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In this thesis we examine some of the interesting aspects of stability for some convection problems. Specifically, the first part of the thesis deals with the Bénard problem for various Non-Newtonian fluids, whereas the second part develops a stability analysis for convection in a porous medium. The work on stability for viscoelastic fluids includes nonlinear stability analyses for the second grade fluid, the generalised second grade fluid, the fluid of dipolar type and the fluid of third grade. It is worth remarking that throughout the work the viscosity is supposed to be any given function of temperature, with the first derivative bounded above by a positive constant. The connection between the two parts of the thesis is made through the method used to approach the nonlinear stability analysis, namely the energy method. It is shown in the introductory chapter how this method works and what are its advantages over the linear analysis. Nonlinear stability results established in both Part I and Part II are the best one can get for the considered physical situations. Different choices of energy have been considered in order to achieve conditional or unconditional nonlinear stability results.

Thesis (M.Sc.)--University of the Witwatersrand, Faculty of Medicine, 1998. / During graded exercise, an intensity is reached where a subjects ability to remove lactate lags behind the rate of lactace production. The influence of body fluid shifts, during exercise of increasing intensity, on the pattern of the blood lactate response was studied. The maximal oxygen uptake (V02 max) was measured using a treadmill, on eleven subjects. Subsequently, lactate accumulation in venous blood was measured, in triplicate, up to an oxygen consumption greater than 90% V02max. During all exercise, oxygen consumption was measured using an online system. In addition, the blood samples at each workload were used to determine haematocrit (Hct) and haemoglobin (Hb) levels. The Hct and Hb values were used to calculate lactate accumulation (corrected for body fluid shifts) as opposed to the absolute or total lactate levels. The correction for body fluid shifts was done using two techniques. The one using haematocrit only and the other using both haematocrit and haemoglobin. The total and accumulated lactate levels were related to %V02max using two different models. Firstly, a lactate threshold (LT) was determined using the classic lactate turning point (LTP) concept, (ie. two straight lines fitted to the data points) . These Tines iii were computer generated. The intercept of the two lines (LT) was compared for total lactate against accumulated lactate (calculated using Hct alone and secondly Hct in combination with Hb. In the latter cases, both the LT intercepts were shifted slightly to the right (ie. to a higher % of V02max) . The average difference in LT when adjusting with Hb and Hct was 0,519 of %V02max (0,72% change) and when adjusting with Hct only was 1,17 of %V02 max (1,65% change). Secondly, an exponential curve was fitted by regression to the data (r=0.989+/-0.018). A substantial shift in the curve, both down and to the right, was obtained when adjusting total lactate to accumulated lactate. The %V02 max at a lactate concentration of 4 mmol/I was used to define the position of the curve. The difference when using Hct alone to calculate accumulated lactate corrected for fluid shift was - 9,20% of V02max (p<0.05), and when using Hb and Hct in combination, -8,71% of V02max (p<0,05) . It is concluded that expressing the lactate curve as an accumulated curve (corrected for body fluid shifts), rather than in absolute terms, significantly alters the construction of the curve during the exercise protocol used in this study. This is especially relevant when using the exponential model,

Le transport de particules solides par les écoulements turbulents près des parois est l'objet de nombreuses applications environnementales telles que les problèmes d'érosion, de dépôt ou de particules de sable en saltation. Malgré les progrès dans les techniques expérimentales et les simulations, des interrogations persistent dans la compréhension des mécanismes de transport des particules près de la paroi. Nombreuses études ont été consacrées à ce problème. Par simulationnumerique directe (DNS) couplée avec le suivi lagrangien de particules ponctuelles, Zamansky et al. (2011) ont trouvé que contrairement à ce qui est observé en turbulence homogène isotrope, près de la paroi les particules solides se concentrent de manière préférentielle dans les régions de forte RMS d'acceleration longitudinale. L'objectif de ce travail est de vérifier si cette observation est toujours vraie lorsque la taille des particules est prise en compte dans les simulations. Pour cela, un code pseudo-spectral de DNS est couplé avec une méthode de frontières immergées (Uhlmann, 2005). Le couplage est valide dans différents cas en 2D ou 3D d'obstacles fixes ou en déplacement. Un bon accord est atteint avec les résultats d'autres études expérimentales ou numériques. Ensuite, des particules de taille finie avec différents nombres de Stokes et densités sont suivies à chaque instant dans un écoulement de canal turbulent. Les statistiques de vitesse et d'accélération sont analysées. Un intérêt particulier est porté sur les PDF d'accélération des particules, du fluide et du fluide au voisinage des particules. Dans la mesure du possible, les résultats sont comparés à ceux obtenus par le suivi lagrangien de particules ponctuelles / Particle transport by turbulent wall flow is a crucial issue in many environmental problems such as erosion, particle deposition and sand saltation. Despite great technological advances in measurement techniques as well as in numerical simulations, the understanding of the transport mechanism close to the wall is still incomplete. Many numerical studies have been devoted to this issue. By direct numerical simulations (DNS) of a turbulent channel flow coupled with Lagrangian tracking of pointwise particles, Zamansky et al. (2011) found that contrary to what is observed in homogeneous isotropic turbulence, close to the wall pointwise particles cluster in regions of high streamwise RMS acceleration. The aim of the present study is to explore if this is still the case when size effects are taken into account in the DNS. Therefore, a pseudo-spectral DNS code is coupled with an immersed boundary technique (Uhlmann, 2005). The coupling is validated in the case of 2D and 3D moving and fixed bodies. Good agreement is achieved with other experimental and numerical studies. Then, finite-size particles with different Stokes numbers and density ratios are tracked at each time step in a turbulent channel flow. The velocity and acceleration statistics are analyzed. Particular attention is given to acceleration PDF of the solid phase, the fluid phase and the fluid in the vicinity of particles. The results are compared to the pointwise model