Partially Averaged Navier-Stokes (PANS) turbulence method provides a closuremodel for any degree of velocity field altering - ranging from completely resolved Di-rect Numerical Simulation (DNS) to completely averaged Reynolds Averaged Navier-Stokes (RANS) method. Preliminary investigations of PANS show promising re-sults but there still exist computational and physical issues that must be addressed.This study investigates the performance of the PANS method for ow past acylinder at a Reynolds number of 140,000. The cylinder ow is a benchmark owproblem for which there are signicant experimental results available for validation ofPANS. First, we examine if RANS convergence criteria and discretization schemes -which are meant for robust, nearly steady-state calculations - are adequate for PANS,which is inherently unsteady and may contain delicate ow features. For the range offk values tested here, it is determined that the standard RANS residual value and the2nd order spatial discretization scheme are appropriate for PANS. The physical clo-sure investigations begin with the validation of turbulent transport models: the ZeroTransport Model, the Maximum Transport Model and the Boundary Layer Trans-port Model. The implementation of the PANS ku-ey!u model is also performed andcompared against the standard PANS ku-ey model. All these studies yield interest-ing insights into the PANS models. This study concludes with an investigation of alow Reynolds number correction for the PANS ku-wu!u model which yields excellent improvement.

Partially Averaged Navier-Stokes (PANS) turbulence method provides a closuremodel for any degree of velocity field altering - ranging from completely resolved Di-rect Numerical Simulation (DNS) to completely averaged Reynolds Averaged Navier-Stokes (RANS) method. Preliminary investigations of PANS show promising re-sults but there still exist computational and physical issues that must be addressed.This study investigates the performance of the PANS method for ow past acylinder at a Reynolds number of 140,000. The cylinder ow is a benchmark owproblem for which there are signicant experimental results available for validation ofPANS. First, we examine if RANS convergence criteria and discretization schemes -which are meant for robust, nearly steady-state calculations - are adequate for PANS,which is inherently unsteady and may contain delicate ow features. For the range offk values tested here, it is determined that the standard RANS residual value and the2nd order spatial discretization scheme are appropriate for PANS. The physical clo-sure investigations begin with the validation of turbulent transport models: the ZeroTransport Model, the Maximum Transport Model and the Boundary Layer Trans-port Model. The implementation of the PANS ku-ey!u model is also performed andcompared against the standard PANS ku-ey model. All these studies yield interest-ing insights into the PANS models. This study concludes with an investigation of alow Reynolds number correction for the PANS ku-wu!u model which yields excellent improvement.

The three-dimensional lid-driven cavity flow is investigated at Reynolds Number(Re)=10,000 for a wide range of spanwise-aspect ratios of 3:1:1, 0.5:1:1, and 1:1:1 using the Partially Averaged Navier-Stokes(PANS) turbulence closure model. The PANS turbulence model is a variable resolution turbulence closure model, where the unresolved-to-total ratios of kinetic energy (fk) and dissipation (fe), serve as resolution control parameters. This study focuses on two main aspects of PANS: (i) the evaluation of Turbulent transport models and (ii) the effect of grid spacing on accuracy of the numerical solution. PANS calculations are tested against LES and experimental results of Jordan (1994), in terms of both qualitative and quantitative quantities. The main coclusions are are: (i) for a given fk value, the Zero-Transport model is superior to the Maximum-Transport model for unresolved dissipation, (ii) both models are adequate for unresolved kinetic energy, and (iii) for a given grid size, the results depend heavily on grid spacing especially for larger fk values.

The three-dimensional lid-driven cavity flow is investigated at Reynolds Number(Re)=10,000 for a wide range of spanwise-aspect ratios of 3:1:1, 0.5:1:1, and 1:1:1 using the Partially Averaged Navier-Stokes(PANS) turbulence closure model. The PANS turbulence model is a variable resolution turbulence closure model, where the unresolved-to-total ratios of kinetic energy (fk) and dissipation (fe), serve as resolution control parameters. This study focuses on two main aspects of PANS: (i) the evaluation of Turbulent transport models and (ii) the effect of grid spacing on accuracy of the numerical solution. PANS calculations are tested against LES and experimental results of Jordan (1994), in terms of both qualitative and quantitative quantities. The main coclusions are are: (i) for a given fk value, the Zero-Transport model is superior to the Maximum-Transport model for unresolved dissipation, (ii) both models are adequate for unresolved kinetic energy, and (iii) for a given grid size, the results depend heavily on grid spacing especially for larger fk values.

M.Sc. / This study concentrates, not only on the physical origin of the pans, but also attempts to define certain guidelines which will contribute to an improved urban environment in the future. The series of pans on the East Rand form part of the greater Highveld pans, which extends in an easterly direction to eventually link up with the Lake Chrissie pan series. The study is however limited to those pans appearing on the 1: 50 000 topographical map 2628 AB Benoni ...

M.A. / Pan are naturally occurring depressions or closed basins and play a very important role in ecosystems. The East Rand is characterized by more than one hundred pans dotting its landscape. The impact of urbanisation on these pans is significant. To determine exactly how the characteristics of the pans on the East Rand has changed, a comparison was done between the characteristics and utilization of the pans in 1992, as then described by Le Grange (1992) and the current situation in 2003. Water samples were also collected over a period of three months and analysed in the laboratories of Rand Water. The current utilization of the pans leaves much to be desired. Informal settlements, industries, residential areas and mine dumps are all found on the pan floors. Large waste dumping sites are developing at five out of the 19 pans in the study area. This has severely negatively affected the water quality within the pans, and the quality of bird life at thee pans. Continuous research is needed from government and private organisations on the pans found on the East Rand to improve their current quality and condition. Responsibility and proper management strategies must be implemented to protect the pans from negative human impacts.

Master of Science / Despite Chrissie Lake being South Africa’s largest freshwater lake, the chemistry of this lake and the surrounding lakes and pans in the Mpumalanga Lake District has never been studied in detail. These closed systems show varying chemistry while being in very close proximity to one another, adding to the uniqueness of this area where pans, usually typical of arid regions, are found in a humid area. The factors affecting the water chemistry of these lakes needed to be identified and explained. In order to evaluate the water chemistry in this unique environment, water samples were taken at the end of the wet and dry seasons, in April and September 2007 respectively. The major pans were sampled, as were adjacent fountains or springs, indicative of the perched groundwater aquifers found in this area, as well as borehole water from the surrounding farms. Alkalinity was determined by manual titration upon returning from the field while pH and conductivity measurements were performed on site. Major cations and anions were analysed for using ICP-OES and Ion Chromatography respectively. Sediment samples were collected from the floor of each pan in the summer sampling and the mineralogy determined by X-ray diffraction (XRD). During September 2007 sampling, precipitates found on the floors and banks of the pans were also collected and analysed using XRD, to identify mineral species precipitating from solution. Results from the above analyses show that each pan in the MLD has a unique chemistry, which cannot be inferred from neighbouring pans. The inorganic chemistry differs from pan to pan as a result of these separate, closed systems being at different stages of the evaporation process. Throughout the path from groundwater to the pan, waters are subject to mineral dissolution and precipitation, adsorption and biological mechanisms, which continually add or remove solutes from solution. Although seemingly simple, there are certainly other factors that play a role in the evolution of the water chemistry. Key to the current inorganic chemistry is the balance between import and export of solutes. The groundwater, predominantly the perched aquifer water, brings solutes into the pans and blowouts of precipitates on the pan floor at the end of the dry season, when the wind is strongest, results in the export of solutes. This process is significant in maintaining the overall freshness of the pans in the MLD, contrasting to their western counter parts that evolve to highly saline saltpans. Other factors such as the periodicity of pans drying completely, the surface area to catchment area ratio (CA/SA), the formation and dissolution of efflorescent crusts and the presence or absence of reeds all have varying effects on the water chemistry of the lakes and pans. Significantly, the amount of evaporative concentration that a pan evolves through has been shown to be dependant on the CA/SA ratio with pans having larger ratios being lower in salinity compared to those with low ratios being the most saline pans. The reservoir available to the pans with the large catchment areas sustains these pans through the dry months and slows the progression of evaporation. It is clear that the factors affecting the hydrochemistry of the pan waters can not be simplified to a single process affecting a single dilute inflow of water to produce our final solution of evaporated pan water. Instead, water in the pans reflects a long-term evolution of solute species, with some memory effect remaining after each season of evaporation. The result is an accumulation of solutes as they are added continuously via dilute inflow and then removed from the waters at various times, particularly during dry periods when evaporite minerals are formed and transported out of the system.

The work presented in this dissertation concerns continued development, validation and verification of the partially averaged Navier-Stokes (PANS) method - a variable resolution closure model for turbulence. Linear eddy viscosity models (LEVM), which are popular because of their simplicity and affordability in terms of computational cost have fundamental deficiencies and cannot be trusted to accurately represent turbulence in realistic complex flows. The more high fidelity approaches such as large eddy simulations (LES) and direct numerical simulations (DNS) are out of realm of engineering applicability because of their high requirements in computing power. PANS, a variable resolution approach considered in this study, lies between LEVM and LES in terms of computational cost and is designed to prudently utilize the available computing power to improve accuracy. This dissertation presents the various studies performed to characterize the PANS fluctuations and extend the model for use in various wall bounded flows. The road map towards our goal includes: (i) Comparing a-priori and a-posteriori eddy viscosity values to establish whether PANS is capable of producing the pre-specified level of reduction. (ii) Investigating the scaling of PANS fluctuations for different levels of prescribed resolution and establishing if the fluctuations abide by known turbulence scaling laws. (iii) Extending PANS to k-w formulation which is better suited for wall-bounded shear flows, and (iv) Modifying the present LEVM to yield reasonable behavior in the rapid distortion limit where the turbulence is elastic in nature which ultimately affects PANS performance. Results reported in this dissertation illustrate that the PANS closure yields reliable and predictable reduction in the modeled viscosity. The accuracy of the simulations improve as the effective damping is reduced by lowering the specified viscosity providing credibility to the PANS method as a bridging model that performs as intended.

The goal of this dissertation is to consolidate the theoretical foundation of variable-resolution (VR) methods in general and the partially-averaged Navier-Stokes (PANS) approach in particular. The accurate simulation of complex turbulent flows remains an outstanding challenge in modern computational fluid dynamics. High- fidelity approaches such as direct numerical simulations (DNS) and large-eddy simulation (LES) are not typically feasible for complex engineering simulations with cur- rent computational technologies. Low-fidelity approaches such as Reynolds-averaged Navier-Stokes (RANS), although widely used, are inherently inadequate for turbulent flows with complex flow features. VR bridging methods fill the gap between DNS and RANS by allowing a tunable degree of resolution ranging from RANS to DNS. While the utility of VR methods is well established, the mathematical foundations and physical characterization require further development. This dissertation focuses on the physical attributes of fluctuations in partially-resolved simulations of turbulence. The specific objectives are to: (i) establish a framework for assessing the physical fidelity of VR methods to examine PANS fluctuations; (ii) investigate PANS simulations subject to multiple resolution changes; (iii) examine turbulent transport closure modeling for partially-resolved fields; (iv) examine the effect of filter control parameters in the limit of spectral cut-off in the dissipative region; and (v) validate low-Reynolds number corrections with RANS for eventual implementation with PANS. While the validation methods are carried out in the context of PANS, they are considered appropriate for all VR bridging methods. The key findings of this dissertation are summarized as follows. The Kolmogorov hypotheses are suitably adapted to describe fluctuations of partially-resolved turbulence fields, and the PANS partially-resolved field is physically consistent with the adapted Kolmogorov hypotheses. PANS adequately recovers the correct energetics in instances of multiple resolution changes. Scaling arguments are used to determine the correct transport closure model for a partially-resolved field in a boundary layer. The need to modify the fε filter control parameter for cut-off in the dissipation range is highlighted. A low-Reynolds number near-wall correction was evaluated on a RANS model with the intent of adapting to it VR methods. Overall, PANS shows promise as a theoretically sound modeling approach, and this work lays the foundation for future PANS investigations.

>Magister Scientiae - MSc / Salt pans are a characteristic feature of many dry deserts. The microbial communities inhabiting salt pans are thought to be particularly complex and are generally dominated by halophilic microorganisms. Although saline pools are frequently found within the hyper-arid Namib Desert, the microbial communities of these saline sites have been scarcely investigated. The aim of the present study was to characterise the archaeal, bacterial and cyanobacterial diversity inhabiting these extreme saline pools using three culture independent molecular techniques (DGGE, T-RFLP and 16S rRNA clone libraries). The physiochemical results, mainly the conductivity readings recorded from the sampling sites, indicated that the Gobabeb (103.0mS/cm) region was less saline than the two Swakopmund [(Sps01) (150.0mS/cm) and Sps02 (180.0mS/cm)] sites. Results obtained from DGGE and T-RFLP data were in agreement for both bacterial and cyanobacterial analysis indicating that the Gobabeb site was more diverse than the two Swakopmund sites (Sps01 and Sps02). In comparison, the archaeal community profiles for DGGE and T-RFLP analysis were in agreement illustrating that the archaeal community were more abundant in the two extreme Swakopmund saline sites. Phylogenetic data obtained from 16S rRNA gene clone libraries identified halophilic phylotypes (Rhodothermaceae, Idiomarinaceae Puniceicoccaceae and Cyanobacteria/Chloroplast, Family VII) normally associated with salt rich sites. In addition, a large number of unclassified taxa were identified. To conclude, the study highlighted the presence of a rich microbial diversity present within the salt pans of the Namib Desert and establishes a platform for future investigations. / National Research Foundation