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In an attempt to contribute the efforts for the robust and effective numerical tools concerning ship motions in astern seas, this thesis presents the development of a coupled non-linear 6-DOF model with frequency dependent coefficients, incorporating memory effects in random waves with a new axis system that allows straightforward combination between seakeeping and manoeuvring model whilst accounting for extreme motions. A combination of seakeeping and manoeuvring is achieved through the adoption of relatively new "horizontal body axis system" which accounts for large vertical motions as well. Furthermore, the frequency dependent terms are incorporated in order to improve the accuracy of the numerical model for non-zero encounter frequencies which are experienced especially when the ship has large heading angle. The effect of encounter frequency and so called "memory effects" are calculated in terms of radiation forces using convolution integrals. Equations of motions and external forces are described in terms of a new axis system. The wave forces are calculated through incident and diffraction wave forces. The incident wave forces are calculated using the instantaneous wave surface while low encounter frequency model is adopted for the calculation of diffraction forces. Finally, the whole numerical model is expressed in random sea environment including the convolution terms to carry out the simulations in more realistic sea environments. The validation of the numerical model with the results of benchmark tests commissioned by ITTC Specialist Group on Stability, showed reasonably satisfactory agreement while the inclusion of frequency dependent terms affected the accuracy of the numerical model. Parametrical studies were carried out to investigate the effect of different environmental and operational parameters to ship motions in extreme astern seas along with the effects of degrees of freedom and encounter frequency. In order to enhance the numerical model and to obtain further information about the coupling of the motions and the adequacy of the numerical model to carry out further simulations regarding dangerous situations during ship motions in random following and quartering seas, extensive captive and free running model tests were carried out. The numerical model provided good agreement with the experiments. The terms resulting from the coupling of vertical motions and large heeling angle to wave forces are obtained. It is believed that the numerical model has a good potential for providing a more rational basis for predicting the dangerous conditions which a ship could face in extreme astern seas, and for offering insights about the link of behaviour with the design parameters of a ship in the light of the validation with the experiment results and parametrical studies.

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A method for performing calculations on the lower bound states of van der Waals trimers is developed, which models atom-atom-diatom trimers with basis functions in all five degrees of freedom. Spherical harmonic and distributed Gaussian functions and solutions of one-dimensional adiabatic Hamiltonians are used as basis functions. Arg was examined as a precursor system. No spectroscopy has been performed on Ara, nor is this currently feasible. For the systems considered, most experimental data exists for (^v)HCI = 0 Ar(_2)HCl so this is the main target of the work. Predictions are made for Ar(_2)DCl, for (_v)HCI = 1 Ar(_2)HCl, and for (^v)HF =0,1 Ar(_2)HF ; experiments are currently in progress on some of these systems. The current state of knowledge of the pair potentials of the Ar-Ar, and Ar-HF/CI systems is summarised. Physical models for important three body potential terms are suggested; these arise from dipoles induced on the argon atoms, dispersion effects, orbital deformation and the Ar(_2) overlap-induced field. The parameters in the models come from the literature, where possible, and otherwise from a fit to some ab-initio data points for the Ar(_3) and Ar(_2)HCl trimers (Chalasinski et al.).Calculations on Ar(_s) with various two- and three-body potentials are presented and discussed in the context of earlier work. For Ar(_2)HCl a comparison is made with earlier, approximate, work (Hutson, Halberstadt and Beswick). The possible effects of Hamilto- nian approximations are discussed before addressing the effects of individual three-body components. Two sets of three-body parameters are assessed, and indicate that the physical models used are substantially appropriate, although deficient in detail; agreement with experiment is good, with changes in frequencies of about 1.5cm(^-1) arising from the best three-body model. The most important three-body component is found to be the interaction of the overlap-induced field with the HCI permanent multipoles, with the dispersion effects slightly less important and other terms much less so.

Turbulence research in the laboratory has confirmed the existence of quasi-coherent structures amidst the chaos of a turbulent boundary layer. It has been observed that a quasi-periodic phenomena called “bursting” accounts for a major contribution to the turbulent Reynolds stress and the production of turbulent kinetic energy. Bursting is the term used for a sequence of events, where a low-speed streak of fluid from the near wall region lifts away from the wall, slowly at first, and then rapidly moves away from the wall as it convects downstream where it becomes unstable and breaks up violently upon interaction with the outer flow. This ejection of low speed fluid into the mean flow is responsible for locally high values of turbulent kinetic energy. Although a great deal is known about these structures in laboratory flows, little has been done to investigate if such structures are universal in turbulent flows, i.e., their existence in large Reynolds number flows such as the turbulent air flow over the ocean. It would seem, intuitively, that such structures, if present in the marine atmospheric boundary layer, would play a major role in the transfer of momentum, mass and heat across the air-sea interface. It is speculated that these motions may also be associated with large scale organized motions in wall bounded turbulent shear flows. The effort aimed at elucidating the physics underlying such structures would be invaluable in contributing to our understanding of the air-sea flux mechanism. In this dissertation, standard ejection detection schemes like the quadrant, the VITA and the modified u-level techniques have been applied to turbulent wind data measured over the ocean to confirm the existence of burst like structures. The proportions of contributions to the Reynolds stress from the four quadrants of the u’w’ plane are in close agreement with the corresponding contributions for a laboratory flow. Ejection detection followed by the grouping of ejections into bursts yielded a mean burst period of 47 s, at a height of 8.2 m above the water surface, where the mean wind velocity was 6.74 m/s. This burst period corresponds well with the peaks obtained from the autocorrelation of the streamwise velocity signal and the first moment of the stress spectrum, confirming the quasi-periodic nature of this phenomena. Furthermore, phase averages of these events show a structure which is similar to the structure of events detected in laboratory flows. The ejection periods are seen to decrease with increasing wind speed. The burst periods decrease at first with increasing wind speed and then appear to attain a constant value after a wind speed of 6-7 m/s. This has been attributed to the breakdown of the grouping algorithm at higher wind speeds. Ejection and burst frequencies exhibit no discernible dependence on the surface wave field. Ejection and sweep motions have been studied at various length scales. The original velocity signal is bandpass filtered for various frequency bands. For each band, the percentage contributions to the Reynolds stress from the quadrants of the u'w’ plane are close to the corresponding quadrant contributions of the other bands. This indicates similar turbulence structure at different scales. The velocity signals for each band have been normalized by their root mean square (RMS) value. Visualizing the signals on nondimensional time shows the signals from each band to be very similar. These results can also be interpreted as evidence for the ejection and sweep motions existing simultaneously at different scales, indicating the fractal nature of these events. Large scale motions, which appear to be associated with ejection and sweep motions, have been identified in the marine atmospheric surface layer using velocity probe measurements at multiple heights. Visualizing these velocity signals suggests that the organized features extend across the depth of the surface layer. Converting the temporal signals to spatial fluctuations suggests that these structures are inclined at an angle while convecting downstream. The inclination angle near the surface (z < 18 m) is approximately 15° and it increases with increasing height to about 45° when z = 45 m. The spatial velocity fluctuations also indicate that these organized features may be large transverse vortical arches. / Ph. D.

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Consider the problem of designing the path of a camera in 3D. As we may identify each camera position with a member of the Euclidean motions, SE(3), the problem may be recast mathematically as constructing interpolating curves on the (non-Euclidean) space SE(3). There exist many ways to formulate this problem, and indeed many solutions. In this thesis we shall examine solutions based on simple geometric constructions, with the goal of discovering well behaved and computable solutions. In affine spaces there exist elegant solutions to the problem of curve design, which are collectively known as the techniques of Computer Aided Geometric Design (CAGD). The approach of this thesis will be the generalization of these methods and an examination of computation on matrix Lie groups. In particular, the Lie groups SO(3) and SE(3) will be examined in some detail.

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