Quartz-rich mylonites present along the Moine Thrust Zone are well suited for the application of various analytical techniques designed for investigating the flow processes by which rock deformation occurred. These analytical techniques were applied to a suite of samples from the footwall and hangingwall of the Moine thrust exposed along the Allt Pol aâ Mhadaich stream located in the northern part of the Assynt window. Vorticity analyses were performed to determine the relative contributions of pure and simple shear deformation within the penetratively deforming thrust sheets. Integration of vorticity data with 3D strain analyses demonstrated that sub-vertical shortening perpendicular to the flow plane, accompanied by thrust transport parallel extension, occurred during mylonitization, and was driven by emplacement of the overlying Moine nappe. Quartz c-axis fabrics in the mylonites are characterized by well-defined asymmetric Type-1 cross girdles in which internal and external skeletal asymmetries are indicative of a top-to-the-WNW shear sense, compatible with regional thrusting. These c-axis fabrics were also used to estimate deformation temperatures. Differential flow stresses associated with mylonitization were estimated from the grain size of dynamically recrystallized quartz. Deformation temperature and flow stress data were then incorporated into a dislocation creep flow law for quartz to estimate strain rates. Finally, along strike variation in these flow properties at the base of the Moine nappe to the north and south of the APM section were investigated and results from the APM section compared with previously published studies of mylonites exposed in eastern Assynt that occupy similar structural positions. / Master of Science

Detailed measurements were taken downstream of several modified trailing edge configurations designed to impart streamwise velocity into the flow behind a cascade of GE Rotor B fan blades. These measurements were conducted in the Virginia Tech Low Speed Linear Cascade wind tunnel. The trailing edge configurations tested utilized passive techniques for producing streamwise vorticity, which in turn causes downstream wake diffusion and increased mixing. A more diffuse wake, when it impinges on the downstream stator, will produce lower noise levels as a result of this rotor-stator interaction. Furthermore, increased mixing in the flow will reduce the levels of turbulence kinetic energy observed downstream of the blade trailing edge. Thus, this project seeks to identify which passive techniques of imparting streamwise vorticity are most effective at improving the flow characteristics responsible for some of the noise production in modern jet aircraft. The three trailing edge configurations tested in detail for this project showed significant ability to widen and stretch the downstream wake by utilizing vorticity generation techniques. The TE-8 configuration was the most effective at increasing the wake width downstream of the trailing edge. Additionally, each configuration was able to successfully reduce some of the turbulence kinetic energy levels observed downstream when compared to the baseline blade, the most effective configuration being TE-8. Finally, the momentum thickness of each configuration was measured. When compared to the baseline, the TE-1 configuration showed an increased momentum thickness, TE-8 showed little change, and TE-7 actually showed an improved momentum thickness value. / Master of Science

In J.D. Jackson's Classical Electrodynamics textbook, the analysis of Dirac's charge quantization condition in the presence of a magnetic monopole has a mathematical omission and an all-too-brief physical argument that might mislead some students. This paper presents a detailed derivation of Jackson's main result, explains the significance of the missing term, and highlights the close connection between Jackson's findings and Dirac's original argument. (C) 2016 Sharif University of Technology. All rights reserved.

The thesis addresses the influence of compressible effects on the stability of deflagration waves. Due to the quasi-isobaric nature of slow flames, compressible effects in laminar flames are usually neglected. Nevertheless, turbulent deflagrations may propagate at substantially higher speeds, suggesting that compressible effects may play a role in their dynamics. In the present thesis, the stability of diffusion-dominated high-speed deflagrations is addressed. The deflagration is studied in the thickened regime, hence addressing the long wavelength limit of these deflagrations. The deflagrations are modelled by the compressible reactive Navier-Stokes equations with a single-step Arrhenius reaction model. The 2D stability of the steady traveling-wave solution is studied by direct simulation. It is found that, as the flame compressibility becomes significant, not only does the growth rates of the cellular profile of the deflagration waves increase, but the traditional correlation of the burning velocity and the flame surface area become far less strong. Significant compression regions form in front of the nonlinear flames. These compression regions have been found to increase the growth rates by increasing the temperature of the unburned gas in front of the flames, as well as convecting the flame forward. The results show that the flame propagation velocity in references to the unburned gas was significantly faster than the burning velocity. The vorticity was given consideration, as the compressibility of flame increase one can expect the baroclinic source to be of greater significance. The vorticity was show to, in effect, increase as compressibility increases while unexpectedly having a stabilizing direction of rotation on the cellular structure of the flames.

Os ciclones secundários são sistemas que ainda não são bem definidos e, assim, são fenômenos de difícil previsibilidade, necessitando de mais estudos para identificar os sinais que disparam seu desenvolvimento. Neste estudo realizou-se um levantamento climatológico e estudo numérico de ciclogênese secundária no sudoeste do Oceano Atlântico Sul com o objetivo de obter informações sobre a atuação destes sistemas e entender os processos dinâmicos envolvidos no seu desenvolvimento. Para o período entre 1980 e 2010, a climatologia mostra que uma média de 3,9 sistemas secundários se forma por ano no Oceano Atlântico Sul. Estes sistemas ocorrem com maior e menor frequência nos meses frios e quentes, respectivamente. Dois tipos distintos de ciclones secundários foram encontrados. TIPO1 que se forma a leste e na região da frente quente do ciclone primário. Estes sistemas se desenvolvem sob advecção quente nos baixos níveis e pouca influência de anomalias de vorticidade potencial (VP) de altos níveis; TIPO2 se desenvolve a oeste/noroeste do ciclone primário onde predomina forte advecção fria em baixos níveis. No entanto, fluxos de calor e umidade intensos contribuem para aquecer a baixa troposfera e em altos níveis são forçados por anomalias de VP. Simulações numéricas com o modelo Weather Research and Forecasting (WRF) indicam os fluxos de calor sensível e latente na superfície como mecanismos de intensificação dos ciclones secundários TIPO1 e TIPO2, sendo o fluxo de calor latente mais importante no abaixamento de pressão destes sistemas. Os experimentos numéricos mostram que o ciclone do TIPO2 não se desenvolve na ausência de anomalia de VP, enquanto que o TIPO1 se desenvolve mais fraco e atrasado no tempo. A análise por separação de fatores indica que a anomalia de VP e algum outro mecanismo não relacionado aos fatores avaliados nas simulações tiveram papel disparador no ciclone do TIPO1, enquanto a interação da anomalia de VP com os fluxos de superfície atuou como intensificador. No TIPO2, o desenvolvimento ocorreu unicamente pela atuação da anomalia de VP, a qual também agiu como um intensificador juntamente com os fluxos de calor e umidade, bem como os processos de interação entre estes dois fatores. / Secondary cyclones are systems that are not well defined yet and they are difficult to predict, requiring further studies to identify the signals that trigger their development. In this study we carried out a climatology and numerical study of secondary cyclogenesis over the southwestern South Atlantic Ocean in order to obtain information about these systems and understand the dynamic processes involved in its development. The climatology for the period 1980-2010 shows that an average of 3.9 secondary systems per year develops in the southwestern South Atlantic Ocean. These systems occur with more and less frequency in the colder and warmer months, respectively. Two distinct types of secondary cyclones were found. TYPE1 forms eastward and over the warm front region of the primary cyclone. These systems develop due to warm advection at lower levels and relatively weak influence of potential vorticity (PV) anomalies at upper levels. TYPE2 develops westward/northwestward of the primary cyclone where strong cold advection predominates at lower levels. However, in this type, the lower troposphere is heated due to intense heat and moisture fluxes and at upper levels it is forced by PV anomalies. Numerical simulations using the Weather Research and Forecasting model (WRF) indicate that the sensible and latent heat fluxes on surface act as intensification mechanisms for both TYPE1 and TYPE2 secondary cyclones and that the latent heat flux influences more on decreasing the pressure in these systems. The numerical experiments show that the cyclone TYPE2 does not develop in the absence of PV anomalies, while the TYPE1 does, but it is relatively weaker and delayed in time. Factors separation analysis indicates that the PV anomaly and some other mechanism unrelated to the factors evaluated in the simulations have a triggering role in the development of the secondary cyclone TYPE1, while the interaction of PV anomaly with surface fluxes acted to intensify the cyclone. The TYPE2 development occurred solely due to PV anomaly, which also acted to intensifying together with heat/moisture fluxes on surface as well as the interaction processes of these two factors.

Rearrangements are two measurable real-valued functions that have equal measure of pre-images of upper level sets. In this thesis, I will investigate several matters and problems relating to rearrangements: the relationship between assumptions on the measure space and desirable properties of the set of rearrangements, and the validity of rearrangement inequalities; generalising the Mountain Pass Lemma over rearrangements; and applying topological degree theory to boundary value problems involving rearrangements. From suppositions on the measure space, such as the measure space having finite measure and no atoms, it can proved that the set of rearrangements is contractible and locally contractible. The Mountain Pass Lemma over rearrangements can be generalised, so instead of considering continuous paths from the closed unit interval to the set of rearrangements; it will consider the continuous functions from the closed unit disc into the set of rearrangements. Topological degree theory is used to associate admissible triples of functions, sets and points with integers. These methods will be applied to a boundary value problem involving rearrangements, where the domain is almost equal to the union of balls, which has been studied using variational methods, providing new multiplicity results. The minimum number of solutions to this boundary value problem is found to be related exponentially to the number of balls contained in the domain.

En zones côtières, une onde se propageant à la surface de l'océan est fortement influencée par le courant sous-jacent. Les profiles de vitesses sont variables en profondeur du fait du vent soufflant à la surface et des frottements au fond. En considérant les équations d'Euler pour un fluide non-visqueux et incompressible, accompagnées des conditions de surface cinématiques et dynamiques appropriées, l'interaction entre une onde de surface bi-dimensionnelle, progressive et périodique et un courant sous-jacent est étudiée. En ne considérant pas uniquement un champs de vitesses dérivant d'un potentiel scalaire, ce travail étend le modèle d'un courant cisaillé linéairement à des profiles de courant définis par une classe de fonctions de vorticité exponentielle.Il est montré que ces profiles de courant bi-dimensionnelles sont linéairement stables en l'absence d'une perturbation à la surface. L'influence du courant sous-jacent sur des ondes d'amplitude et de profondeur arbitraire est ensuite étudiée numériquement, en présence ou non de capillarité. Malgré le fait que la célérité et l'énergie potentielle et cinématique de l'onde sont fortement influencées par le paramètre de non-linéarité que représente la cambrure, il est montré que l'effet de la vorticité est non-négligeable, surtout pour des ondes de gravité pure. Finalement, des résultats sont présentés pour une étude de stabilité linéaire d'ondes d'amplitude finie (2D) perturbées en trois dimensions. Les classes d'instabilité classiques sont détectées en présence de vorticité constante et non-constante. De plus, un mécanisme est proposé pour une instabilité tri-dimensionnelle dominante en présence de vorticité. / In coastal zones, waves propagating at the surface of the ocean are strongly influenced by underlying shear currents. Depth-dependent velocity profiles are generated by wind blowing at the surface and friction at the bed. Considering the Euler equations for an inviscid and incompressible fluid, along with the appropriate free-surface kinematic and dynamic boundary conditions, the interaction between a two-dimensional progressive periodic free-surface wave of permanent form and an underlying current is studied. By not assuming that the velocity field derives from a scalar potential, this work extends the linear, constant vorticity, shear model to velocity profiles defined by a class of exponential vorticity functions. The two-dimensional current profiles are first shown to be linearly stable in the absence of a free-surface perturbation. The influence of the underlying shear on waves of arbitrary amplitude and depth is then studied numerically, both in the absence and presence of capillarity. Although the celerity and potential and kinetic energy of the wave are strongly influenced by the nonlinear wave steepness parameter, the effect of vorticity is shown to be non-negligible, especially for pure gravity waves. Finally, results are presented for a linear stability analysis of these finite amplitude (2D) waves under three-dimensional perturbations. It is found that the classical classes of instability corresponding to four and five wave resonances are recovered in three-dimensions in the presence of constant or depth-dependent vorticities. Finally, a mechanism is proposed for the dominant three-dimensional instability caused by the presence of an underlying shear current.

Vortices interacting with the solid surface of aerodynamic bodies are prevalent across a broad range of geometries and applications, such as dynamic stall on wind turbine and helicopter rotors, the separated flows over flapping wings of insects, birds and micro-air vehicles, formation of the vortex wakes of bluff bodies, and the lift-producing vortices formed by aircraft leading-edge extensions and delta wings. This study provides fundamental insights into the formation and evolution of such vortices by considering the leading-edge vortices formed in variations of a canonical flapping wing problem. Specifically, the vorticity transport within three distinct experimental cases--2D plunging airfoil, 3D plunging airfoil and 2D plunging airfoil with suction applied at the leading edge--were analyzed in order to characterize the formation and evolution of the leading-edge vortex (LEV). Three-dimensional representations of the velocity and vorticity fields were obtained via multi-plane particle image velocimetry (PIV) measurements and used to perform a vorticity flux analysis that served to identify the sources and sinks of vorticity within the flow. Time-resolved pressure measurements were obtained from the surface of the airfoil and used to characterize the flux of vorticity diffusing from the solid surface, and a method for correcting dynamic pressure data was developed and validated for the application within the current study. Upon characterizing all of the sources and sinks of vorticity, the circulation budget was found to be fully accounted for. Interpretation of the individual vorticity balance terms demonstrated vorticity generation and transport characteristics that were consistent among all three cases that were investigated. Three-dimensional vorticity fluxes were found to be an almost negligible contributor to the overall circulation budget, mostly due to the individual terms canceling each other out. In all cases, the diffusive flux of vorticity from the surface of the airfoil was shown to act primarily as a sink of LEV vorticity, with a magnitude roughly half that of the flux of vorticity emanating from the leading-edge shear layer. Inspection of the chordwise distribution of the diffusive flux within the 2D case showed it to correlate very well with the evolution of the flow field. Specifically, the diffusive flux experienced a major increase during the phase interval in which the LEV remained attached to the downstream boundary layer. It was also noted that the accumulation of secondary vorticity near the leading edge prevented the diffusive flux from continuing to increase after the roll-up of the LEV. This result was validated within the 3D case, which demonstrated that maintaining an LEV that stays attached to the downstream boundary layer produces a larger diffusive flux of vorticity--presumably enhancing both lift and thrust. Through the use of a spanwise array of suction ports, the suction case was able to successfully alter the total circulation of the flow by removing positive vorticity from the opposite-signed vortex (OSV) that formed beneath the LEV. This removal of positive vorticity produced a measured increase in the total lift, and it was noted that weakening this region of secondary vorticity allowed the LEV to impose more suction on the surface of the airfoil. However, it was also noted that weakening the OSV resulted in a loss of thrust, which was attributed to the loss of suction that occurred near the leading edge when the removal of secondary vorticity caused the energetic OSV to be reverted into a low energy region of separated flow. The physical insights provided by this work can form the basis of novel flow control strategies for enhancing the aerodynamic loads produced in unsteady, separated flows.

This thesis investigates vortex dynamics of a plunging airfoil by studying the vorticity transport mechanisms of two-dimensional direct numerical simulations. The simulations were used to study a simplified flat airfoil in a freestream that was subject to pure plunging motion. Quantitative and qualitative analyses were used the validate the two-dimensional simulations and gain insight into the effects of eliminating three-dimensional physics in a nominally two-dimensional flow. Additionally, a parametric study was conducted to analyze the effects of Reynolds and Strouhal numbers on the transport of vorticity.

This study investigates the hydrodynamic variations in the coastal region of Nan-bin, Hualien influence by the topography and water stratification. The data used were collected from four cruises of field observations in 2008/4/29¡B2008/9/5~6¡B2009/3/17~18 and 2009/7/21. Instruments applied include sb-ADCP and CTD. Parameters recorded include flow velocities, water temperature and salinity and tidal elevations. The collected data are analyzed through a variety of time series analysis technique, including buoyancy frequency EOF analysis, potential vorticity and kinetic energy. The results show that (1) the flow field and vorticity in the south side of Hualien Harbor indicate there exist a counterclockwise eddy during flood. The flow pattern reverse to be a clockwise eddy during ebb. The current speed and vorticity is smaller in the surface layer, while the bottom current speed and vorticity is much larger. (2) Currents in transects of along slope, along canyon and along shore all reveal two layers flow separated around 25m, with upper layer flowing eastward and lower layer westward. The current velocity reaches to a maximum at 55m, and the current directions were dominated by the orientation of bottom topography. The baroclinic kinetic energy increase to 0.15m2/s2 along the down slope transect, while the up slope kinetic energy reduced to 0.05m2/s2. (3) The CTD data suggest that the upper layer is warm-fresh water due to river outputs, while the lower layer is dominated by cold-salty open ocean water. (4) The density interface at 25 m is confirmed by buoyance frequency analysis. The EOF analysis of density distribution shows eigenvalue of first mode has maximum at 53m, while the second mode has peaks at 25m and 65m, which match well with the vertical of distribution of flow structures.