Dissertations / Theses on the topic 'Mixing – Mathematical models'

The onset of summer stratification in temperate lakes and reservoirs forces a decoupling of the hypolimnion from the epilimnion that is sustained by strong density gradients in the metalimnion. These strong gradients act as a barrier to the vertical transport of mass and scalars leading to bottom anoxia and subsequent nutrient release from the sediments. The stratification is intermittently overcome by turbulent mixing events that redistribute mass, heat, dissolved parameters and particulates in the vertical. The redistribution of ecological parameters then exerts some control over the ecological response of the lake. This dissertation is focused on the physics of deep vertical mixing that occurs beneath the well-mixed surface layer in stratified lakes and reservoirs. The overall aim is to improve the ability of numerical models to reproduce deep vertical mixing, thus providing better tools for water quality prediction and management. In the first part of this research the framework of a one-dimensional mixed-layer hydrodynamic model was used to construct a pseudo two-dimensional model that computes vertical fluxes generated by deep mixing processes. The parameterisations developed for the model were based on the relationship found between lake-wide vertical buoyancy flux and the first-order internal wave response of the lake to surface wind forcing. The ability of the model to reproduce the observed thermal structure in a range of lakes and reservoirs was greatly improved by incorporating an explicit turbulent benthic boundary layer routine. Although laterally-integrated models reproduce the net effect of turbulent mixing in a vertical sense, they fail to resolve the transient distribution of turbulent mixing events triggered by local flow properties defined at far smaller scales. Importantly, the distribution of events may promote tertiary motions and ecological niches. In the second part of the study a large body of microstructure data collected in Lake Kinneret, Israel, was used to show that the nature of turbulent mixing events varied considerably between the epilimnion, metalimnion, hypolimnion and benthic boundary layer, yet the turbulent scales of the events and the buoyancy flux they produced collapsed into functions of the local gradient Richardson number. It was found that the most intense events in the metalimnion were triggered by high-frequency waves generated near the surface that grew and imparted a strain on the metalimnion density field, which led to secondary instabilities with low gradient Richardson numbers. The microstructure observations suggest that the local gradient Richardson number could be used to parameterise vertical mixing in coarse-grid numerical models of lakes and reservoirs. However, any effort to incorporate such parameterisations becomes meaningless without measures to reduce numerical diffusion, which often dominates over parameterised physical mixing. As a third part of the research, an explicit filtering tool was developed to negate numerical diffusion in a threedimensional hydrodynamic model. The adaptive filter ensured that temperature gradients in the metalimnion remained within bounds of the measured values and so the computation preserved the spectrum of internal wave motions that trigger diapycnal mixing events in the deeper reaches of a lake. The results showed that the ratio of physical to numerical diffusion is dictated by the character of the dominant internal wave motions.

Sediment-laden turbulent buoyant jets are commonly encountered in the natural and man-made environments. Examples of sediment-laden buoyant jets include volcanic eruptions, deep ocean hydrothermal vents (“black smokers”), ocean dumping of dredged spoils and sludge, and submarine discharge of wastewater effluent. It is important to understand the fluid mechanics of sediment jets for environmental impact assessment, and yet there is currently no general model for predicting the mixing of sediment-laden jets. This study reports a theoretical and experimental investigation the sediment mixing, fall-out and deposition from sediment-laden buoyant jets. It is well known that turbulence generates fluctuations to the particle motion, modulating the particle settling velocity. A general three-dimensional (3D) stochastic particle tracking model is developed to predict the particle settling out and deposition from a sediment-laden jet. Particle velocity fluctuations are modelled by a Lagrangian velocity autocorrelation function that accounts for the loitering and trapping of sediment particles in turbulent eddies which results in the reduction of settling velocity. The model is validated against results of independent experimental studies. Consistent with basic experiments using grid-generated turbulence, the model predicts that the apparent settling velocity can be reduced by as much as 30% of the stillwater settling velocity. The mixing and deposition of sediment-laden horizontal momentum jets are studied using laboratory experiments and 3D computational fluid dynamics (CFD) modelling. It is shown that there is a significant settling velocity reduction up to about 25-35%, dependent on jet turbulent fluctuations and particle properties. The CFD approach necessitates an ad hoc adjustment/reduction on settling velocity and lacks generality. Using classical solutions of mean velocity, and turbulent fluctuation and dissipation rate profiles derived from CFD solutions, 3D particle tracking model predictions of sediment deposition and concentration profiles are in excellent agreement with measured data over a wide range of jet flow and particle properties. Unlike CFD calculations, the present method does not require any a priori adjustment of particle settling velocity. A general particle tracking model for predicting sediment fall-out and deposition from an arbitrarily inclined buoyant jets in stagnant ambient is successfully developed. The model incorporates the three flow regimes affecting the sediment dynamics in a buoyant jet, namely turbulent jet flow, jet entrainment-induced external flow and surface spreading current. The jet mean flow velocity is determined using a well-validated jet integral model. The external jet-induced irrotational flow field is computed by a distribution of point sinks along the jet trajectory. The surface spreading current is predicted using an integral model accounting for the interfacial shear. The model is validated against experimental data of sediment deposition from vertical and horizontal sediment-laden buoyant jets.
published_or_final_version
Civil Engineering
Doctoral
Doctor of Philosophy

In Chapter 1, we study the effects of behavioral changes in a smallpox attack model. Response strategies to a smallpox bioterrorist attack have focused on interventions such as isolation, contact tracing, quarantine, ring vaccination, and mass vaccination. We formulate and analyze a mathematical model in which some individuals lower their daily contact activity rates once an epidemic has been identified in a community. We use computer simulations to analyze the effects of behavior change alone and in combination with other control measures. We demonstrate that the spread of the disease is highly sensitive to how rapidly people reduce their contact activity. In Chapter 2, we study mixing patterns between age groups using social networks. The course of an epidemic through a population is determined by the interactions among individuals. To capture these elements of reality, we use the contact network simulations for the city of Portland, Oregon that were developed as part of the TRANSIMS/EpiSims project to study and identify mixing patterns. We analyze contact patterns between different age groups and identify those groups who are at higher risk of infection. We describe a new method for estimating transmission matrices that describe the mixing and the probability of transmission between the age groups. We use this matrix in a simple differential equation model for the spread of smallpox. Our differential equation model shows that the epidemic size of a smallpox outbreak could be greatly affected by the level of residual immunity in the population. In Chapter 3, we study the effects of mixing patterns in the presence of population heterogeneity. We investigate the impact that different mixing assumptions have on the spread of a disease in an age-structured differential equation model. We use realistic, semi-bias and bias mixing matrices and investigate the impact that these mixing patterns have on epidemic outcomes when compared to random mixing. Furthermore, we investigate the impact of population heterogeneity such as differences in susceptibility and infectivity within the population for a smallpox epidemic outbreak. We find that different mixing assumptions lead to differences in disease prevalence and final epidemic size.

The turbulent mixing process between two liquid streams in a standard tank stirred by a Rushton turbine has been studied. Experimental measurements of concentration and segregation (fluctuating concentration) have been made for both reacting and non-reacting flows. For the non-reacting case, one stream was marked with a fluorescent dye; the local concentration was measured using a fluorescence technique and a bifurcated fiber optic probe of custom design. Measurements were taken at two axial-radial planes within the tank. In the reacting case, the second-order reaction between sodium hydroxide and hydrochloric acid was studied, and urinine acted as a fluorescent indicator which became non-fluorescent as the reaction proceeded. Numerical studies of the mixing in the laboratory-scale vessel were made. FLUENT, a general-purpose fluid flow modelling program, was used to simulate the flow within the tank. This program uses a k-epsilon closure of the turbulent momentum equations. The program was modified to allow the inclusion of a segregation balance equation. Using this segregation balance technique, the turbulent species balance equations were solved. The results of these simulations agreed with the experimental measurements in all regions except the region near the entrance jets, where the model could not adequately predict the fluid behavior. This study has successfully predicted the behavior of reacting fluids in a bench-scale turbulently mixed stirred tank by the implementation of a segregation balance throughout the entire domain.

Thesis (Ph. D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, and the Woods Hole Oceanographic Institution), 2003.
Includes bibliographical references (p. 145-148).
Oceanic observations indicate that abyssal mixing is localized in regions of rough topography. How locally mixed fluid interacts with the ambient fluid is an open question. Laboratory experiments explore the interaction of mechanically induced boundary mixing and an interior body of linearly stratified rotating fluid. Turbulence is generated by a vertically oscillating horizontal bar, located at middepth along the tank wall. The turbulence forms a region of mixed fluid which quickly reaches a steady state height and collapses into the interior. The mixed layer thickness ... is independent of the Coriolis frequency f. N is the buoyancy frequency, co is the bar frequency, and the constant, Y=1 cm, is empirically determined by bar mechanics. In initial experiments, the bar is exposed on three sides. Mixed fluid intrudes directly into the interior as a radial front of uniform height, rather than as a boundary current. Mixed fluid volume grows linearly with time ... The circulation patterns suggest a model of unmixed fluid being laterally entrained with velocity, e Nhm, into the sides of a turbulent zone with height hm and width Lf ... where Lf is an equilibrium scale associated with rotational control of bar-generated turbulence. In accord with the model, outflux is constant, independent of stratification and restricted by rotation ... Later experiments investigate the role of lateral entrainment by confining the sides of the mixing bar between two walls, forming a channel open to the basin at one end. A small percentage of exported fluid enters a boundary current, but the bulk forms a cyclonic circulation in front of the bar. As the recirculation region expands to fill the channel, it restricts horizontal entrainment into the turbulent zone. The flux of mixed fluid decays with time.
(cont.) ... The production of mixed fluid depends on the size of the mixing zone as well as on the balance between turbulence, rotation and stratification. As horizontal entrainment is shut down, longterm production of mixed fluid may be determined through much weaker vertical entrainment. Ultimately, the export of mixed fluid from the channel is restricted to the weak boundary current.
by Judith R. Wells.
Ph.D.

In this thesis, a theoretical investigation is undertaken into fluid and mixing flows generated by various geometries for Newtonian and non-Newtonian fluids, on both sequential and parallel computer systems. The thesis begins by giving the necessary background to the mixing process and a summary of the fundamental characteristics of parallel architecture machines. This is followed by a literature review which covers accomplished work in mixing flows, numerical methods employed to simulate fluid mechanics problems and also a review of relevant parallel algorithms. Next, an overview is given of the numerical methods that have been reviewed, discussing the advantages and disadvantages of the different methods. In the first section of the work the implementation of the primitive variable finite element method to solve a simple two dimensional fluid flow problem is studied. For the same geometry colour band mixing is also investigated. Further investigational work is undertaken into the flows generated by various rotors for both Newtonian and non-Newtonian fluids. An extended version of the primitive variable formulation is employed, colour band mixing is also carried out on two of these geometries. The latter work is carried out on a parallel architecture machine. The design specifications of a parallel algorithm for a MIMD system are discussed, with particular emphasis placed on frontal and multifrontal methods. This is followed by an explanation of the implementation of the proposed parallel algorithm, applied to the same fluid flow problems as considered earlier and a discussion of the efficiency of the system is given. Finally, a discussion of the conclusions of the entire accomplished work is presented. A number of suggestions for future work are also given. Three published papers relating to the work carried out on the transputer networks are included in the appendices.

A numerical model has been developed which simulates the three-dimensional stability and transition of a periodically forced free shear layer in an incompressible fluid. Unlike previous simulations of temporally evolving shear layers, the current simulations examine spatial stability. The spatial model accommodates features of free shear flow, observed in experiments, which in the temporal model are precluded by the assumption of streamwise periodicity; e.g., divergence of the mean flow and wave dispersion. The Navier-Stokes equations in vorticity-velocity form are integrated using a combination of numerical methods tailored to the physical problem. A spectral method is adopted in the spanwise dimension in which the flow variables, assumed to be periodic, are approximated by finite Fourier series. In complex Fourier space, the governing equations are spatially two-dimensional. Standard central finite differences are exploited in the remaining two spatial dimensions. For computational efficiency, time evolution is accomplished by a combination of implicit and explicit methods. Linear diffusion terms are advanced by an Alternating Direction Implicit/Crank-Nicolson scheme whereas the Adams-Bashforth method is applied to convection terms. Nonlinear terms are evaluated at each new time level by the pseudospectral (collocation) method. Solutions to the velocity equations, which are elliptic, are obtained iteratively by approximate factorization. The spatial model requires that inflow-outflow boundary conditions be prescribed. Inflow conditions are derived from a similarity solution for the mean inflow profile onto which periodic forcing is superimposed. Forcing functions are derived from inviscid linear stability theory. A numerical test case is selected which closely parallels a well-known physical experiment. Many of the aspects of forced shear layer behavior observed in the physical experiment are captured by the spatial simulation. These include initial linear growth of the fundamental, vorticity roll-up, fundamental saturation, eventual domination of the subharmonic, vortex pairing, emergence of streamwise vorticity, and temporary stabilization of the secondary instability. Moreover, the spatial simulation predicts the experimentally observed superlinear growth of harmonics at rates 1.5 times that of the fundamental. Superlinear growth rates suggest nonlinear resonances between fundamental and harmonic modes which are not captured by temporal simulations.

The influence of climate and antecedent moisture conditions on hydrological and biogeochemical fluxes was studied and contrasted in three nested, high-elevation, snowmelt-dominated catchments in the Sierra Nevada, California and one basin-floor, semi-arid catchment in southeastern Arizona. Investigations were completed within a different two-year period at each site, with the second year being climatically different (typically drier) than the first. Spring snowmelt, widespread winter frontal precipitation, and episodic summer rains induce surface water flow in these catchments, though the timing and magnitude of nutrient redistribution among soil and stream compartments varies in each. Surface water flow from spring snowmelt in high-elevation catchments travels through the subsurface or across the surface as direct runoff A more typical process producing surface water flow in semi-arid catchments is flooding during episodic or widespread rainfall. Hydrograph separations at Emerald Lake, Topaz Lake and Marble Fork catchments in Sequoia National Park, California, revealed that the majority of snowmelt flowed through soil before entering the stream in both average and highsnow years. The Emerald Lake watershed had a higher fraction of old water in its outflow in the average accumulation year because of the previous year's high accumulation and longer melt season. A mixing model analysis performed of the upper San Pedro River, Arizona, for wet and dry years showed that summer flood hydrographs were composed mainly of precipitation and surface runoff in both years, though a higher soil-water input occurred in the wetter year and in early season floods in the dry year. Stream and soil water nitrate concentrations were higher during floods in the dry year. Early season floods in the dry year exhibited more variability in stream water nitrate and sulfate, whereas late season flood concentrations reflected a well-mixed system and therefore less variation of these species during flood hydrographs. These data showed that periods of below average precipitation preceding major runoff periods result both in less soil water and solute export during summer floods in basin-floor catchments and less direct snowmelt in high-elevation catchments. Hydrologic and solute export in each catchment, despite their differing geographical locations, responds in similar ways to climate variability.

[Truncated abstract] Mine lakes are a water body created after an open-cut mine ceases operating. The lakes develop in the former mine-pit due to the combination of groundwater inflow, surface run-off and, in some cases, due to rapid filling from river diversion. While potentially valuable water resources, these lakes often have poor water quality and managing the water body is an important part of the overall process of mine site rehabilitation. As mine lakes form in man-made pits, they have a bathymetry that is typically quite distinct from natural lakes and this can, in turn, strongly influence the hydrodynamics and hence the water quality of the water body. Despite the potential importance of these water bodies, there have been very few studies on the hydrodynamics of mine lakes. This study describes a field investigation of the hydrodynamics of a former coal mine lake, Lake Kepwari, in south-western Western Australia. In particular, this study examines the hydrodynamic processes in both the surface mixing layers and the internal mixing in the density stratified lake. Wind sheltering in the surface mixing layer occurs due to the presence of the steep walls and lake embankments. A week long field experiment was conducted in December 2003 using a combination of moored thermistor chains with meteorological stations and the deployment of rapid vertical profiling turbulent microstructure instruments and CTD drops from two boats operating on the lake. ... Simulations indicated that inclusion of a site specific sheltering effect, based on the results of the field campaign, significantly improved the models‘ performance in capturing the surface mixed layer deepening associated with episodic strong wind events that occur on the lake. Considerable internal mixing was indicated by the high dissipation rates observed, particularly near the boundaries. Large basin-wide diffusivities were also calculated from the heat budget method over long periods, showed a consistency with time, and were slightly higher in summer than during the Autumn Winter period. Although light, there are persistent winds over the lake and yet little basin-scale internal wave activity or seiching. It is hypothesized that any seiching motion was rapidly damped by strong mixing over the hydraulically rough bathymetry bathymetry created by the remnant benches from the open cut mining operation itself. This boundary mixing, in turn, drives secondary relaxation currents that transport mixed fluid from the boundaries to the interior, resulting in high effective basin-wide diffusivities. A simple boundary mixing model is proposed to describe this process.

This thesis aims to improve the understanding of transport and critical layer mixing in the troposphere and stratosphere. A dynamical approach is taken based on potential vorticity which has long been recognised as the essential field inducing the flow and thermodynamic structure of the atmosphere. Within the dynamical framework of critical layer mixing of potential vorticity, three main topics are addressed. First, an idealised model of critical layer mixing in the stratospheric surf zone is examined. The effect of the shear across the critical layer on the critical layer evolution itself is investigated. In particular it is found that at small shear barotropic instability occurs and the mixing efficiency of the critical layer increases due to the instability. The effect of finite deformation length is also considered which extends previous work. Secondly, the dynamical coupling between the stratosphere and troposphere is examined by considering the effect of direct perturbations to stratospheric potential vorticity on the evolution of midlatitude baroclinic instability. Both zonally symmetric and asymmetric perturbations to the stratospheric potential vorticity are considered, the former representative of a strong polar vortex, the latter representative of the stratospheric state following a major sudden warming. A comparison of these perturbations gives some insight into the possible influence of pre or post-sudden warming conditions on the tropospheric evolution. Finally, the influence of the stratospheric potential vorticity distribution on lateral mixing and transport into and out of the tropical pipe, the low latitude ascending branch of the Brewer-Dobson circulation, is investigated. The stratospheric potential vorticity distribution in the tropical stratosphere is found to have a clear pattern according to the phase of the quasi-biennial oscillation (QBO). The extent of the QBO influence is quantified, by analysing trajectories of Lagrangian particles using an online trajectory code recently implemented in the Met Office's Unified Model.

Thesis (Ph. D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution), 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 187-195).
Large-scale thermal forcing and freshwater fluxes play an essential role in setting temperature and salinity in the ocean. A number of recent estimates of the global oceanic freshwater balance as well as the global oceanic surface net heat flux are used to investigate the effects of heat- and freshwater forcing at the ocean surface. Such forcing induces changes in both density and density-compensated temperature and salinity changes ('spice'). The ratio of the relative contributions of haline and thermal forcing in the mixed layer is maintained by large-scale surface fluxes, leading to important consequences for mixing in the ocean interior. In a stratified ocean, mixing processes can be either along lines of constant density (isopycnal) or across those lines (diapycnal). The contribution of these processes to the total mixing rate in the ocean can be estimated from the large-scale forcing by evaluating the production of thermal variance, salinity variance and temperature-salinity covariance. Here, I use new estimates of surface fluxes to evaluate these terms and combine them to generate estimates of the production of density and spice variance under the assumption of a linear equation of state. As a consequence, it is possible to estimate the relative importance of isopycnal and diapycnal mixing in the ocean. While isopycnal and diapycnal processes occur on very different length scales, I find that the surface-driven production of density and spice variance requires an approximate equipartition between isopycnal and diapycnal mixing in the ocean interior. In addition, consideration of the full nonlinear equation of state reveals that surface fluxes require an apparent buoyancy gain (expansion) of the ocean, which allows an estimate of the amount of contraction on mixing due to cabbeling in the ocean interior.
by Julian J. Schanze.
Ph.D.

Halogen-driven ozone and nonmethane hydrocarbon losses in springtime Arctic boundary layer are investigated using a regional chemical transport model (CTM). Surface observation of O3 at Alert and Barrow and aircraft observations of O3 and hydrocarbons during the TOPSE experiment from February to May in 2000 are analyzed. We prescribe halogen radical distributions based on GOME BrO observations and calculated or observed other halogen radical to BrO ratios. GOME BrO shows an apparent anti-correlation with surface temperature over high BrO regions. At its peak, area of simulated near-surface O3 depletions (O3 LT 20ppbv) covers GT 50% of the north high latitudes. Model simulated O3 losses are in agreement with surface and aircraft O3 observations. Simulation of halogen distributions are constrained using aircraft hydrocarbon measurements. We find the currently chemical mechanism overestimate the Cl/BrO ratios. The model can reproduce the observed halogen loss of NMHCs using the empirical Cl/BrO ratios. We find that the hydrocarbon loss is not as sensitive to the prescribed boundary layer height of halogen as that of O3, therefore producing a more robust measure for evaluating satellite column measurement. Tropospheric tracer transport and chemical oxidation processes are examined on the basis of the observations at northern mid-high latitudes and over the tropical Pacific and the corresponding global 3D CTM (GEOS-CHEM) simulations. The correlation between propane and ethane/propane ratio is employed using a finite mixing model to examine the mixing in addition to the OH oxidations. At northern mid-high latitudes the model agrees with the observations before March. The model appears to overestimate the transport from lower to middle latitudes and the horizontal transport and mixing at high latitudes in May. Over the tropical Pacific the model reproduces the observed two-branch slope values reflecting an underestimate of continental convective transport at northern mid-latitudes and an overestimate of latitudinal transport into the tropics. Inverse modeling using the subsets of observed and simulated data is more reliable by reducing (systematic) biases introduced by systematic model transport model transport errors. On the basis of this subset we find the model underestimates the emissions of ethane and propane by 14 5%.

The purpose of this study is to develop mathematical models to explore the mixing and its related phenomena in converter bath. Specifically, first, a mathematical model of a physical model converter, which was scaled down to 1/6th of a 30 t vessel, was developed in this study. A number of parameters were studied and their effects on the mixing time were recorded in a top blown converter. Second, a mathematical model for a combined top-bottom blown was built to investigate the optimization process. Then, a side tuyere was introduced in the combined top-bottom blown converter and its effects on the mixing and wall shear stress were studied. Moreover, based on the above results, the kinetic energy transfer phenomena in a real converter were investigated by applying the mathematical models. A simplified model, in which the calculation region was reduced to save calculation compared to simulations of the whole region of the converter, was used in the mathematical simulation. In addition, this method was also used in the simulation of real converters. This approach makes it possible to simulate the Laval nozzle flow jet and the cavity separately when using different turbulence models. In the top blown converter model, a comparison between the physical model and the mathematical model showed a good relative difference of 2.5% and 6.1% for the cavity depth and radius, respectively. In addition, the predicted mixing time showed a good relative difference of 2.8% in comparison to the experimental data. In an optimization of a combined top-bottom blown converter, a new bottom tuyere scheme with an asymmetrical configuration was found to be one of the best cases with respect to a decreased mixing time in the bath. An industrial investigation showed that the application effects of the new tuyere scheme yield a better stirring condition in the bath compared to the original case. Furthermore, the results indicated that the mixing time for a combined top-bottom-side blown converter was decreased profoundly compared to a conventional combined top-bottom blown converter. It was found that the side wall shear stress is increased by introducing side blowing, especially in the region near the side blowing plume. For a 100 t converter in real, the fundamental aspects of kinetic energy transfer from a top and bottom gas to the bath were explored. The analyses revealed that the energy transfer is less efficient when the top lance height is lowered or the flowrate is increased in the top blowing operations. However, an inverse trend was found. Namely, that the kinetic energy transfer is increased when the bottom flowrate is increased in the current bottom blowing operations. In addition, the slag on top of the bath is found to dissipate 6.6%, 9.4% and 11.2% for the slag masses 5, 9 and 15 t compared to the case without slag on top of the surface of the bath, respectively.

QC 20151015

Field measurements and numerical modelling of the shallow coastal waters offshore in south-western Australia were used to describe changes in the water column's vertical structure and the biological response on temporal scales of the order of hours and days. A cycle of chlorophyll a concentration, primary production, and photosystem II function on a diel timescale, which was related to changes in the solar irradiance and thermal structure, was identified. The diel cycle included (1) vertically well-mixed (or weakly linear) conditions in density and chlorophyll a early in the morning, resulting from vertical mixing through penetrative overnight convection; (2) depleted chlorophyll a concentration in the surface layer during the middle of the day due to photoinhibition; (3) an increased chlorophyll a concentration in the bottom layer by late afternoon due to optimum light conditions; and (4) the formation of a chlorophyll a break point (CBP) at the thermocline, which migrated downwards with the deepening surface mixed layer. On a longer timescale (days), moored acoustic instruments were used to derive echo level (EL), which approximated suspended particulate matter (SPM). Wind events ultimately controlled SPM, a conclusion based on (1) elevated EL during high windgenerated turbulence and bed shear stress, (2) positive time-lagged correlations between wind speed and EL at three field sites with different exposures to wave action, and (3) significant negative correlations between wind speed and depth-differentiated echo level (d(EL)/dz) at all sites. Sea breezes produced a similar response in EL through the water column to a small storm event, and wind-driven SPM resuspension resulted in a reduction in the sub-surface light climate (kd). Near-bed dissolved oxygen concentrations varied in accord with elevated wind speeds, EL and kd, highlighting a possible suppression of photosynthesis. One-dimensional modelling revealed that wind stirring was most often the dominant process in these waters. It was found that for a brief period during thermal stratification there was shear production of turbulent instabilities that migrated from the thermocline to the surface and the seabed. Convective cooling was not able to mix the water column entirely overnight without the addition of wind, and minimum wind speeds were determined for this complete vertical mixing. Bottom-generated turbulence was limited to a small region above the bed, and was deemed insignificant compared with mixing generated at the surface. Minimum wind speeds required for de-stratification and prevention of stratification were determined for summer, autumn and winter. A hypothetical desalination outfall was simulated for all seasons and it was concluded that positioning of the discharge at middepth was preferable compared to at the seabed. The results of this thesis advance the current knowledge of coastal biophysical oceanography and provide new insights into the temporal dynamics of the coastal water column of south-western Australia.

La Self-Mixing Interférométrie (SMI) a été étudiée de manière approfondie au cours des cinq dernières décennies dans diverses applications. Les capteurs selon la technique SMI ont la diode laser comme la source de lumière, l'interféromètre et le détecteur. La lumière de la diode laser se propage vers une cible éloignée où elle est partiellement réfléchie ou rétrodiffusée avant d'être réinjectée dans la cavité active du laser. Lorsque la diode laser subit le retour optique externe, la lumière réfléchie imprimée avec des informations provenant de la cible éloignée ou du milieu de cavité externe induit une perturbation des paramètres de fonctionnement du laser. Pour les capteurs de mesure SMI tels que les applications de mouvement harmonique et de distance absolue, la méthode de comptage des franges est essentiellement utilisée pour déterminer respectivement le déplacement et la distance de la cible. La modélisation du phénomène SMI a été développée. L'équation unique qui décrit la condition de phase imposée par la rétro-injection optique est généralement appelée équation de phase. L'un des paramètres les plus importants cet équation est le paramètre C. Quand le C 1, le comportement du laser est stable. En revanche, quand le C > 1, des phénomènes plus complexes sont observés tels que l'effet d'hystérésis, la présence de multiples fréquences d'émission, la séparation de la ligne d'émission de fréquence causer la saut de mode et le phénomène de disparition des franges. Une approche bien acceptée dans la communauté décrit les régimes de SMI en fonction de la valeur du C de sorte que : le régime faible (0.1 < C < 1), le régime modéré (1 < C < 4.6) et le régime fort (C > 4,6). Le paramètre de rétro-injection C est directement impliqué dans le phénomène de disparition des franges. Bernal et al. a décrit que ce phénomène dépend de la régime qui décrits ci-dessus, c'està-dire que les franges commencent à disparaître uniquement dans le régime forte de la rétroinjection d’optique, tandis que Yu et al. a démontré que le nombre des franges est divisée par 2 dans la région 2 (7,8 < C < 14,0), 3 dans la région 3 (14,0 < C < 20,3) et ainsi de suite. Autres publications a proposé que deux paires de franges interférométriques pour une période complète de modulation disparaissent quand il y a une variation de C de 2. Cependant, à notre connaissance, aucune explication ou théorie précise sur le mécanisme de ce phénomène n'a été publiée jusqu'à présent. Dans cette thèse, nous rapportons l'observation de la disparition des franges dans le schéma de mesure de distance absolue. Par rapport au schéma de détection des vibrations, l'approche de la distance absolue garantit un paramètre de rétro-injection C stable permettant ainsi des conditions expérimentales plus répétables. Comme la cible est fixée à une certaine distance, l'amplitude de la lumière rétrodiffusée est facile à contrôler en utilisant des atténuateurs d’optiques variables. Les résultats expérimentaux montrent que le nombre de franges interférométriques continue de diminuer dans le signal SMI lorsque l'amplitude du coefficient de réflexion de la cible augmente
Self-mixing Interferometry has been studied extensively in the last five decades in various sensing applications. Sensors under the SMI technique have the laser diode as the light source, the interferometer, and the detector. The light from the laser diode propagates towards a distant target where it is partially reflected or back-scattered before being re-injected into the active cavity of the laser. When the laser diode experiences the external optical feedback, the reflected light imprinted with information from the distant target or from the external cavity medium induces perturbation to the operating parameters of the laser. For SMI measurement sensors such as harmonic motion and absolute distance applications, the fringe counting method is basically used to determine the target's displacement and distance respectively. Two different approaches to modelling the SMI phenomenon have been developed: the three-mirror cavity and the perturbation of the rate equation. The single equation that describes the phase condition imposed by the optical feedback is usually referred to as the excess phase equation. One of the most important and most useful parameters in the excess phase equation is the feedback parameter C as it can be used to qualitatively categorize the regime of the laser under optical feedback. When the feedback level C < 1, the laser behaviour is stable. On the other hand, when the feedback level C > 1, more complex phenomena are observed such as hysteresis effect, presence of multiple emission frequencies (including the unstable frequencies), apparent splitting of the emission line due to mode hopping and fringe disappearance phenomenon. The fringes disappearance phenomenon in the self-mixing interferometry occurs whenever the external round-trip phase at free-running state is modulated by either external modulation such as external cavity length changes or internal modulation when the laser injection current is modulated with a high back-scattered light power. This phenomenon has been observed by many authors for harmonic motion or vibration application and more recently in the case of the absolute distance measurement scheme when the laser injection current is modulated in the triangle waveform. This phenomenon is highly dependent on the feedback parameter C and it is described in detail based on the coupled cavity model. The primary cause for fringes disappearance is demonstrated to be the expansion of the excess phase equation stable solutions range with the increment of the parameter C, thus reducing the number of stable solutions for a given phase stimulus. This new approach in the modelling of the fringe disappearance phenomenon allows determination of the C values for which a pair of fringes are expected to disappear and as a consequence correlates the number of missing fringes to the value of C. This approach is validated both by a behavioural model of the laser under optical feedback and by a series of measurements in the SMI absolute distance configuration

The Standard Model of Elementary Particle Physics (SM) is the present theoryfor the elementary particles and their interactions and is a well-established theorywithin the physics community. The SM is a combination of Quantum Chromodynamics(QCD) and the Glashow{Weinberg{Salam (GWS) electroweak model. QCDis a theory for the strong force, whereas the GWS electroweak model is a theoryfor the weak and electromagnetic forces. This means that the SM describes allfundamental forces in Nature, except for the gravitational force. However, the SMis not a nal theory and some of its problems will be discussed in this thesis.In the rst part of this thesis, several properties of baryons are studied suchas spin structure, spin polarizations, magnetic moments, weak form factors, andnucleon quark sea isospin asymmetries, using the chiral quark model (QM). TheQM is an eective chiral eld theory developed to describe low energy phenomena of baryons, since perturbative QCD is not applicable at low energies. The resultsof the QM are in good agreement with experimental data.The second part of the thesis is devoted to the concept of quantum mechanicalneutrino oscillations. Neutrino oscillations can, however, not occur within the GWSelectroweak model. Thus, this model has to be extended in some way. All studiesincluding neutrino oscillation are done within three avor neutrino oscillationmodels. Both vacuum and matter neutrino oscillations are considered. Especially,global ts to all data of candidates for neutrino oscillations are presented and alsoan analytical formalism for matter enhanced three avor neutrino oscillations usingtime evolution operators is derived. Furthermore, investigations of matter eectswhen neutrinos traverse the Earth are included.The thesis begins with an introductory review of the QM and neutrino oscillationsand ends with the research results, which are given in the nine accompanyingscientic articles.
QC 20100616

There are numerous techniques for improving the mixing of fuel and oxidant species. However, many of these methods cannot be applied to combustion systems due to material limitations. A means of mixing the reacting species without physically invading the flow stream is therefore desired. In this work, induced electromagnetic forces known as Lorentz forces are considered as a means of enhancing the combustion of co-flowing reactant streams. To evaluate the effect of various parameters on the mixing process, a non-dimensional description is derived and used to develop a numerical model. Numerical experiments are performed based on a three level Box-Behnken design in which the dimensionless Lorentz force parameter, Reynolds number, and Euler number are varied. The Lorentz force parameter has a large effect on the mixing process. The Reynolds number has a minor effect on mixing, and the Euler number has a negligible effect. Confirmation of these results through experimental work is needed. Approaches that could be used to verify these results experimentally are outlined, and the construction and testing of a burner suitable for further experiments on Lorentz mixing is described.
Graduation date: 1997

The purpose of this research was to determine if it is feasible to apply Lorentz mixing to supersonic diffusion flames, such as those found in SCRAMjet engines. The combustion rate in supersonic diffusion flames is limited by the rate at which air and fuel mix. Lorentz mixing increases turbulence within a flow, which increases the rate at which species mix and thus increases the rate of combustion. In order to determine the feasibility of Lorentz mixing for this application, a two-dimensional model of supersonic reacting flow with the application of a Lorentz force has been examined numerically. The flow model includes the complete Navier-Stokes equations, the ideal gas law, and terms to account for diffusion of chemical species, heat release due to chemical reaction, change in species density due to chemical reaction, and the Lorentz forces applied during Lorentz mixing. In addition, the Baldwin-Lomax turbulence model is used to approximate turbulent transport properties. A FORTRAN program using the MacCormack method, a commonly used computational fluid dynamics algorithm, was used to solve the governing equations. The accuracy of the program was verified by using the program to model flows with known solutions. Results were obtained for flows with Lorentz forces applied over a series of power levels and frequencies. The results show significant increases in the rate of combustion when Lorentz mixing is applied. The amount of power required to drive Lorentz mixing is small relative to the rate at which energy is released in the chemical reaction. An optimum frequency at which to apply Lorentz mixing was also found for the flow being considered. The results of the current study show that Lorentz mixing looks promising for increasing combustion rates in supersonic reacting flows, and that future study is warranted. In particular, researchers attempting to improve combustion in SCRAMjet engines may want to consider Lorentz mixing as a way to improve combustion.
Graduation date: 1997

Lorentz forces provide a unique method for the control and mixing of gas flows without the physical intrusion of objects into the flow. Lorentz forces arise when an electric current is passed through a volume in the presence of a magnetic field. The interaction between the electric current and the electric and magnetic fields produces a body force which affects the flow. These forces have been investigated experimentally by other researchers and show promise as a way to accelerate combustion in diffusion flames by increasing the mixing rate of fuel and oxidant streams. Theoretical and numerical models were developed to gain insight into this process. Alkali metal seeding raises the electrical conductivity of a flame by two to three orders of magnitude. This has two significant effects: the Lorentz force becomes stronger for the same applied electric current and magnetic field, and the alkali seed concentration becomes a dominant factor in determining electrical conductivity of seeded gases. This makes electrical conductivity much easier to predict, and so the Lorentz body force produced is easier to determine. A theoretical basis for numerical modeling of reactive flows with variable body forces has been developed. Many issues are important in simulating gas flows. Conservation of chemical species must be carefully maintained. Mass transport by gaseous diffusion, which limits combustion rates in a diffusion flame, must be appropriately modeled. Viscous action is also important, since it promotes mixing of the fuel and oxidant streams. Convective, conductive, and diffusive transport of energy must be carefully treated since energy transport directly affects the fluid flow. A numerical model of an incompressible gas flow affected by Lorentz forces was written and tested. Although assumptions made in the model, such as isothermal conditions and uniform density, are not found in diffusion flames, the numerical model predicts velocity vector patterns similar to those observed in actual Lorentz force tests on diffusion flames. A simulation code for compressible, reactive gas flows which include Lorentz forces has also been written. Several parts of the model have been validated, and the approach used appears likely to produce successful simulations. Further validation studies will be required, however, before complete modeling of the diffusion flame can proceed.
Graduation date: 1995

A two-scale approach for the turbulent mixing of momentum in an unstable stratified boundary layer is proposed in an attempt to eliminate existing inconsistencies between parameterized mixing of heat and momentum. The parameterization of the large eddy stress is suitable for simple boundary layer models where computational efficiency is important. We test the proposed formulation in a simple boundary layer model and compare predicted momentum profiles with Lidar mean momentum profiles from FIFE 1989. We examine the sensitivity of the proposed mixing scheme to baroclinicity. While the proposed two-scale approach is able to better predict observed conditions of well mixed momentum profiles, the complexity of momentum transport in baroclinic conditions is not well approximated.
Graduation date: 1994

This thesis examines the mixing times for one-dimensional interacting particle systems. We use the coupling method to study the mixing rates for particle systems on the circle which move according to specific permutations e.g., transpositions and 3-cycles.
Graduation date: 2008

Indiana University-Purdue University Indianapolis (IUPUI)
Heat generation is a major safety concern in the design and development of Li ion batteries (LIBs) for large scale applications, such as electric vehicles. The total heat generation in LIBs includes entropic heat, enthalpy, reaction heat, and heat of mixing. The main objective of this study is to investigate the influence of heat of mixing on the LIBs and to understand whether it is necessary to consider the heat of mixing during the design and development of LIBs. In the previous research, Thomas and Newman derived methods to compute heat of mixing in LIB cells. Their results show that the heat of mixing cannot be neglected in comparison with the other heat sources at 2 C rate. In this study, the heat of mixing in different materials, porosity, particle sizes, and charging/discharging rate was investigated. A COMSOL mathematical model was built to simulate the heat generation of LIBs. The LIB model was based on Newman’s model. LiMn2O4 and LiCoO2 were applied as the cathode materials, and LiC6 was applied as the anode material. The results of heat of mixing were compared with the other heat sources to investigate the weight of heat of mixing in the total heat generation. The heat of mixing in cathode is smaller than the heat of mixing in anode, because of the diffusivity of LiCoO2 is 1 ×10-13 m2/s, which is larger than LiC6's diffusivity 2.52 × 10-14 m2/s. In the comparison, the heat of mixing is not as much as the irreversible heat and reversible heat, but it still cannot be neglected. Finally, a special situation will be discussed, which is the heat of mixing under the relaxation status. For instance, after the drivers turn off their vehicles, the entropy, ix enthalpy and reaction heat in LIBs will stop generating, but the heat will still be generated due to the release of heat of mixing. Therefore, it is meaningful to investigate to see if this process has significant influence on the safety and cycle life of LIBs.