Matching Items (11)

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Asymptotic Stability of Biharmonic Shallow Water Equations

Description

The dissipative shallow-water equations (SWE) possess both real-world application and extensive analysis in theoretical partial differential equations. This analysis is dominated by modeling the dissipation as diffusion, with its mathematical

The dissipative shallow-water equations (SWE) possess both real-world application and extensive analysis in theoretical partial differential equations. This analysis is dominated by modeling the dissipation as diffusion, with its mathematical representation being the Laplacian. However, the usage of the biharmonic as a dissipative operator by oceanographers and atmospheric scientists and its underwhelming amount of analysis indicates a gap in SWE theory. In order to provide rigorous mathematical justification for the utilization of these equations in simulations with real-world implications, we extend an energy method utilized by Matsumura and Nishida for initial value problems relating to the equations of motion for compressible, vsicous, heat-conductive fluids ([6], [7]) and applied by Kloeden to the diffusive SWE ([4]) to prove global time existence of classical solutions to the biharmonic SWE. In particular, we develop appropriate a priori growth estimates that allow one to extend the solution's temporal existence infinitely under sufficient constraints on initial data and external forcing, resulting in convergence to steady-state.

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  • 2017-05

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Modeling the Effects of Flow Conditions and Rheology on Lava Flows with Polyethylene Glycol

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This study explores the relationship between three physics-based predictive models defined by Castruccio et al. (2013), and four different distinct experimental morphologies of lava flows produced in a series of

This study explores the relationship between three physics-based predictive models defined by Castruccio et al. (2013), and four different distinct experimental morphologies of lava flows produced in a series of laboratory simulations where polyethylene glycol 600 (PEG) was pumped into an inclined chilled bath of water. The length of the experimental flow was recorded over time to create an experimental model to later be compared to the physics-based predictive models. The experimental morphologies are pillowed, rifted, folded, and leveed flows which can be characterized by a dimensionless parameter 𝛹, which scales natural lava flows to experimental lava flows and is a ratio of timescales, the characteristic timescale of thermal flux from the vent and the characteristic timescale of crust formation caused by surface cooling (Fink and Griffiths 1990). The three physics-based models are presented such that the downslope gravitational acceleration drives the flow, while either the Newtonian viscosity of the flow, the Yield Strength of the core (YS), or the Yield Strength of the growing crust (YSC) is the primary retarding factor in flow propagation. This study concluded that low 𝛹-value flows (low flux, low temperature, extensive crust formation) are better captured by the YSC model. And although the Newtonian model did not perfectly capture the behavior of any experimental flows in this study, high 𝛹-value flows (high flux, high temperature, little crust formation) that formed levees exhibited the most Newtonian behavior.

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  • 2020-05

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Computer Model Predicting the Ideal Pitch of the Coiling Umbilical Arteries

Description

A fetus physiologically relies on blood for nutrients given by the mother. Blood supply is provided to a fetus through an umbilical cord having the structure of two pulsatile arteries

A fetus physiologically relies on blood for nutrients given by the mother. Blood supply is provided to a fetus through an umbilical cord having the structure of two pulsatile arteries with smooth muscle surrounding a thin walled vein. The two arteries transport deoxygenated blood from the fetus in the direction of the placenta while the one vein transports oxygenated blood in the direction of the fetus. This process of the movement of blood is continuous throughout the gestation cycle. Conventionally, there are two arterial coils for every one coil of the vein. Undercoiling and overcoiling of the arteries leads to fetal distress, resulting in researchers to speculate that there is a relationship between these geometries with altered blood flow patterns that may be deleterious to the fetus. The fluid dynamics of an umbilical cord artery blood flow has not been extensively modeled on a computer, meaning there is an absence of knowledge on the ideal pitch of the coiling of the umbilical cord arteries. In this study, I developed computer models with ANSYS Fluent containing fluid dynamic variables and boundary conditions including: density of blood, viscosity of blood, diameter of each artery, pitch of artery coil, flow rate in each artery, and inlet velocity. Care was taken to investigate the effect of fluid finite element size, through mesh refinement, to improve accuracy of the models. The finalized models illustrate velocity and stress distribution in a coiled artery, showing different patterns in a model representing normal as compared to abnormal pitch. Further study of the fluid mechanics in the coil of the umbilical cord arteries, may elucidate the correlation between ideal pitch and fetal distress.

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  • 2016-05

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Validating a New CFD Algorithm by Finding the Drag Coefficient of a Sphere

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A novel CFD algorithm called LEAP is currently being developed by the Kasbaoui Research Group (KRG) using the Immersed Boundary Method (IBM) to describe complex geometries. To validate the algorithm,

A novel CFD algorithm called LEAP is currently being developed by the Kasbaoui Research Group (KRG) using the Immersed Boundary Method (IBM) to describe complex geometries. To validate the algorithm, this research project focused on testing the algorithm in three dimensions by simulating a sphere placed in a moving fluid. The simulation results were compared against the experimentally derived Schiller-Naumann Correlation. Over the course of 36 trials, various spatial and temporal resolutions were tested at specific Reynolds numbers between 10 and 300. It was observed that numerical errors decreased with increasing spatial and temporal resolution. This result was expected as increased resolution should give results closer to experimental values. Having shown the accuracy and robustness of this method, KRG will continue to develop this algorithm to explore more complex geometries such as aircraft engines or human lungs.

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  • 2021-05

Dynamics of Tilted Stably Stratified Square Cavities

Description

The dynamics of a stably and thermally stratified, two dimensional fluid-filled cavity are the subject of numerical study. When gravity is orthogonal to the endwalls, a closed form for a

The dynamics of a stably and thermally stratified, two dimensional fluid-filled cavity are the subject of numerical study. When gravity is orthogonal to the endwalls, a closed form for a steady state solution with trivial flow may be obtained. However, as soon as the cavity is tilted the flow becomes nontrivial. Previous studies have investigated when this tilt angle is 180 degrees (Rayleigh-BĂ©nard convection), 90 degrees, and 0 degrees, or have done a sweep while solving the steady-state equations. When buoyancy is sufficiently weak the flow is stable and steady up to 90 degrees of tilt. Above a certain level of buoyancy, as measured by the temperature difference between the top and bottom walls, the flow becomes unsteady above a tilt angle less than 90 degrees. Specifically, In this study we examine the relationship between the critical tilt angle and the buoyancy level at the onset of unsteadiness, as well as the dynamical mechanisms by which it occurs.

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  • 2019-05

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The domain dependence of chemotaxis in a two-dimensional turbulent flow

Description

Presented is a study on the chemotaxis reaction process and its relation with flow topology. The effect of coherent structures in turbulent flows is characterized by studying nutrient uptake and

Presented is a study on the chemotaxis reaction process and its relation with flow topology. The effect of coherent structures in turbulent flows is characterized by studying nutrient uptake and the advantage that is received from motile bacteria over other non-motile bacteria. Variability is found to be dependent on the initial location of scalar impurity and can be tied to Lagrangian coherent structures through recent advances in the identification of finite-time transport barriers. Advantage is relatively small for initial nutrient found within high stretching regions of the flow, and nutrient within elliptic structures provide the greatest advantage for motile species. How the flow field and the relevant flow topology lead to such a relation is analyzed.

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Date Created
  • 2015

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Field and Flume Investigations of Bedload Transport and Bedforms in Sand-Bedded Rivers

Description

Worldwide, rivers and streams make up dense, interconnected conveyor belts of sediment– removing carved away earth and transporting it downstream. The propensity of alluvial river beds to self-organize into complex

Worldwide, rivers and streams make up dense, interconnected conveyor belts of sediment– removing carved away earth and transporting it downstream. The propensity of alluvial river beds to self-organize into complex trains of bedforms (i.e. ripples and dunes) suggests that the associated fluid and sediment dynamics over individual bedforms are an integral component of bedload transport (sediment rolled or bounced along the river bed) over larger scales. Generally speaking, asymmetric bedforms (such as alluvial ripples and dunes) migrate downstream via erosion on the stoss side of the bedform and deposition on the lee side of the bedform. Thus, the migration of bedforms is intrinsically linked to the downstream flux of bedload sediment. Accurate quantification of bedload transport is important for the management of waters, civil engineering, and river restoration efforts. Although important, accurate qualification of bedload transport is a difficult task that continues t elude researchers. This dissertation focuses on improving our understanding and quantification of bedload transport on the two spatial scales: the bedform scale and the reach (~100m) scale.

Despite a breadth of work investigating the spatiotemporal details of fluid dynamics over bedforms and bedload transport dynamics over flat beds, there remains a relative dearth of investigations into the spatiotemporal details of bedload transport over bedforms and on a sub-bedform scale. To address this, we conducted two sets of flume experiments focused on the two fundamental regions of flow associated with bedforms: flow separation/reattachment on the lee side of the bedform (Chapter 1; backward facing-step) and flow reacceleration up the stoss side of the next bedform (Chapter 2; two-dimensional bedform). Using Laser and Acoustic Doppler Velocimetry to record fluid turbulent events and manual particle tracking of high-speed imagery to record bedload transport dynamics, we identified the existence and importance of “permeable splat events” in the region proximal to flow reattachment.

These coupled turbulent and sediment transport events are integral to the spatiotemporal pattern of bedload transport over bedforms. Splat events are localized, high magnitude, intermittent flow features in which fluid impinges on the bed, infiltrates the top portion of bed, and then exfiltrates in all directions surrounding the point of impingement. This initiates bedload transport in a radial pattern. These turbulent structures are primarily associated with quadrant 1 and 4 turbulent structures (i.e. instantaneous fluid fluctuations in the streamwise direction that bring fluid down into the bed in the case of quadrant 1 events, or up away from the bed in the case of quadrant 4 events) and generate a distinct pattern of bedload transport compared to transport dynamics distal to flow reattachment. Distal to flow reattachment, bedload transport is characterized by relatively unidirectional transport. The dynamics of splat events, specifically their potential for inducing significant magnitudes of cross-stream transport, has important implications for the evolution of bedforms from simple, two dimensional features to complex, three-dimensional features.

New advancements in sonar technology have enabled more detailed quantification of bedload transport on the reach scale, a process paramount to the effective management of rivers with sand or gravel-dominated bed material. However, a practical and scalable field methodology for reliably estimating bedload remains elusive. A popular approach involves calculating transport from the geometry and celerity of migrating bedforms, extracted from time-series of bed elevation profiles (BEPs) acquired using echosounders. Using two sets of repeat multibeam sonar surveys from the Diamond Creek USGS gage station in Grand Canyon National Park with large spatio-temporal resolution and coverage, we compute bedload using three field techniques for acquiring BEPs: repeat multi-, single-, and multiple single-beam sonar. Significant differences in flux arise between repeat multibeam and single beam sonar. Mulitbeam and multiple single beam sonar systems can potentially yield comparable results, but the latter relies on knowledge of bedform geometries and flow that collectively inform optimal beam spacing and sampling rate. These results serve to guide design of optimal sampling, and for comparing transport estimates from different sonar configurations.

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Date Created
  • 2018

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Minimizing hydraulic resistance of a plant root by shape optimization

Description

Analytical solution of the pressure field for water uptake through a composite root, coupled with fully saturated soil is derived by using the slender body approximation. It is shown that

Analytical solution of the pressure field for water uptake through a composite root, coupled with fully saturated soil is derived by using the slender body approximation. It is shown that in general, the resistance of the root and soil are not additive. This result can play a very important role in modelling water uptake through plant roots and determination of hydraulic resistances of plant roots. Optimum plant root structure that minimizes a single root’s hydraulic resistance is also studied in this work with the constraint of prescribed root volume. Hydraulic resistances under the slender body approximation and without such a limitation are considered. It is found that for large stele-to-cortex permeability ratio, there exists an optimum root length-to-base-radius ratio that minimizes the hydraulic resistance. A remarkable feature of the optimum root structure is that the optimum dimensionless stele conductivity depends only on a single geometrical parameter, the stele-to-root base-radius ratio. Once the stele-to-root base-radius ratio and the stele-to-cortex permeability ratio are given, the optimum root length-to-radius ratio can be found. While these findings remain to be verified by experiments for real plant roots, they offer theoretical guidance for the design of bio-inspired structures that minimizes hydraulic resistance for fluid production from porous media.

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Date Created
  • 2016

Parametric Forcing of Confined and Stratified Flows

Description

A continuously and stably stratified fluid contained in a square cavity subjected to harmonic body forcing is studied numerically by solving the Navier-Stokes equations under the Boussinesq approximation. Complex dynamics

A continuously and stably stratified fluid contained in a square cavity subjected to harmonic body forcing is studied numerically by solving the Navier-Stokes equations under the Boussinesq approximation. Complex dynamics are observed near the onset of instability of the basic state, which is a flow configuration that is always an exact analytical solution of the governing equations. The instability of the basic state to perturbations is first studied with linear stability analysis (Floquet analysis), revealing a multitude of intersecting synchronous and subharmonic resonance tongues in parameter space. A modal reduction method for determining the locus of basic state instability is also shown, greatly simplifying the computational overhead normally required by a Floquet study. Then, a study of the nonlinear governing equations determines the criticality of the basic state's instability, and ultimately characterizes the dynamics of the lowest order spatial mode by the three discovered codimension-two bifurcation points within the resonance tongue. The rich dynamics include a homoclinic doubling cascade that resembles the logistic map and a multitude of gluing bifurcations.

The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation.

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Date Created
  • 2019

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Micro-particle streak velocimetry: theory, simulation methods and applications

Description

This dissertation describes a novel, low cost strategy of using particle streak (track) images for accurate micro-channel velocity field mapping. It is shown that 2-dimensional, 2-component fields can be efficiently

This dissertation describes a novel, low cost strategy of using particle streak (track) images for accurate micro-channel velocity field mapping. It is shown that 2-dimensional, 2-component fields can be efficiently obtained using the spatial variation of particle track lengths in micro-channels. The velocity field is a critical performance feature of many microfluidic devices. Since it is often the case that un-modeled micro-scale physics frustrates principled design methodologies, particle based velocity field estimation is an essential design and validation tool. Current technologies that achieve this goal use particle constellation correlation strategies and rely heavily on costly, high-speed imaging hardware. The proposed image/ video processing based method achieves comparable accuracy for fraction of the cost. In the context of micro-channel velocimetry, the usability of particle streaks has been poorly studied so far. Their use has remained restricted mostly to bulk flow measurements and occasional ad-hoc uses in microfluidics. A second look at the usability of particle streak lengths in this work reveals that they can be efficiently used, after approximately 15 years from their first use for micro-channel velocimetry. Particle tracks in steady, smooth microfluidic flows is mathematically modeled and a framework for using experimentally observed particle track lengths for local velocity field estimation is introduced here, followed by algorithm implementation and quantitative verification. Further, experimental considerations and image processing techniques that can facilitate the proposed methods are also discussed in this dissertation. Unavailability of benchmarked particle track image data motivated the implementation of a simulation framework with the capability to generate exposure time controlled particle track image sequence for velocity vector fields. This dissertation also describes this work and shows that arbitrary velocity fields designed in computational fluid dynamics software tools can be used to obtain such images. Apart from aiding gold-standard data generation, such images would find use for quick microfluidic flow field visualization and help improve device designs.

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Date Created
  • 2011