The present work addresses the fundamental question involving the modeling of subgrid-scale turbulence as a function of resolved field. A new-nonlinear model has been developed from the constitutive equation of subgrid stresses extending the Reynolds stress model proposed by Warsi. The time scale is expressed in terms of subgrid scale kinetic energy as opposed to strain rate tensor. Effort has been made to identify the terms appearing in the modeled subgrid stresses with "Reynolds term", "Leonard's term" and "cross term". The physical nature of these terms can be best understood from the triadic interactions in wave number space. Understanding these three terms leads to decouple the complex nature of the subgrid stresses. Modeling of these terms separately helps to capture the physics of the problem accurately. The turbulent field is assumed to be isotropic and Kolmogrov's hypothesis is used. The model coefficients are expressed as universal constants for Gaussian filter so as to satisfy the dissipation criteria in inertial subrange. Further dissipation term is assumed to be isotropic and equilibrium condition is used. Although the definition of the subgrid stress terms becomes less clear and separate for smooth filter, an attempt has been made to compare the stress terms with the exact definition obtained for sharp cut-off filter. An estimate of the backscatter of energy can be obtained from the Eddy-Damped Quasi Normal Markovian (EDQNM) theory. The model coefficients thus obtained are tested with results of plain homogeneous shear layer. The model results have been compared with the mixed-nonlinear model and Smagorinsky model. A priori test shows that new-nonlinear model has a good correlation with Smagorinsky model, which in turn has good correlation with experimental results, and has the behavior of the mixed-nonlinear model. The above model has been used for solving two-dimensional flow over backward facing step as a test case. The numerical model solves the vertically hydrostatic boundary layer equation. The top boundary is assumed to be a free surface. Terrain following coordinate system has been used. Because of the non-negativity of the subgrid scale dissipation term i.e. backscatter of energy, the nature of the solution is stochastic. The deterministic solution is obtained by clipping the dissipation term. The results are compared with the experimental data of Kim et al. Good agreement with the experimental data is obtained for the velocity profile and SGS kinetic energy. The reattachment point obtained is at 5.2h (h is the step height), which is less compared to 6h as suggested by other authors. This discrepancy may be due to the assumptions involved in the equations, which is being solved. The model is further extended for the diffusion of scalar variables and to include the buoyancy effect. It is implemented to explore the hydrostatic flow over three dimensional elliptical mountain ridges, where Boussinesq approximation is used for variable density. The flow characteristics have been studied for the various aspect ratios of the mountain and Froude?s number (Nh/U) based on Brunt-Vaisala frequency (N). The phenomenon of upstream blocking and Lee-vortices generation has been studied.

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<p> The motor driven treadmill is often used in research as a convenient tool for simulating overground running. There has been varied opinion in the literature regarding the accuracy of this assumption. The major difference that has been quantified is the variation in treadmill belt speed as a result of the forces applied by a runner. In comparison, the earth does not vary its speed during overground running. The aim of the present study was to more clearly define the causes of treadmill belt-speed variation and to elucidate its effects on running mechanics. </p> <p> An in-lab fabricated tachometer was used to determine accurate treadmill belt speed while the treadmill was challenged by five subjects weighing 55.2 to 99.6 kg running at four speeds of 2.6, 3.1, 3.5 and 4.0 m/s. The actual running velocity was found on average to be 0.62% higher than the treadmill display setting. The intra-step belt-speed variation ranged from 4.2 to 8.6 % of average belt velocity. Linear regression analysis showed that 86 % of the variance in intra-step belt-speed variation was attributed to total body mass and a further 10 % attributed to running speed. </p> <p> The effect that this variation had on running mechanics was determined from the power transfer between the foot and belt, as calculated from the product of the change in belt speed and the horizontal ground reaction force. The horizontal force, as calculated using a segmental acceleration approach, did not show complete agreement with simultaneously recorded forceplate data. It was found that an average of 4.49 J flowed to the treadmill during the eccentric phase of running and 3.37 J of energy flowed to the runner during the concentric phase of running. Despite inaccuracies in the calculation, the mathematical approach used in this study permitted insight into the theoretical benefit of belt-speed variation in treadmill running. </p> / Thesis / Candidate in Philosophy

Introduction: Wearable technologies play an important contemporary role in the measurement of physical activity (PA) and promotion of human health across the lifespan, including for young people (i.e., children, adolescents, and young adults). As new objective wearable technologies continue to develop, standardized approaches to documenting validation parameters (i.e., measures of accuracy, precision, and bias) are needed to ensure confidence and comparability in step-defined PA. Purpose: To produce validity parameters for step counting wearable technologies during treadmill walking in young people 6-20 years of age Methods: 120 participants completed 5-minute treadmill bouts from13.4 to 134.1 m·min-1. Participants wore eight technologies (two at the arm/wrist, four at the waist, one on the thigh, and one on the ankle) while steps were directly observed. Speed, wear location, and age -specific measures of accuracy (mean absolute percent error; MAPE), precision (correlation coefficient, standard deviation; SD, coefficient of variation; CoV), and bias (percent error; PE) were computed and cataloged. Results: Speed and wear location had a significant effect on accuracy and bias measures for wearable technologies (pConclusion: While the analyses indicate the significance of speed and wear location on wearable technology performance, the useful and comprehensive validity reference values cataloged herein will help optimize measurement of PA in youth. Future research should continue to rigorously validate new wearable technologies as they are developed, and also extend these standardized reference values developed in the laboratory to the free-living environment.