The objective of this study is to investigate the fully nonlinear interactions of wave-current and submerged bodies by a BEM-based numerical wave tank (NWT). In this paper, a new concept, a total velocity potential function (a combining form of a regular wave and a uniform current potential function), is adopted to solve the wave-current- body interaction problems. Two sets of the boundary integral equation (BIE) included velocity and local acceleration fields are adopted in order to find the surface wave forms and to calculate the hydrodynamic forces on the body. Applying the linear wave-current solution as a feeding function to the input boundary, it can generate waves similar to a wave maker. A numerical damping zone performed by Cointe(1990) is modified and deployed to dissipate the wave energy of the wave-current field near the end-wall and input boundary. Finally, both Mixed Eulerian-Lagrangian method (MEL) and Runge-Kutta 4th order scheme (RK4) are used to update the water elevation and velocity potential. To prove the reliability of this study, a fully nonlinear NWT is established and examined by comparing the simulated results with other researches'. It shows well agreement with analytic solutions published by others. On the other hand, three different types of structures which are submerged circular cylinder, rectangular and dual-cylinder are adopted to investigate the effects of nonlinear interactions of wave-current-body. The simulated results in weak nonlinear effect show excellent agreement with the linear solutions. Therefore, we conclude that the current method adopting the total velocity potential in the wave-current-body interaction problems is very robust and stable, and lay a good foundation for the advanced ydrodynamic problems.

The geometrically nonlinear constant moment triangle based on the von Karman theory of thin plates is first described. This finite element, which is believed to be the simplest possible element to pass the totality of the von Karman patch test, is employed throughout the present work. It possesses the special characteristic of providing a tangent stiffness matrix which is accurate and without approximation. The stability of equilibrium of discrete conservative systems is discussed. The criteria which identify the critical points (limit and bifurcation), and the method of determination of the stability coefficients are presented in a simple matrix formulation which is suitable for computation. An alternative formulation which makes direct use of higher order directional derivatives of the total potential energy is also presented. Continuation along the stable equilibrium solution path is achieved by using a recently developed Newton method specially modified so that stable points are points of attraction. In conjunction with this solution technique, a branch switching method is introduced which directly computes any intersecting branches. Bifurcational buckling often exhibits huge structural changes and it is believed that the computation of the required switch procedure is performed here, and for the first time, in a satisfactory manner. Hence, both limit and bifurcation points can be treated without difficulty and with continuation into the post buckling regime. In this way, the ability to compute the stable equilibrium path throughout the load-deformation history is accomplished. Two numerical examples which exhibit bifurcational buckling are treated in detail and provide numerical evidence as to the ability of the employed techniques to handle even the most complex problems. Although only relatively coarse finite element meshes are used it is evident that the technique provides a powerful tool for any kind of thin elastic plate and shell problem. The thesis concludes with a proposal for an algorithm to automate the computation of the unknown parameter in the branch switching method.

O conhecimento das propriedades hidráulicas do solo referentes ao movimento da água é essencial para a solução de problemas que envolvem a poluição de mananciais e aquíferos, a conservação da água e o controle da erosão. Neste contexto, as propriedades hidráulicas do solo de maior importância são a curva de retenção da água no solo, a condutividade hidráulica e a difusividade hidráulica em função do conteúdo de água no solo. O método do perfil instantâneo é um dos métodos mais utilizados na determinação da condutividade hidráulica do solo não saturado, no entanto, a suposição do gradiente de potencial total unitário, adotado nos modelos de simplificação do método do perfil instantâneo, é ainda muito questionada em perfis de solo que não sejam estritamente homogêneos e com conteúdo de água afastado da saturação. Nesse sentido, os objetivos do projeto são: (1) obter e comparar a função condutividade hidráulica do solo pelo modelo de Hillel et al. (1972) com o modelo propostos por Libardi et al. (1980) e por van Genuchten (1980); (2) verificar a influência da adoção do gradiente de potencial total unitário no modelo de Libardi et al. (1980). O método simplificado de Libardi et al. (1980) apresenta boa concordância com o método padrão de Hillel et al. (1972) em estimar a condutividade hidráulica do solo não saturado para tempos de observação superiores a 24 horas, mesmo quando o gradiente de potencial total fica relativamente distante da unidade. Para tempos de observação inferiores a 24 horas, onde o conteúdo de água é maior, o modelo de Libardi et al. (1980) superestima o valor de condutividade hidráulica. A aplicação do método de Libardi et al. (1980), também em tempos de redistribuição inferiores a 24 horas, permite obter valores mais precisos de condutividade hidráulica do solo, expressos assim por duas funções com relação ao tempo de redistribuição observado. A presença de horizontes pedológicos ocasionou o impedimento hidráulico ao movimento da água, ou seja, reduziram a condutividade hidráulica do solo não saturado. O impedimento foi proporcional à maior proximidade dos horizontes. O aumento do valor médio e da variação do gradiente de potencial total se correlacionou exponencialmente com a redução da concordância do modelo simplificado de Libardi et al. (1980) com o modelo padrão de determinação da condutividade hidráulica do solo não saturado (Hillel et al., 1972). / The knowledge of the soil hydraulic properties related to the water movement is essential for the solution of problems involving the pollution of water sources and aquifers, water conservation and erosion control. In this context, the most important hydraulic properties of the soil are the soil water retention curve, the hydraulic conductivity and the hydraulic diffusivity as a function of soil water content. The instantaneous profile method is one of the most used methods to determine the unsaturated soil hydraulic conductivity, however, the assumption of the total potential gradient, adopted in the simplification models of the instantaneous profile method, is still very questioned in soil profiles that are not strictly homogeneous and with water content far from saturation. In this sense, the objectives of the project are: (1) obtain and compare the hydraulic conductivity function of the soil by the model of Hillel et al. (1972) with the model proposed by Libardi et al. (1980) and van Genuchten (1980); (2) verify the influence of the adoption of the unit total potential gradient in the model of Libardi et al. (1980). The simplified method of Libardi et al. (1980) shows good agreement with the standard method of Hillel et al. (1972) to estimate the hydraulic conductivity of the unsaturated soil for observation times greater than 24 hours, even when the total potential gradient is relatively far from the unit. For observation times shorter than 24 hours, where the water content is higher, the method by Libardi et al. (1980) overestimates the value of hydraulic conductivity. The application of the method, also in redistribution times less than 24 hours, allows to obtain more precise values of hydraulic conductivity of the soil, thus expressed by two functions with respect to the redistribution time observed. The presence of pedological horizons caused the hydraulic impedance to the water movement, that is, has reduced the hydraulic conductivity. The impediment was proportional as greater proximity the horizons have from each other. The increase in the mean value and variation of the total potential gradient correlated exponentially with the reduction of the agreement index comparing the simplified model of Libardi et al. (1980) with the standard model for determining the hydraulic conductivity of the unsaturated soil (Hillel et al., 1972).

O conhecimento das propriedades hidráulicas do solo referentes ao movimento da água é essencial para a solução de problemas que envolvem a poluição de mananciais e aquíferos, a conservação da água e o controle da erosão. Neste contexto, as propriedades hidráulicas do solo de maior importância são a curva de retenção da água no solo, a condutividade hidráulica e a difusividade hidráulica em função do conteúdo de água no solo. O método do perfil instantâneo é um dos métodos mais utilizados na determinação da condutividade hidráulica do solo não saturado, no entanto, a suposição do gradiente de potencial total unitário, adotado nos modelos de simplificação do método do perfil instantâneo, é ainda muito questionada em perfis de solo que não sejam estritamente homogêneos e com conteúdo de água afastado da saturação. Nesse sentido, os objetivos do projeto são: (1) obter e comparar a função condutividade hidráulica do solo pelo modelo de Hillel et al. (1972) com o modelo propostos por Libardi et al. (1980) e por van Genuchten (1980); (2) verificar a influência da adoção do gradiente de potencial total unitário no modelo de Libardi et al. (1980). O método simplificado de Libardi et al. (1980) apresenta boa concordância com o método padrão de Hillel et al. (1972) em estimar a condutividade hidráulica do solo não saturado para tempos de observação superiores a 24 horas, mesmo quando o gradiente de potencial total fica relativamente distante da unidade. Para tempos de observação inferiores a 24 horas, onde o conteúdo de água é maior, o modelo de Libardi et al. (1980) superestima o valor de condutividade hidráulica. A aplicação do método de Libardi et al. (1980), também em tempos de redistribuição inferiores a 24 horas, permite obter valores mais precisos de condutividade hidráulica do solo, expressos assim por duas funções com relação ao tempo de redistribuição observado. A presença de horizontes pedológicos ocasionou o impedimento hidráulico ao movimento da água, ou seja, reduziram a condutividade hidráulica do solo não saturado. O impedimento foi proporcional à maior proximidade dos horizontes. O aumento do valor médio e da variação do gradiente de potencial total se correlacionou exponencialmente com a redução da concordância do modelo simplificado de Libardi et al. (1980) com o modelo padrão de determinação da condutividade hidráulica do solo não saturado (Hillel et al., 1972). / The knowledge of the soil hydraulic properties related to the water movement is essential for the solution of problems involving the pollution of water sources and aquifers, water conservation and erosion control. In this context, the most important hydraulic properties of the soil are the soil water retention curve, the hydraulic conductivity and the hydraulic diffusivity as a function of soil water content. The instantaneous profile method is one of the most used methods to determine the unsaturated soil hydraulic conductivity, however, the assumption of the total potential gradient, adopted in the simplification models of the instantaneous profile method, is still very questioned in soil profiles that are not strictly homogeneous and with water content far from saturation. In this sense, the objectives of the project are: (1) obtain and compare the hydraulic conductivity function of the soil by the model of Hillel et al. (1972) with the model proposed by Libardi et al. (1980) and van Genuchten (1980); (2) verify the influence of the adoption of the unit total potential gradient in the model of Libardi et al. (1980). The simplified method of Libardi et al. (1980) shows good agreement with the standard method of Hillel et al. (1972) to estimate the hydraulic conductivity of the unsaturated soil for observation times greater than 24 hours, even when the total potential gradient is relatively far from the unit. For observation times shorter than 24 hours, where the water content is higher, the method by Libardi et al. (1980) overestimates the value of hydraulic conductivity. The application of the method, also in redistribution times less than 24 hours, allows to obtain more precise values of hydraulic conductivity of the soil, thus expressed by two functions with respect to the redistribution time observed. The presence of pedological horizons caused the hydraulic impedance to the water movement, that is, has reduced the hydraulic conductivity. The impediment was proportional as greater proximity the horizons have from each other. The increase in the mean value and variation of the total potential gradient correlated exponentially with the reduction of the agreement index comparing the simplified model of Libardi et al. (1980) with the standard model for determining the hydraulic conductivity of the unsaturated soil (Hillel et al., 1972).

The settling of spherical and cylindrical particles in a linearly stratified fluid is investigated using experiments. The double-tank method is used to generate a linear stratification with a red colored dye homogeneously mixed in the heavy water tank. As a result of feeding the stratification using dyed heavy water, the concentration of dye varies with depth in the experiment tank. A powerful back-light and a digital camera are used to record the events. Assuming the concentration of dye is directly proportional to density of fluid, Beer-Lambert's law is used to generate a calibration between intensity of the light measured by the camera and density of the fluid. Using this calibration, density is evaluated in all the images captured. In the parameter space of this study, the spheres have three different wake patterns. The area of fluid disturbed by a suspension of spheres increases with <i>Re</i> and <i>Fr</i>. As a result, the amount of energy available for the mixing and the irreversible change of total potential energy in the system increases with <i>Re</i>, <i>Fr</i> and number of particles. Cylinders drag volumes of light fluid to larger depths in their wake than spheres and shed the light fluid in the form of vortices. This results in lower volumes of fluid perturbed by the cylinders. However, as the light fluid is dragged to larger depths, the amount of energy generated for mixing and the change in total potential energy of the system is higher. Spheres are thus more efficient in disturbing volumes of fluid but cylinders are more efficient in causing irreversible changes to the state of the system.