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Measurements were made on three forward steps with step height to boundary layer ratio of approximately 3.8%, 15% and 60% and Reynolds number based on step height ranging from 6640 to 213,000. The measurements included mean wall pressure, single and 2 point wall pressure fluctuations, single and 2 point velocity fluctuations and, oil flow visualization. Pressure fluctuation measurements were made 5 boundary layer thicknesses upstream of step to 22 boundary layer thickness (or 600 step heights for smallest step size) downstream of the step. The results show that the steps remarkably enhance the wall pressure fluctuations that scale on the step height in the vicinity of the step and far downstream of the step. The decay of wall pressure fluctuations post reattachment is a slow process and elevated levels can be seen as far as 150 step heights downstream for the mid step size. The enhanced pressure fluctuations come from the unsteady reattachment region on top face of the step which was found to be a strong function of flow geometry and flow parameters such as Reynolds number. The 2 point pressure and velocity space-time correlations show a quasi-periodic structure which begins to develop close to the reattachment and grows in intensity and scale further downstream of reattachment and is responsible for the elevated pressure fluctuations downstream of the step. However, the velocity correlations lack in scale reflecting the fact that large scales reflected in pressure are masked by smaller scales that exist within them. / Master of Science

Equilibrium statistical mechanics has a remarkable property: the steady state probability distribution can be calculated by a procedure independent of the detailed dynamics of the system under consideration. The partition function contains the complete thermodynamics of the system. The calculation of the partition function itself might be a daunting task and one might need to resort to approximate methods in practice. But there is no problem in principle on how to do the statistical mechanics of a system that is at thermal equilibrium. Nonequilibrium statistical mechanics is a completely different story. There is no general formalism, even in principle, the application of which is guaranteed to yield the probability distribution, even for stationary states, without explicit consideration of the dynamics of the system. Instead, there are several methods of wide applicability drawn from experience which work for particular classes of systems. Frequently, one writes down phenomenological equations of motion based on general principles of conservation and symmetry and attempts to extract the dynamical response and correlations. The motivation for studying nonequilibrium systems is the very simple fact that they are ubiquitous in nature and exhibit very rich, diverse and often counter-intuitive phenomenon. We ourselves are an example of a very complex nonequilibrium system. This thesis examines three problems which illustrate the generic features of a typical driven system maintained out of thermal equilibrium. The first chapter provides a very brief discussion of nonequilibrium systems. We outline the tools that are commonly employed in the theoretical description of driven systems, and discuss the response of physical systems to applied perturbations. Chapter two considers a very simple model for a single self-propelled particle with an internal asymmetry, and nonequilibrium energy input in the form of Gaussianwhite noise. Our model connects three key nonequilibrium quantities – drift velocity, mean internal force and position-velocity correlations. We examine this model in detail and solve it using perturbative, numerical and exact methods. We begin chapter three with a brief introduction to the sedimentation of particle-fluid suspensions. Some peculiarities of low Reynolds number hydrodynamics are discussed with particular emphasis on the sedimentation of colloidal particles in a viscous fluid. We then introduce the problem of velocity fluctuations in steady sedi-mentation. The relevance of the current study to an earlier model and improvements made in the present work are then discussed. A physical understanding of our model and the conclusions that result from its analysis are an attempt to resolve the old problem of divergent velocity fluctuations in steadily sedimentating suspensions. The fourth chapter is a study to probe the nature of the fluctuations in a driven suspension of point-particles. Fluctuation relations that characterise large-deviations are a current topic of intense study. We show in this chapter that the random dynamics of suspended particles in a driven suspension occasionally move against the driving force, and that the probability of such rare events obeys a steady state fluctuation relation. In the final chapter, we summarise the models studied and point out the common features that they display. We conclude by pointing out some ways in which the problems discussed in this thesis can be extended upon in the future.