Numerical simulations of atmospheric and oceanic flows are fundamentally limited by a lack of model resolution. This thesis describes the application of unstructured mesh finite element methods to geophysical fluid dynamics simulations. These methods permit the mesh resolution to be concentrated in regions of relatively increased dynamical importance. Dynamic mesh adaptivity can further be used to maintain an optimised mesh even as the flow develops. Hence unstructured dynamic mesh adaptive methods have the potential to enable efficient simulations of high Reynolds number flows in complex geometries. In this thesis, the thermally driven rotating annulus is used to test these numerical methods. This system is a classic laboratory scale analogue for large scale geophysical flows. The thermally driven rotating annulus has a long history of experimental and numerical research, and hence it is ideally suited for the validation of new numerical methods. For geophysical systems there is a leading order balance between the Coriolis and buoyancy accelerations and the pressure gradient acceleration: geostrophic and hydrostatic balance. It is essential that any numerical model for these systems is able to represent these balances accurately. In this thesis a balanced pressure decomposition method is described, whereby the pressure is decomposed into a ``balanced'' component associated with the Coriolis and buoyancy accelerations, and a ``residual'' component associated with other forcings and that enforces incompressibility. It is demonstrated that this method can be used to enable a more accurate representation of geostrophic and hydrostatic balance in finite element modelling. Furthermore, when applying dynamic mesh adaptivity, there is a further potential for imbalance injection by the mesh optimisation procedure. This issue is tested in the context of shallow-water ocean modelling. For the linearised system on an $f$-plane, and with a steady balance permitting numerical discretisation, an interpolant is formulated that guarantees that a steady and balanced state remains steady and in balance after interpolation onto an arbitrary target mesh. The application of unstructured dynamic mesh adaptive methods to the thermally driven rotating annulus is presented. Fixed structured mesh finite element simulations are conducted, and compared against a finite difference model and against experiment. Further dynamic mesh adaptive simulations are then conducted, and compared against the structured mesh simulations. These tests are used to identify weaknesses in the application of dynamic mesh adaptivity to geophysical systems. The simulations are extended to a more challenging system: the thermally driven rotating annulus at high Taylor number and with sloping base and lid topography. Analysis of the high Taylor number simulations reveals a direct energy transfer from the eddies to the mean flow, confirming the results of previous experimental work.

A ideia deste trabalho é apresentar a conjetura de Boyland para o anel e mostrar algums resultados nessa direção. Tal conjectura diz que: Dado um homeomorfismo irrotacional do anel, que possui uma medida com número de rotação positivo, é verdade que, neste caso, existem pontos com número de rotação negativo? Para dar uma resposta parcial a esta pregunta, nesta dissertação (baseada no estudo do [7]) começamos considerando os homeomorfismos do anel que preservam orientação, as componentes de fronteira, com número de rotação positivos em ambas fronteiras, e que tem un levantamento transitivo (o motivo desta hipoteses vem de [3]), mostrando que neste caso 0 está no interior do conjunto de rotação. Este resultado vai permitir provar a conjetura para os homeomorfismos do anel irrotacionais, sem pontos fixos na fronteira e com um levantamento transitivo. Além disso vai permitir estudar a dinâmica de tais homeomorfismos. No final do trabalho, estendemos algums dos teoremas provados ao longo dos capítulos anteriores a um conjunto maior de homeomorfismos e estudamos o comportamento de tais homeomorfismos com base nestes resultados. / The idea of this work is to present Boyland´s Conjecture for the annulus and show some results in its direction. The conjecture is the following: Given a homeomorphism of the annulus, which has a measure with positive rotation number, is it true that, in this case, there are points with negative rotation number?. To give a partial answer to this question, in this dissertation (based on [7]) we begin considering the homeomorphisms of the annulus that preserve orientation and boundary components, with positive rotation numbers in the boundaries, with has a transitive lift (the reason for this hypothesis is in [3]), and we show that 0 is in the interior of the rotation set. This result will be of help to prove the Boyland´s Conjecture for rotationless homeomorphisms of the annulus, without fixed points in the boundaries and with a transitive lift. In addition, we will be able to study the dynamics of such homeomorphisms. In the end of this work, we extend some of the theorems proved in the previous chapters to a bigger set of homeomorphisms and we study the behavior of such homeomorphisms using these results.

A exploração de petróleo em alto mar traz consigo desafios crescentes com o aumento da lâmina d’água e do grau de agressividade dos contaminantes presentes no fluido produzido. Sendo a produção no País majoritariamente escoada do poço para as unidades de produção por dutos flexíveis, faz-se necessária a realização de estudos aprofundados da influência destas condições na vida em fadiga destes equipamentos. Tais condições quando associadas ao alagamento da região anular dos dutos flexíveis, pode favorecer a corrosão das armaduras de tração, responsáveis por conferir resistência axial ao duto. Este fato compromete a integridade da estrutura, levando a operação à uma condição não segura. Com o intuito de elevar o grau de conhecimento sobre estes mecanismos de degradação, o presente estudo tem por objetivo estabelecer uma relação entre os parâmetros construtivos e operacionais destes dutos, com o seu desempenho em campo frente a carregamentos cíclicos e na condição de anular alagado Para tal, tendo como base a literatura disponível no tema, foram selecionados parâmetros de estudo para, a partir destes, determinar fatores de redução de vida em fadiga (FRVFs). Estes fatores foram quantificados e estudados através de correlações numéricas e experimentais, sendo validadas através da realização de um ensaio em escala real de um duto flexível com anular alagado com água do mar sintética saturada com dióxido de carbono. Como resultados foram obtidos fatores de redução de vida em fadiga para as condições estudadas. Ainda, foi estabelecida uma metodologia para a determinação destes e sua utilização para o cálculo do dano acumulado de fadiga nestes dutos. / Offshore oil exploration involves growing challenges as water depth increases and aggressive oil contaminants are present in production fluid. As Brazilian production is conducted from the well to the production units mostly through flexible pipes, studies regarding the influence of this conditions on fatigue life of these structures are necessary. When the annulus is flooded with seawater the above conditions turns the environment corrosive for tensile armor wires, that are responsible to provide axial strength to the pipe. This fact compromises the integrity of the structure as a whole turning the operation unsafe. To increase the knowledge regarding these degradation mechanisms this study aims to stablish a relationship between constructive and operational parameters with field performance considering dynamic loadings and flooded annulus conditions. For such, using the literature data available it was selected some relevant parameters and from these it was determined fatigue life reduction factors (FRVFs). The FRVF was quantified and studied using numeric and experimental relations and validated through a full scale fatigue test in flooded annulus condition with synthetic seawater saturated with CO2. As a result, it was obtained the FRFV to explored conditions. Even more, it was stablished a methodology for its determination and applicability for calculation of cumulative fatigue damage in flexible pipes.

A ideia deste trabalho é apresentar a conjetura de Boyland para o anel e mostrar algums resultados nessa direção. Tal conjectura diz que: Dado um homeomorfismo irrotacional do anel, que possui uma medida com número de rotação positivo, é verdade que, neste caso, existem pontos com número de rotação negativo? Para dar uma resposta parcial a esta pregunta, nesta dissertação (baseada no estudo do [7]) começamos considerando os homeomorfismos do anel que preservam orientação, as componentes de fronteira, com número de rotação positivos em ambas fronteiras, e que tem un levantamento transitivo (o motivo desta hipoteses vem de [3]), mostrando que neste caso 0 está no interior do conjunto de rotação. Este resultado vai permitir provar a conjetura para os homeomorfismos do anel irrotacionais, sem pontos fixos na fronteira e com um levantamento transitivo. Além disso vai permitir estudar a dinâmica de tais homeomorfismos. No final do trabalho, estendemos algums dos teoremas provados ao longo dos capítulos anteriores a um conjunto maior de homeomorfismos e estudamos o comportamento de tais homeomorfismos com base nestes resultados. / The idea of this work is to present Boyland´s Conjecture for the annulus and show some results in its direction. The conjecture is the following: Given a homeomorphism of the annulus, which has a measure with positive rotation number, is it true that, in this case, there are points with negative rotation number?. To give a partial answer to this question, in this dissertation (based on [7]) we begin considering the homeomorphisms of the annulus that preserve orientation and boundary components, with positive rotation numbers in the boundaries, with has a transitive lift (the reason for this hypothesis is in [3]), and we show that 0 is in the interior of the rotation set. This result will be of help to prove the Boyland´s Conjecture for rotationless homeomorphisms of the annulus, without fixed points in the boundaries and with a transitive lift. In addition, we will be able to study the dynamics of such homeomorphisms. In the end of this work, we extend some of the theorems proved in the previous chapters to a bigger set of homeomorphisms and we study the behavior of such homeomorphisms using these results.

Low back pain represents a significant concern in the United States, with 70% of individuals experiencing symptoms at some point in their lifetime. Although the specific cause of low back pain remains unclear, symptoms have been strongly associated with degeneration of the intervertebral disc. Insufficient nutritional supply to the disc is believed to be a major mechanism for tissue degeneration. Understanding nutrients' transport in intervertebral disc is crucial to elucidate the mechanisms of disc degeneration, and to develop strategies for tissue repair (in vivo), and tissue engineering (in vitro). Transport in intervertebral disc is complex and involves a series of electromechanical, chemical and biological coupled events. Despite of the large amount of studies performed in the past, transport phenomena in the disc are still poorly understood. This is partly due to the limited number of available experimental techniques for investigating transport properties, and the paucity of theoretical or numerical methods for systematically predicting the mechanisms of solute transport in intervertebral disc. In this dissertation, a theoretical and experimental approach was taken in order to investigate the mechanisms of solute transport and binding interactions in intervertebral disc. New imaging techniques were developed for the experimental determination of diffusive and binding parameters in biological tissues. The techniques are based on the principle of fluorescence recovery after photobleaching, and allow the determination of the anisotropic diffusion tensor, and the rates of binding and unbinding of a solute to the extracellular matrix of a biological tissue. When applied to the characterization of transport properties of intervertebral disc, these methods allowed the establishment of a relationship between solute anisotropic and inhomogeneous diffusivity and the unique morphology of human lumbar annulus fibrosus. A mixture theory for charged hydrated soft tissues was presented as a framework for theoretical investigations on solute transport and binding interactions in cartilaginous tissues. Based on this theoretical framework and on experimental observations, a finite element model was developed to predict solute diffusive-convective-reactive transport in cartilaginous tissues. The numerical model was applied to simulate the effect of mechanical loading on solute transport and binding interactions in cartilage explants and intervertebral disc.

In this thesis, the seminal work of Stokes concerning the ow of a Navier-Stokesuid due to a suddenly accelerated or oscillating plate and the ow due to torsionaloscillations of an innitely long rod in a Navier-Stokes uid is extended to a uid withpressure dependent viscosity. The viscosity of many uids varies signicantly withpressure, a fact recognized by Stokes; and Barus, in fact, conducted experiments thatshowed that the variation of the viscosity with pressure was exponential. Given sucha tremendous variation, we study how this change in viscosity aects the nature of thesolution to these problems. We nd that the velocity eld, and hence the structureof the vorticity and the shear stress at the walls for uids with pressure dependentviscosity, are markedly dierent from those for the classical Navier-Stokes uid.

CANDU (CANada Deuterium Uranium) reactor utilizes Pressure Tube (PT) fuel channel design and heavy water as a coolant. Fuel channel annulus gas acts as an insulator to minimize heat losses from the coolant to the moderator. Since fuel bundles are continuously under high neutron fluxes, annulus gas nuclides undergo different nuclear transformations generating new composition of the gas that might have different physical properties which are undesirable for the annulus system. In addition, gas nuclides become radioactive and lead to an increase of the radioactive material inventory in the reactor and consequently to an increase of radiation levels. Pressure Tube Reactor (PTR) and Pressure Tube Supercritical Water Reactor (PT SCWR) fuel channel models have been developed in Monte Carlo N-Particle (MCNP) code. Neutron fluxes in the fuel channel annulus gas have been obtained by simulating different types of neutron sources in both PTR and PT SCWR fuel channels. Transmutation rates of annulus gases have been calculated for different gases (CO2, N2, Ar and Kr) at different pressures and temperatures in both fuel channels. The variation of the transmutation rates, neutron fluxes and gas densities in the annulus gas have been investigated in PTR and PT SCWR fuel channels at constant pressures and different temperatures. MCNP code along with NIST REFPROP [14] and other software tools have been used to conduct the calculations. / UOIT

In this thesis, the seminal work of Stokes concerning the ow of a Navier-Stokesuid due to a suddenly accelerated or oscillating plate and the ow due to torsionaloscillations of an innitely long rod in a Navier-Stokes uid is extended to a uid withpressure dependent viscosity. The viscosity of many uids varies signicantly withpressure, a fact recognized by Stokes; and Barus, in fact, conducted experiments thatshowed that the variation of the viscosity with pressure was exponential. Given sucha tremendous variation, we study how this change in viscosity aects the nature of thesolution to these problems. We nd that the velocity eld, and hence the structureof the vorticity and the shear stress at the walls for uids with pressure dependentviscosity, are markedly dierent from those for the classical Navier-Stokes uid.

The problem of low Mach number (non-Boussin´esq) conjugate laminar natural convection combined with surface radiation in a vertical annulus with a centrally located vertical heat generating rod is studied numerically, taking into account the variable transport properties of the fluid. Such problems arise often in practical applications like spent nuclear fuel casks, cooling of electrical and electronic equipment, convection in ovens, cooling of enclosed vertical bus bars and underground transmission cables. The physical model consists of a vertical heat generating rod, a concentric outer isothermal boundary and adiabatic top and bottom surfaces. The heat generation in the rod drives the natural convection in the annulus. Surface radiation is coupled to natural convection through the solid-fluid interface condition and the adiabatic condition of the top and bottom surfaces. A mathematical formulation is written using the governing equations expressing the conservation of mass, momentum and energy for the fluid as well as the energy balance for the solid heat generating rod. The governing equations are discretized on a staggered mesh and are solved using a pressure-correction algorithm. Steady-state solutions are obtained by time-marching of the time dependent equations. The discretized equations for the dependent variables are solved using the Modified Strongly Implicit Procedure. A global iteration is introduced on the variables at each time step for better coupling. The parameters of the problem are the heat generation and gap width based Grashof number, aspect ratio, radius ratio and the solid-to-fluid thermal conductivity ratio. The coupling of radiation introduces the wall emissivity and the radiation number as the additional parameters and also necessitates the calculation of radiation configuration factors between the elemental surfaces formed by the computational mesh. The radiant heat exchange is calculated using the radiosity matrix method. A parametric study is performed by varying Grashof number from 106 to 1010 , aspect ratio from 1 to 15, radius ratio from 2 to 8, the solid-to-fluid thermal conductivity ratio from 1 to 100, with the Prandtl number 0.7 corresponding to air as the working medium. The characteristic dimension and the outer boundary temperature are fixed. For Radiative calculations, and the emissivity is varied between 0.25 and 0.75. Converged solutions with laminar model could be obtained for high Grashof numbers also as the heat generation based Grashof number is generally two orders of magnitude higher than the temperature difference based Grashof number. Results are presented for the flow and temperature distributions in the form of streamline and isotherm maps. Results are also presented for the variation of various quantities of interest such as the local Nusselt numbers on the inner and outer boundaries, the axial variation of the centerline and interface temperatures, maximum solid, average solid and average interface temperature variations with Grashof number and the average Nusselt number variation for the inner and outer boundaries with Grashof number. The results show that simplification of conjugate problems involving heat generation by the prescription of an isoflux boundary condition on the rod surface is inadequate because a truly isoflux condition cannot be realised on the one hand and because the solid temperature distribution remains unknown with such an approach. The average Nusselt numbers on the inner and outer boundaries show an increasing trend with the Grashof number. For pure natural convection, the Boussin´esq model predicts higher temperatures in the solid and lower average Nusselt numbers on the inner and outer boundaries, compared to the non-Boussin´esq model and the Boussin´esq approximation appears to be adequate roughly upto a Grashof number of 109, beyond which the non-Boussin´esq model is to be invoked. The average pressure in the annulus is found to increase with an increase in the Grashof number. Radiation is found to cause convective drop and homogenize the temperature distribution in the fluid.

Replacing a diseased disc with a tissue engineered disc has the potential to restore normal spinal biomechanics. However, recreating the interface between annulus fibrosus (AF) and vertebral bone (VB) will be necessary to facilitate proper function of the implant in vivo. This study characterizes the native bovine AF-VB interface and assesses adult human discs. The AF insertion site in humans and cows is uniquely differentiated from other soft tissue-bone interfaces, as AF collagen fibers anchor into the calcified region of vertebral endplate through a zone of hyaline cartilage and have a different organization in inner and outer AF. Mineralization-associated proteins are present in this region and the chondroid tissue undergoes calcification over time. Based on these observations an in vitro AF culture system was developed and demonstrated that AF cells can induce mineralization. Understanding mechanism(s) regulating AF mineralization will help develop conditions to ensure proper integration of bioengineered AF.