The thesis develops singly-periodic mathematical models for complex laminar wakes which are formed behind vortex-shedding bluff bodies. These wake structures exhibit a variety of patterns as the bodies oscillate or are in close proximity of one another. The most well-known formation comprises two counter-rotating vortices in each shedding cycle and is popularly known as the vk vortex street. Of the more complex configurations, as a specific example, this thesis investigates one of the most commonly occurring wake arrangements, which consists of two pairs of vortices in each shedding period. The paired vortices are, in general, counter-rotating and belong to a more general definition of the 2P mode, which involves periodic release of four vortices into the flow. The 2P arrangement can, primarily, be sub-classed into two types: one with a symmetric orientation of the two vortex pairs about the streamwise direction in a periodic domain and the other in which the two vortex pairs per period are placed in a staggered geometry about the wake centerline. The thesis explores the governing dynamics of such wakes and characterizes the corresponding relative vortex motion. In general, for both the symmetric as well as the staggered four vortex periodic arrangements, the thesis develops two-dimensional potential flow models (consisting of an integrable Hamiltonian system of point vortices) that consider spatially periodic arrays of four vortices with their strengths being +/-1 and +/-2. Vortex formations observed in the experiments inspire the assumed spatial symmetry. The models demonstrate a number of dynamic modes that are classified using a bifurcation analysis of the phase space topology, consisting of level curves of the Hamiltonian. Despite the vortex strengths in each pair being unequal in magnitude, some initial conditions lead to relative equilibrium when the vortex configuration moves with invariant size and shape. The scaled comparisons of the model results with experiments conducted in a flowing soap film with an airfoil, which was imparted with forced oscillations, are satisfactory and validate the reduced order modeling framework. The experiments have been performed by a collaborator group at the Department of Physics and Fluid Dynamics at the Technical University of Denmark (DTU), led by Dr. Anders Andersen. Similar experiments have also been run at Virginia Tech as part of this dissertation and the preliminary results are included in this treatise. The thesis also employs the same dynamical systems techniques, which have been applied to study the 2P regime dynamics, to develop a mathematical model for the P+S mode vortex wakes, with three vortices present in each shedding cycle. The model results have also been compared favorably with an experiment and the predictions regarding the vortex circulation data match well with the previous results from literature. Finally, the thesis introduces a novel concept of clean and renewable energy extraction from vortex-induced vibrations of bluff bodies. The slow-moving currents in the off-shore marine environments and riverine flows are beyond the operational capabilities of the more established hydrokinetic energy converters and the discussed technology promises to be a significant tool to generate useful power from these copiously available but previously untapped sources. / Ph. D.

Un corps en chute libre dans un fluide sous l'effet de la gravité peut être soumis à des perturbations. De façon générale, celles-ci peuvent être dues aux mouvements propres du fluide porteur, à la présence d'autres corps mobiles ou encore à la présence de parois. Dans un premier temps, nous avons choisi de nous intéresser à l'interaction de deux disques identiques chutant dans un fluide de densité proche de celle du corps. Différents comportements d'interaction sont observés pour des disques de rapports de forme variable (diamètre sur épaisseur) et des nombres de Reynolds (effets inertiel sur effets visqueux) couvrant des trajectoires rectilignes et périodiques oscillantes. Lorsque les disques sont lâchés en tandem, ils s'attirent et se rencontrent. Après le contact, le comportement dépend du rapport de forme : les disques épais se séparent et tombent côte à côte, tandis que les disques minces continuent leur évolution ensemble dans une configuration relative stable. Lorsque les corps sont lâchés côte à côte, on observe une répulsion des corps qui se traduit par un éloignement horizontal. Une modélisation pour chacun de ces comportements (attraction, répulsion) a été proposée. Dans un deuxième temps, nous avons étudié l’effet de parois fixes sur le mouvement d'un disque isolé en chute libre. Les disques sont lâchés dans des tubes cylindriques créant différents rapports de confinement (diamètre du disque sur diamètre du tube). Nous avons mis en évidence que le comportement du corps dépendait du rapport de forme : la trajectoire d'un disque mince est déstabilisée par le confinement, alors que celle d'un disque épais est stabilisée. Des visualisations des sillages à l'aide de colorants ainsi que des simulations numériques de l'écoulement autour de disques fixes ont été réalisées et ont permis de mieux comprendre le rôle du sillage sur les interactions / A body falling in a fluid under the effect of gravity may be perturbed by the presence of other bodies or fixed boundaries. We first focused our attention on the interaction of two identical disks in freefall. We investigated the kinematics of disks with different aspect ratios (ratio of diameter to thickness) and with different initial relative positions, for a range of Reynolds numbers (ratio of inertial effects to viscous effects) covering both rectilinear trajectories and periodic, oscillating trajectories. When the disks are falling in tandem, the trailing body accelerates until it catches up the leading one. After the contact, the behaviour depends on the aspect ratio. Thicker disks separate and fall side by side and separated while thinner disks continue their fall together in Y or T reversed position. A model of the different types of interaction (entrainment by the wake and horizontal repulsion) is proposed. The second part of the study is devoted to the effect of fixed walls on the kinematics of freely falling bodies. The behaviour again depends strongly on the aspect ratio : a thin disk is destabilized when the blockage ratio (ratio of disk diameter to tube diameter) increases, whereas thicks disks are stabilized. In addition, visualizations of the wakes using dyes and numerical simulations for fixed disks were performed and provide a better understanding of the role of the wake in the interaction

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