Turbulence has long been believed to be associated with the behavior of vorticity. Ever since experiments showed clearly the presence of vortex structures in turbulent flow, concentrated efforts have tried to identify the important dynamics of three-dimensional vortex flow. In particular, conjectures abound about the importance of vortex stretching and vortex line reconnection. Numerical experiments based on ad hoc assumptions on the nature of the cores of vortex filaments have shown interesting behavior. In some cases, it has been argued that singularities develop in finite time and in other cases that the filament exhibits fractal dimensions. These inviscid calculations also show that filaments of opposite signed vorticity tend to pair up and that the local flow is two-dimensional. Consequently, we have begun a study that clarifies the behavior of a pair of counter-rotating vortices in the presence of an external strain flow that would be induced by the presence of vorticity well away from the local two-dimensional plane. So far, the results are quite interesting and depend on the nature of the strain flow. We always assume that the horizontal component of the strain pushes the filaments together. It is the other two components that then affect the results. Without any strain along the axes of the filaments, the vortex cores are pulled into parallel elliptical shapes. Eventually, the cores are so deformed that they become unstable in the same way a parallel shear flow would and the vortex structures disrupt. This phenomenon will be missed by filament codes that assume the cores remain circular. On the other hand, a strain component along the filaments increases the vorticity but keeps the core structure mostly circular. As the cores approach one another, viscous effects overcome the increase in vorticity due to stretching and the cores dissipate away.

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Recent observations and numerical simulations have significantly improved our understanding of tornadic storms. However, our knowledge of tornado-genesis remains rudimentary. Necessary atmospheric conditions favoring the formation of tornadoes in supercell storms are known, but sufficient conditions remain elusive. The underlying reason is that the processes involved in environment-storm and storm-tornado interactions are not fully understood, as numerical models in the past lacked sufficient resolution to resolve these interactions satisfactorily. In this thesis, an attempt is made to fill this gap by performing a multi-grid high resolution simulation of a supercell storm spawning a tornado-like vortex. Four grids, with grid sizes of 600 m, 200 m, 70 m, and 30 m, are used to allow explicit simulation of storm-tornado interactions. Diagnostic analysis of the modeling results allows an investigation of the origin of rotation at both the storm scale and the tornado scale. / The simulation results showed that the origin of vertical rotation at storm scale during the early stage of storm development is due to tilting of the horizontal vorticity in the environment. This so called mesocyclone then further strengthens by the mechanism of stretching and Dynamic Pipe Effect and descends downwards. During the time of mesocyclone intensification, incipient surface vertical vortices form along the outflow boundary created by the rear flank downdraft due to the process of horizontal shear instability. / One of the surface vortices experiences an initial exponential growth in its vorticity by interacting with the descending mesocyclone and merging with multiple smaller satellite vortices. The tornado-like vortex (TLV) which forms has a maximum horizontal wind of 103 m s-1 and a minimum central pressure of 927 hPa. Vorticity budgets of the mesocyclone and the TLV are computed to assess quantitatively the importance of various processes for rotation. / Sensitivity experiments were also performed to determine the effect of varying the environmental conditions on the mesocyclone and surface vorticity. It was found that as the low-level vertical shear of the environmental wind increases, the mesocyclone intensifies and favors the intensification of near surface vorticity. The presence of drier layers in the upper and middle troposphere eventually produces a weaker mesocyclone and weaker outflow boundaries. On the other hand, inclusion of the ice phase processes produces a stronger mesocyclone and more intense outflow boundaries to enhance the intensification of near surface vorticity.

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Experiment shows that the steady axisymmetric flow past a sphere becomes unstable in the range 120 < Re < 300. The resulting time-dependent nonaxisymmetric flow gives rise to nonaxisymmetric vortex shedding at higher Reynolds numbers. The present work reports a computational investigation of the linear stability of the axisymmetric base flow. When the sphere is towed, fixed, or otherwise constrained, stability is determined solely by the Reynolds number. On the other hand, when the sphere falls due to gravity, the present work shows that a additional parameter, the ratio of fluid density to sphere density (β = ρ(f)/ρ(s)) is involved. We use a spectral technique to compute the steady axisymmetric flow, which is in closer agreement with experiment than previous calculations. We then perform a linear stability analysis of the base flow with respect to axisymmetric and nonaxisymmetric disturbances. A spectral technique similar to that employed in the base flow calculation is used to solve the linear disturbance equations in streamfunction form for axisymmetric disturbances, and in a modified primitive variable form for nonaxisymmetric disturbances. For the density ratio β = 0, which corresponds to a fixed sphere, the analysis shows that the axisymmetric base flow undergoes a Hopf bifurcation at Re = 175.1, with the critical disturbance having azimuthal wavenumber m = 1. The results are favorably compared to previous experimental work.

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Nondestructive methods of detecting cracks in structural components and machinery are important, both in preventing failures and in establishing maintenance procedures. This thesis considers how the vibration behavior of cracked members can be modelled mathematically and how these mathematical models may lead to advancements in crack detection procedures. Two separate cases are considered: the longitudinal vibration of a cracked bar and the coupled vibrations of a cracked rotating shaft. In the longitudinal vibration study, the equation of motion is developed for a cantilevered bar with a symmetric surface crack. Next, Galerkin's Method is used to obtain one- and two-term approximate solutions. Both forced and free vibrations of the bar are analyzed. Graphical results showing the relationships between displacement and crack size, crack position, and forcing frequency are presented and discussed. Spectral analysis is used to compare uncracked and cracked bar behavior. Finally, a sensitivity analysis of the forced vibration case is conducted to observe how the forcing frequency affects the rate of change of steady-state response at the onset of cracking. In the second part of the thesis, a similar analysis is conducted for a cracked, simply-supported Timoshenko shaft rotating at a constant angular speed. The equations of motion derived by Wauer (b) are used as the basis of the study. Again, Galerkin's Method is applied to obtain approximate solutions. Time histories and spectra are used to observe how changes in various parameters influence the vibration behavior. The effects of mass eccentricity and gravity are studied. Finally, the effect of a periodic axial impact load is considered. / Master of Science

A theoretical technique to extract drilling-angular velocities from a nodal-spatial array of in-plane translational velocities is developed. The technique utilizes numerical methods for simulation of solutions. A finite element method using I-DEAS 4.1 is used for calculation of in-plane translational velocities and a MATLAB code is written for extraction of the drilling-angular velocities. The case of data with noise content is also considered. All numerical results are compared to a closed-form theoretical solution which is used as a reference for accuracy. Recommendations are made for future testing and experimental applications of this technique. / Master of Science

This work uses computational fluid dynamics to study the flowfield around a hypersonic missile with two lateral jets to provide control in place of control surfaces. The jets exhaust an H2-O2 mixture at Mach number of 2.9 with a jet pressure ratio of roughly 10,500. The jets are staggered axially and circumferentially in such a way to produce pitch and yaw. The flowfield of such a jet configuration is characterized at several angles of attack and the corresponding force coefficients and amplification factors are provided. The freestream air and H2-O2 plume is treated as inert for the majority of the calculations. Special cases are treated with finite rate chemical kinetics and compared to the inert flowfield to ascertain the effects that chemical reactions have on the force coefficients. It was found that the flowfield was only slightly altered from the familiar one jet flowfield when the second jet is active. The flow topology and vortex structures tend to shift towards the second jet but the overall structure remains the same. The normal force amplification factors are close to unity over the range of angle of attack due to the thrust being so high with the two jet configuration having a lower amplification factor compared to firing a single jet. Treating the flowfield as chemically reacting did not affect the force values much: the difference being 0.3% for an angle of attack of 0°. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection