Thesis (M.S.) University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on August 21, 2007) Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Directional acoustic beams are used in diverse sonar systems. For efficient transmission of a sonar signal, the sound energy is projected in a narrow beam . For reduced interference in reception, the sound signal is received from a narrow spatial sector. Typically, such beams have associated sidelobes which adversely affect sonar performance. The goal of this thesis is to propose several novel acoustic arrays which are capable of generating desired search-light-type and fan-type beams with greatly reduced sidelobes. These novel acoustic arrays have fewer elements than conventional arrays of similar performance. The design of such novel arrays is inherently more difficult, however, since it involves nonlinear optimization. Such an optimization is normally computationally intensive and may not be globally convergent. This difficulty has been overcome by newly developed concepts and associated array pattern synthesis methods. A new concept called the equivalent linear array is introduced; a design method based on this concept benefits from existing design techniques developed for linear arrays. The equivalent linear array concept is further developed to lead to a new and effective method for array radiation pattern synthesis. A second new concept called the scale-invariance radiation pattern is introduced, and the subsequent relation between two novel arrays is discovered. Using this concept an angle mapping approach is developed which transforms a radiation pattern generated by a circular ring array to that of an elliptic ring array. This approach takes advantage of methodologies developed for the design of circular ring arrays. A third concept, constraint directions, is introduced; a subsequent new iterative method for array pattern synthesis is developed to meet the need in compact receiving/transmitting array design. With the help of these new concepts, the proposed synthesis methods avoid the use of nonlinear optimization techniques and merely require simple matrix operations. The methods can be applied to the problems of synthesizing radiation patterns of arrays with arbitrary sidelobe envelopes, with nonisotropic elements, and with nonuniform spacing between elements. The usefulness of the developed methodologies is demonstrated in various design examples. The methods developed provide powerfuI tools not only to design novel acoustic arrays but also to design antenna arrays. / Graduate

The dynamics of the Arctic ocean are studied on a polar projection of the sphere. The density structure is idealized as a two-layer system, and a general formulation is developed which allows inclusion of latitudinal and longitudinal depth variations as well as asymmetries in the boundaries of the ocean. For simplicity, the density structure is neglected when depth variations are present. Time dependent displacements from equilibrium levels are assumed to be waves of constant zonal wave number; no radial propagation is considered. Amplitude equations are derived for these displacements, subject to the assumption that the polar basin is small enough to keep only a first approximation to the curvature of the Earth. A semi-qualitative investigation of the possible solutions is made in the case of a symmetrical basin, using the Method of Signatures, and existence criteria are found for the solutions in the presence of radial depth variations. Concentrating thereafter on planetary waves, explicit solution for such motions in the simplest case (depth constant, symmetrical boundaries) allows comparison with the results of other investigators (Longuet-Higgins, 1964 b; Goldsbrough, 1914 a) . It is found that the polar projection and first approximation to the curvature give quite good results, so that this method may be applied to polar regions in the same way as the β-plane is used in mid-latitudes. The general effects of radial bottom slopes are discussed and a simple example treated more explicitly. Some theorems of Ball (1963) on the motions of shallow rotating fluids in paraboloidal basins are found to hold for such basins in the polar plane approximation to the sphere. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

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