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.

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.

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

Thesis (Ph. D.)--University of Hawaii at Manoa, 1990. / Includes bibliographical references (leaves 125-128) / Microfiche. / xii, 128 leaves, bound ill. 29 cm

Donaldson's single-point second-order model [13] is used to close the Reynolds stress transport equations in cylindrical coordinates. A reduced set of equations are then solved for the decay of axisymmetric vortices and jets. A self-similar solution to the axisymmetric vortices is obtained numerically. The characteristics of the mean flow variables as well as the Reynolds stresses in this solution are discussed. Comparisons of the current results with Donaldson[13J and Donaldson and Sullivan[16] are also presented. The results show that the vortex core is free from turbulent shear stresses. The turbulent kinetic energy is also found to be relatively weak within the core region. The overshoot of the circulation is found to be 5% of the circulation at infinity over a wide range of Reynolds numbers. The effects of Reynolds number on the decay of the vortices are computed and discussed. Some of the quantities, such as mean flow circulation and turbulent kinetic energy, are found to be sensitive to the Reynolds number. However, the overshoot is found to be insensitive to the Reynolds number but its location does. A set of suitable model constants for the axisymmetric jets is also found and a self similar solution for the jet case is obtained. Comparisons of the computed results with some recent experimental data are presented. / Master of Science

In this dissertation large-eddy simulation(LES) is used to study the transitional and turbulent structures of vortices and free shear layers. The recently developed dynamic model and the basic Smagorinsky model are utilized to model the subgrid-scale(SGS) stress tensor. The dynamic model has many advantages over the existing SGS models. This model has the ability to vary in time and space depending on the local turbulence conditions. This eliminates the need to tune the model constants a priori to suit the flow field being simulated. Three different flow fields are considered. First, the evolution of large-scale turbulent structures in centrifugally unstable vortices is studied. It is found that these structures appear as counter rotating vortex rings encircling the vortex core. The interaction of these structures with the core results in the transfer of angular momentum between the core and the surroundings. The mean tangential velocity decays due to this exchange of angular momentum. Second, the generation and decay of turbulent structures in a vortex with an axial velocity deficit are studied. The presence of a destabilizing wake-like axial velocity field in an otherwise centrifugally stable vortex results in a very complex flow field. The inflectional instability mechanism of the axial velocity deficit amplifies the initial disturbances and results in the generation of large-scale turbulent structures. These structures appear as branches sprouting out of the vortex core. The breakdown of these structures leads to small-scale motions. But the stabilizing effects of the rotational flow field tend to quench the small-scale motions and the vortex returns to its initial laminar state. The mean axial velocity deficit is weakened, but the mean tangential velocity shows no significant decay. Third, a transitional mixing layer calculation is performed.The growth and breakdown to small scales of vortical structures are studied. Emphasis is given to the identification of late transition structures and their subsequent break down. Formation of streamwise vortices in place of the original Kelvin-Helmholtz vortices and the subsequent appearance of hair-pin vortices at the edges of the mixing layer mark the completion of transition. The basic Smagorinsky model is also used in the mixing layer simulations. The performance of the dynamic model is compared with the previous results obtained using the basic Smagorinsky model. As expected, the basic Smagorinsky model is found to be more dissipative. / Ph. D.

The interactions of trailing vortex pairs shed from the tips of two rectangular wings have been studied through helium bubble flow visualizations and extensive hot wire velocity measurements made between 10 and 30 chord lengths downstream. The wings were placed tip to tip at equal and opposite angles of attack, generating pairs of co-rotating and counter rotating vortices. Meaningful hot wire measurements could be made because the vortices were found to be insensitive to probe interference and experienced very small wandering motions. The co-rotating pairs were observed to rotate around each other and merge. Upstream of the merging location, the vortices have approximately elliptical cores. These are surrounded by the two wing wakes which join together around the two cores. Flow in the vicinity of the cores appears fully developed. During the merging process, the cores rotate rapidly about each other, winding the wing wakes into a fine spiral structure. Merger roughly doubles the core size and appears to produce turbulence over abroad range of frequencies. The counter rotating pairs move sideways under their mutual induction and slightly apart; their flow structure changing little with downstream location. These cores remain fairly circular and do not become fully developed within 30 chord lengths of the measurements. / Master of Science

A vortex-panel method for potential flow is used as a basis for modeling surface effects and creating a finite-element interface so that an arbitrary body can be analyzed. The basic model consists of triangular panels of linearly varying vorticity which represent the body, vortex cores on the lifting edges of the body, and vortex filaments representing the wake. The interface modification is made by using a finite-element application's output as the basis for an input file for the model, executing the main program, and writing body and wake output readable by the finite-element application. The surface-effect modification is made by including an image of the body below the real body to create a surface boundary condition through symmetry. / Master of Science