette devices, using both gas and liquid sodium. The experimental geometry is motivated by the Earth's outer core, the seat of the geodynamo, and consists of an outer spherical shell and an inner sphere, both of which can be rotated independently to drive a shear flow in the fluid lying between them. In the case of experiments with liquid sodium, we apply DC axial magnetic fields, with a dominant dipole or quadrupole component, to the system. We measure the magnetic field induced by the flow of liquid sodium using an external array of Hall effect magnetic field probes, as well as two probes inserted into the fluid volume. This gives information about possible velocity patterns present, and we extend previous work categorizing flow states, noting further information that can be extracted from the induced field measurements. The limitations due to a lack of direct velocity measurements prompted us to work on developing the technique of using acoustic modes to measure zonal flows. Using gas as the working fluid in our 60~cm diameter spherical Couette experiment, we identified acoustic modes of the container, and obtained excellent agreement with theoretical predictions. For the case of uniform rotation of the system, we compared the acoustic mode frequency splittings with theoretical predictions for solid body flow, and obtained excellent agreement. This gave us confidence in extending this work to the case of differential rotation, with a turbulent flow state. Using the measured splittings for this case, our colleagues performed an inversion to infer the pattern of zonal velocities within the flow, the first such inversion in a rotating laboratory experiment. This technique holds promise for use in liquid sodium experiments, for which zonal flow measurements have historically been challenging.Item Transport in Rayleigh-Stable Experimental Taylor-Couette Flow and Granular Electrification in a Shaking Experiment(2015) Nordsiek, Freja; Lathrop, Daniel P; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation consists of two projects: Rayleigh-stable Taylor-Couette flow and granular electrification. Taylor-Couette flow is the fluid flow in the gap between two cylinders rotating at different rates. Azimuthal velocity profiles, dye visualization, and inner cylinder torques were measured on two geometrically similar Taylor-Couettes with axial boundaries attached to the outer cylinder, the Maryland and Twente T3C experiments. This was done in the Rayleigh stable regime, where the specific angular momentum increases radially, which is relevant to astrophysical and geophysical flows and in particular, stellar and planetary accretion disks. The flow substantially deviates from laminar Taylor-Couette flow beginning at moderate Reynolds number. Angular momentum is primarily transported to the axial boundaries instead of the outer cylinder due to Ekman pumping when the inner cylinder is rotating faster than the outer cylinder. A phase diagram was constructed from the transitions identified from torque measurements taken over four decades of the Reynolds number. Flow angular velocities larger and smaller than both cylinders were found. Together, these results indicate that experimental Taylor-Couette with axial boundaries attached to the outer cylinder is an imperfect model for accretion disk flows. Thunderstorms, thunder-snow, volcanic ash clouds, and dust storms all display lightning, which results from electrification of droplets and particles in the atmosphere. While lightning is fairly well understood (plasma discharge), the mechanisms that result in million-volt differences across the storm are not. A novel granular electrification experiment was upgraded and used to study some of these mechanisms in the lab. The relative importance of collective interactions between particles versus particle properties (material, size, etc.) on collisional electrification was investigated. While particle properties have an order of magnitude effect on the strength of macroscopic electrification, all particle types electrified with dynamics that suggest a major role for collective interactions in electrification. Moreover, mixing two types of particles together does not lead to increased electrification except for specific combinations of particles which clump, which further points towards the importance of collective phenomena. These results help us better understand the mechanisms of electrification and lightning generation in certain atmospheric systems.Item Characterization of Quantum Vortex Dynamics in Superfluid Helium(2015) Meichle, David P.; Lathrop, Daniel P; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Liquid helium obtains superfluid properties when cooled below the Lambda transition temperature of 2.17 K. A superfluid, which is a partial Bose Einstein condensate, has many exotic properties including free flow without friction, and ballistic instead of diffusive heat transport. A superfluid is also uniquely characterized by the presence of quantized vortices, dynamical line-like topological phase defects around which all circulation in the flow is constrained. Two vortices can undergo a violent process called reconnection when they approach, cross, and retract having exchanged tails. With a numerical examination of a local, linearized solution near reconnection we discovered a dynamically unstable stationary solution to the Gross-Pitaevskii equation, which was relaxed to a fully non-linear solution using imaginary time propagation. This investigation explored vortex reconnection in the context of the changing topology of the order parameter, a complex field governing the superfluid dynamics at zero temperature. The dynamics of the vortices can be studied experimentally by dispersing tracer particles into a superfluid flow and recording their motions with movie cameras. The pioneering work of Bewley et al. provided the first visualization technique using frozen gases to create tracer particles. Using this technique, we experimentally observed for the first time the excitation of helical traveling waves on a vortex core called Kelvin waves. Kelvin waves are thought to be a central mechanism for dissipation in this inviscid fluid, as they provide an efficient cascade mechanism for transferring energy from large to microscopic length scales. We examined the Kelvin waves in detail, and compared their dynamics in fully self-similar non-dimensional coordinates to theoretical predictions. Additionally, two experimental advances are presented. A newly invented technique for reliably dispersing robust, nanometer-scale fluorescent tracer particles directly into the superfluid is described. A detailed numerical investigation of the particle-vortex interactions provides novel calculations of the force trapping particles on vortices, and a scaling was found suggesting that smaller particles may remain bound to the vortices at much higher speeds than larger particles. Lastly, a new stereographic imaging system has been developed, allowing for the world-first three-dimensional reconstruction of individual particles and vortex filament trajectories. Preliminary data, including the first three-dimensional observation of a vortex reconnection are presented.Item Inertial waves in a laboratory model of the Earth's core(2011) Triana, Santiago Andres; Lathrop, Daniel P; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A water-filled three-meter diameter spherical shell built as a model of the Earth's core shows evidence of precessionally forced flows and, when spinning the inner sphere differentially, inertial modes are excited. We identified the precessionally forced flow to be primarily the spin-over inertial mode, i.e., a uniform vorticity flow whose rotation axis is not aligned with the container's rotation axis. A systematic study of the spin-over mode is carried out, showing that the amplitude dependence on the Poincaré number is in qualitative agreement with Busse's laminar theory while its phase differs significantly, likely due to topographic effects. At high rotation rates free shear layers concentrating most of the kinetic energy of the spin-over mode have been observed. When spinning the inner sphere differentially, a total of 12 inertial modes have been identified, reproducing and extending previous experimental results. The inertial modes excited appear ordered according to their azimuthal drift speed as the Rossby number is varied.