Physics Commons^™

On Weak Solutions And The Navier-Stokes Equations, Aryan Prabhudesai

Mathematical Sciences Undergraduate Honors Theses

In this paper, I will discuss a partial differential equation that has solutions that are discontinuous. This example motivates the need for distribution theory, which will provide an interpretation of what it means for a discontinuous function to be a “solution” to a PDE. Then I will give a detailed foundation of distributions, including the definition of the derivative of a distribution. Then I will introduce and give background on the Navier-Stokes equations. Following that, I will explain the Millennium Problem concerning global regularity for the Navier-Stokes equations and share mathematical results regarding weak solutions. Finally, I will go over …

Aspects Of Parity Breaking In Classical And Quantum Fluids, Dylan J. Reynolds

Dissertations, Theses, and Capstone Projects

Parity-breaking is ubiquitous across many scales of physics, from the rotation of galaxies at the largest of scales, to the cyclotron orbits of electrons at the microscopic scale. In describing the collective dynamics of many particle systems, parity breaking effects typically originate from some form of chirality, such as angular momentum, at the level of the constituent particles. External forces can also induce chiral motion, with the primary examples being the Lorentz and Coriolis forces.

The effects of parity breaking are perhaps most strikingly seen in active matter, systems of complex particles that tend to convert energy into some directed …

Quantics Tensor Trains: The Study Of A Continuous Lattice Model And Beyond, Aleix Bou Comas

Dissertations, Theses, and Capstone Projects

This four-chapter dissertation studies the efficient discretization of continuous variable functions with tensor train representation. The first chapter describes all the methodology used to discretize functions and store them efficiently. In this section, the algorithm tensor renormalization group is explained for self-containment purposes. The second chapter centers around the XY model. Quantics tensor trains are used to describe the transfer matrix of the model and compute one and two-dimensional quantities. The one dimensional magnitudes are compared to analytical results with an agreement close to machine precision. As for two dimensions, the analytical results cannot be computed. However, the critical temperature …

Oscillations Of Capillary Surfaces With Volume And Edge Effects, Dingqian Ding

All Dissertations

Capillary surfaces are defined by an interface endowed with surface tension that is partially supported by a solid substrate and are susceptible to oscillations reflecting a balance between fluid inertia and the restorative force of surface tension. The wave dynamics strongly depend upon volume change within the domain and edge effects through the boundary conditions applied at the contact-line formed at the liquid-gas-solid interface, while the spatial wave structure conforms to the geometry of the capillary surface. This dissertation develops mathematical models to address these effects for several canonical capillary surfaces, which are organized into two parts that are focused …

Investigation Of Gas Dynamics In Water And Oil-Based Muds Using Das, Dts, And Dss Measurements, Temitayo S. Adeyemi

LSU Master's Theses

Reliable prediction of gas migration velocity, void fraction, and length of gas-affected region in water and oil-based muds is essential for effective planning, control, and optimization of drilling operations. However, there is a gap in our understanding of gas behavior and dynamics in water and oil-based muds. This is a consequence of the use of experimental systems that are not representative of field-scale conditions. This study seeks to bridge the gap via the well-scale deployment of distributed fiber-optic sensors for real-time monitoring of gas behavior and dynamics in water and oil-based mud. The aforementioned parameters were estimated in real-time using …

Modeling Thermosyphon And Heat Pipe Performance For Mold Cooling Applications, Dwaipayan Sarkar

Electronic Thesis and Dissertation Repository

Thermosyphons are enhanced heat transfer devices that can continuously transfer very large amounts of heat rapidly over long distances with small temperature differences. The high heat transfer rate is achieved through simultaneous boiling and condensation of the working fluid and the continuous heat transfer is achieved through recirculation of the working fluid in its liquid and vapor phase. A potentially important application of the thermosyphons has been towards reducing the cycle times of the mold cooling processes which would provide economic incentives to the automotive industry.

Different operational and geometrical parameters such as the input heating power, fill ratio (FR), …

Les-C Turbulence Models And Fluid Flow Modeling: Analysis And Application To Incompressible Turbulence And Fluid-Fluid Interaction, Kyle J. Schwiebert

Dissertations, Master's Theses and Master's Reports

In the first chapter of this dissertation, we give some background on the Navier-Stokes equations and turbulence modeling. The next two chapters in this dissertation focus on two important numerical difficulties arising in fluid flow modeling: poor mass-conservation and nonphysical oscillations. We investigate two different formulations of the Crank-Nicolson method for the Navier-Stokes equations. The most attractive implementation, second order accurate for both velocity and pressure, is shown to introduce non-physical oscillations. We then propose two options which are shown to avoid the poor behavior. Next, we show that grad-div stabilization, previously assumed to have no effect on the target …

Computational Fluid Dynamics Modeling Of Internal Wave Interactions On Conch Reef, Florida Keys, Megan Miller

All HCAS Student Capstones, Theses, and Dissertations

Internal waves breaking on continental shelves play a significant role in mixing and nutrient delivery to coral reef ecosystems. As internal solitary waves, or solitons, propagate shoreward onto continental slopes, they can become unstable and break into turbulent bores that bring cool, nutrient-rich sub-thermocline water shoreward onto coral reefs. The propagation of turbulent bores generated by internal waves interacting with a complex surface creates high-frequency variabilities in the thermal and nutrient environment of Conch Reef in the Florida Keys, which has been studied previously. Here, I have created a three-dimensional model using ANSYS Fluent Computational Fluid Dynamics (CFD) software to …

Investigating The Effects Of A Southward Flow In The Southeastern Florida Shelf Using Robotic Instruments, Alfredo Quezada

All HCAS Student Capstones, Theses, and Dissertations

We deployed a Slocum G3 glider fitted with an acoustic Doppler current profiler (ADCP), a Conductivity-Temperature-Depth sensor (CTD), optics sensor channels, and a propeller on the Southeastern Florida shelf. The ADCP and CTD provide continuous measurements of Northern and Eastern current velocity components, salinity, temperature, and density, throughout the water column in a high-current environment. The optics sensor channels are able to provide measurements of chlorophyll concentrations, colored dissolved organic matter (CDOM), and backscatter particle counts. Additionally, for one of the glider deployments, we deployed a Wirewalker wave-powered profiling platform system also fitted with an ADCP and a CTD in …

Wavelet Compression As An Observational Operator In Data Assimilation Systems For Sea Surface Temperature, Bradley J. Sciacca

University of New Orleans Theses and Dissertations

The ocean remains severely under-observed, in part due to its sheer size. Containing nearly billion of water with most of the subsurface being invisible because water is extremely difficult to penetrate using electromagnetic radiation, as is typically used by satellite measuring instruments. For this reason, most observations of the ocean have very low spatial-temporal coverage to get a broad capture of the ocean’s features. However, recent “dense but patchy” data have increased the availability of high-resolution – low spatial coverage observations. These novel data sets have motivated research into multi-scale data assimilation methods. Here, we demonstrate a new assimilation approach …

Interactive Water Vortex Exhibit, Simon Way, Emily Laing, Roqaya Naseri, Makenzie Kan

Mechanical Engineering

The San Luis Obispo Children’s Museum requested an interactive water vortex exhibit to both engage and entertain inquisitive guests, ages two to eight. The goal was to design and manufacture an exhibit that would educate its users on the fluid mechanics behind water vortices. They activate the mechanics by spinning a wheel, which is perceived as the catalyst to manipulate the flow of water to successfully create a whirlpool. Our team has created an interactive display that will enlighten young minds, providing the museum with an educational exhibit which shares a concept not currently taught by any other. Our project …

Controlled Manipulation And Transport By Microswimmers In Stokes Flows, Jake Buzhardt

All Dissertations

Remotely actuated microscale swimming robots have the potential to revolutionize many aspects of biomedicine. However, for the longterm goals of this field of research to be achievable, it is necessary to develop modelling, simulation, and control strategies which effectively and efficiently account for not only the motion of individual swimmers, but also the complex interactions of such swimmers with their environment including other nearby swimmers, boundaries, other cargo and passive particles, and the fluid medium itself. The aim of this thesis is to study these problems in simulation from the perspective of controls and dynamical systems, with a particular focus …

Microscale To Mesoscale Modeling Of The Ocean Under Tropical Cyclones: Effects Of Sea Spray And Surfactants On Tropical Cyclone Intensity And Air-Sea Gas Exchange, Breanna Lynn Cain Vanderplow

All HCAS Student Capstones, Theses, and Dissertations

Tropical cyclone intensity prediction remains a challenge despite computational and observational developments because successful intensity forecasting requires implementing a multitude of atmospheric and oceanic processes. Hurricane Maria 2017 and Hurricane Dorian 2019 serve as prime examples of rapidly intensifying storms that devastated communities in the Caribbean. A lack of understanding and parameterization of crucial physics involved in tropical cyclone intensity in existing forecast models may have led to these and other forecasting errors.

Microscale physical processes at the air-sea interface are a major factor in intensification of tropical cyclones that are often unaccounted for in forecasting models since they are …

Patterned Heating Induced Propulsion, Saajid A. Aman

Electronic Thesis and Dissertation Repository

This study explores propulsion effects generated by patterned heating acting on smooth and corrugated surfaces. The model problem assumes that the upper plate moves freely, and the lower plate is stationary, equipped with grooves, and exposed to spatially distributed heating. Our findings identify two distinct propulsion effects: thermal streaming and thermal drift. Thermal streaming occurs when given sufficient heating intensity with net flow in the left or right direction characterized by a pitchfork bifurcation. The efficiency of this technique can be controlled using the wavelength of heating. Thermal drift represents a pattern interaction effect. Its strength depends on the relative …

Faster, Cheaper, And Better Cfd: A Case For Machine Learning To Augment Reynolds-Averaged Navier-Stokes, John Peter Romano Ii

Mechanical & Aerospace Engineering Theses & Dissertations

In recent years, the field of machine learning (ML) has made significant advances, particularly through applying deep learning (DL) algorithms and artificial intelligence (AI). The literature shows several ways that ML may enhance the power of computational fluid dynamics (CFD) to improve its solution accuracy, reduce the needed computational resources and reduce overall simulation cost. ML techniques have also expanded the understanding of underlying flow physics and improved data capture from experimental fluid dynamics.

This dissertation presents an in-depth literature review and discusses ways the field of fluid dynamics has leveraged ML modeling to date. The author selects and describes …

Interplay Of Forces In Impinging Jet Flow And Circular Hydraulic Jump, Abdelkader Baayoun

Electronic Thesis and Dissertation Repository

The circular liquid jet impingement with subsequent hydraulic jump formation is studied theoretically using boundary-layer and thin-film approaches. Three different scenarios are tackled, namely, an accelerated Newtonian jet impinging on a stationary disk, a steady Newtonian jet impinging on a rotating disk, and a steady viscoelastic liquid jet impinging on a stationary disk. Accordingly, the effects of jet acceleration, gravity, centrifugal forces, and fluid elasticity on the flow behaviour and the jump are examined. The results are validated against numerical simulation and existing measurements. The findings show that the thickness of the boundary layer developing near impingement diminishes with jet …

Bacterial Motion And Spread In Porous Environments, Yasser Almoteri

Dissertations

Micro-swimmers are ubiquitous in nature from soil and water to mammalian bodies and even many technological processes. Common known examples are microbes such as bacteria, micro-algae and micro-plankton, cells such as spermatozoa and organisms such as nematodes. These swimmers live and have evolved in multiplex environments and complex flows in the presence of other swimmers and types, inert particles and fibers, interfaces and non-trivial confinements and more. Understanding the locomotion and interactions of these individual micro-swimmers in such impure viscous fluids is crucial to understanding the emergent dynamics of such complex systems, and to further enabling us to control and …

Fluid Dynamics Of Interacting Particles: Bouncing Droplets And Colloid-Polymer Mixtures, Lauren Barnes

Dissertations

Interacting particles are a common theme across various physical systems, particularly on the atomic and sub-atomic scales. While these particles cannot be seen with the human eye, insight into such systems can be gained by observing macroscopic systems whose physical behavior is similar. This dissertation consists of three different chapters, each presenting a different problem related to interacting particles, as follows:

Chapter 1 explores chaotic trajectories of a droplet bouncing on the surface of a vertically vibrating fluid bath, with a simple harmonic force acting on the droplet. The bouncing droplet system has attracted recent interest because it exhibits behaviors …

Boundary Integral Equation Methods For Superhydrophobic Flow And Integrated Photonics, Kosuke Sugita

Dissertations

This dissertation presents fast integral equation methods (FIEMs) for solving two important problems encountered in practical engineering applications.

The first problem involves the mixed boundary value problem in two-dimensional Stokes flow, which appears commonly in computational fluid mechanics. This problem is particularly relevant to the design of microfluidic devices, especially those involving superhydrophobic (SH) flows over surfaces made of composite solid materials with alternating solid portions, grooves, or air pockets, leading to enhanced slip.

The second problem addresses waveguide devices in two dimensions, governed by the Helmholtz equation with Dirichlet conditions imposed on the boundary. This problem serves as a …

Variable Resolution Smoothed Particle Hydrodynamics Schemes For 2-D And 3-D Viscous Flows, Francesco Ricci

Dissertations

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian particle-based method for the numerical solution of the partial differential equations that govern the motion of fluids. The main aim of this thesis work is to better enable the applicability of SPH to problems involving multi-scale fluid dynamics. In the first part of the thesis, the capability of the SPH method to simulate three-dimensional isotropic turbulence is investigated with a detailed comparison of Lagrangian and Eulerian SPH formulations. The main reason for this first investigation is to provide an assessment of the error introduced by the particle disorder on the SPH discrete operators …

Effect Of Morphology And An Upstream Tall Building On A Street Canyon Flow, Haoran Du

Electronic Thesis and Dissertation Repository

The effects of the morphological model and the existence of an upstream tall building on the turbulent street canyon flow and the overlying boundary layer are investigated in a wind tunnel, using Stereoscopic Particle Image Velocimetry (S-PIV) measurements. The velocity variances, Reynolds shear stress, and turbulent kinetic energy are found to be larger than in a similar idealized street canyon model. Increasing building height results in a decrease in vertical mass fluxes across the opening of the canyon, at least in the canyon portion directly downstream of the building. The interaction between the large-scale structures in the overlying boundary layer …

Hydrodynamic And Physicochemical Interactions Between An Active Janus Particle And An Inactive Particle, Jessica S. Rosenberg

Dissertations, Theses, and Capstone Projects

Active matter is an area of soft matter science in which units consume energy and turn it into autonomous motion. Groups of these units – whether flocks of birds, bacterial colonies, or even collections of synthetically-made active particles – may exhibit complex behavior on large scales. While the large-scale picture is of great importance, so is the microscopic scale. Studying the individual particles that make up active matter will allow us to understand how they move, and whether and under what circumstances their activity can be controlled.

Here we delve into the world of active matter by studying colloidal-sized (100 …

Diffusion-Driven Aggregation Of Particles In Quasi-2d Membranes, Oscar Gullickson Rausis

Physics

Many biological membranes can be modeled as two-dimensional (2D) viscous fluid sheets surrounded by three-dimensional (3D) fluids of different viscosity. Such membranes are dubbed quasi-2D as they exhibit properties of both 2D and 3D fluids. The Saffman length is a parameter that describes the energy exchange between the membrane and bulk fluids and controls the cross-over from 2D to 3D hydrodynamics. We aim to model diffusion-driven aggregation of particles embedded in a quasi-2D membrane. It is known that hydrodynamic interactions between solute particles significantly reduce their aggregation rate in 3D fluids. It is expected that in quasi-2D membranes the reduction …

Optimization Of Flagellar Locomotion In The Low Reynolds Number Regime, Aidan M. Trodden, Aidan M. Trodden

Physics

This report investigates the computational and theoretical techniques - modeled by E. Lauga and C. Eloy - used to optimize the shape of an activated flagellum for enhanced cell motility. Cell motility is ubiquitous and has a large affect on biological systems such as marine life ecosystems, reproduction, and infection. The physical principles governing flagellar propulsion are explored using computational fluid dynamics simulations, mathematical modeling, and the sequential quadratic programming (SQP) optimization algorithm. Through iterative refinement, we can identify optimized flagellar shapes that would minimize the energetic cost dependent on a single dimensionless sperm numbers (Sp). The computation of the …

Importance Of Vegetation In Tsunami Mitigation: Evidence From Large Eddy Simulations With Fluid-Structure Interactions, Abhishek Mukherjee

Dissertations

Communities worldwide are increasingly interested in nature-based solutions like coastal forests for the mitigation of coastal risks. Still, it remains unclear how much protective benefit vegetation provides, particularly in the limit of highly energetic flows after tsunami impact. The present thesis, using a three-dimensional incompressible computational fluid dynamics model with a fluid-structure interaction approach, aims to quantify how energy reflection and dissipation vary with different degrees of rigidity and vegetation density of a coastal forest.

In this study, tree trunks are represented as cylinders, and the elastic modulus of hardwood trees such as pine or oak is used to characterize …

Monolithic Multiphysics Simulation Of Hypersonic Aerothermoelasticity Using A Hybridized Discontinuous Galerkin Method, William Paul England

Theses and Dissertations

This work presents implementation of a hybridized discontinuous Galerkin (DG) method for robust simulation of the hypersonic aerothermoelastic multiphysics system. Simulation of hypersonic vehicles requires accurate resolution of complex multiphysics interactions including the effects of high-speed turbulent flow, extreme heating, and vehicle deformation due to considerable pressure loads and thermal stresses. However, the state-of-the-art procedures for hypersonic aerothermoelasticity are comprised of low-fidelity approaches and partitioned coupling schemes. These approaches preclude robust design and analysis of hypersonic vehicles for a number of reasons. First, low-fidelity approaches limit their application to simple geometries and lack the ability to capture small scale flow …

Sub-Chandrasekhar Type Ia Supernovae Scenarios With Increased Pathways For Neutronization, Fernando Hernan Rivas

Doctoral Dissertations

Type Ia supernovae are thermonuclear explosions of white dwarfs (WD), electron-degenerate cores of old intermediate mass stars(under 8$M_{\odot}$). Reaching energies of $10^{51}$\si{\erg}, they outshine whole galaxies as they synthesize and distribute most of the iron group elements (IGE; V, Cr, Mn, Fe, Co, Ni) into the interstellar medium, thus being one of the main agents in cosmic chemical evolution. Also, given their notably homogeneous lightcurves, they form the last step in the cosmic distance ladder outdistancing Cepheid variables by orders of magnitude. Though calibration of said lightcurves is dependent on a high number of confirmed events, the limits of statistical …

Sexual Dimorphism Of Glomerular Capillary Morphology In Rats, Zackarias Coker

Undergraduate Honors Theses

Chronic kidney disease (CKD) progresses faster in males than females; however, the underlying mechanisms remain poorly understood. Sex differences in glomerular capillary morphology has been hypothesized to contribute, in part, to the increased susceptibility to hypertension-induced renal injury and CKD progression in males, but this has not been investigated. The goal of the present study was to assess glomerular capillary morphology in male vs. female rats with intact kidneys and after uninephrectomy (UNX). We hypothesized that glomerular capillary radii (R_CAP) and length (L_CAP) would be greater in male rats.

Male (n=4) and female (n=4) with intact …

Asymptotic Properties And Separation Rates For Navier-Stokes Flows, Patrick Michael Phelps

Graduate Theses and Dissertations

In this dissertation, we investigate asymptotic properties of local energy solutions to the Navier-Stokes equations and develop an application which controls the separation of non-unique solutions in this class. Specifically, we quantify the rate at which two, possibly unique solutions evolving from the same data may separate pointwise away from a singularity. This is motivated by recent results on non-uniqueness for forced and unforced Navier-Stokes and analytical and numerical evidence suggesting non-uniqueness in the Leray class. Our investigation begins with discretely self-similar solutions known to exist globally in time and to be regular outside a space-time paraboloid. We prove decay …

A Study Of Reciprocal Underwater Motion And Its Use In Algae Harvesting, Marguerite Bright

Undergraduate Honors Theses

In 2009, many research groups at different companies and universities were funded by Statoil to study the use of algae as a potential biofuel. Combined with the Chesapeake Bay TMDL given by the EPA, a team at William & Mary and VIMS studied the growth and harvest of wild algae in the York River. This method also removed harmful nutrients such as nitrogen and phosphorus from the waterways. Other independent research projects stemmed from this. In 2014, a research team sought to commercialize and automate the IWAGS system, and found that a single oscillating blade was the most effective. This …