In this thesis a high order finite difference scheme is derived and implemented solving the shallow water equations using the SBP-SAT method. This method was tested against various benchmark problems were convergence was verified. The shallow water equations were also solved on a multi-block setup representing a tsunami approaching a shoreline from the ocean. Experiments show that a bottom topography with many spikes provides a dispersing effect on the incoming tsunami wave. Higher order convergence is not guaranteed for the multi-block simulations and could be investigated further in a future study.

Ocean acidification may cause biodiversity loss, alter ecosystems and impact food security, yet uncertainty over ecological responses to ocean acidification remains considerable. Most work on the impact of ocean acidification on foraminifera has been short-term laboratory experiments on single species. To expand this, benthic foraminiferal assemblages were examined across shallow water CO2 gradients in the Gulf of California, off the islands of Ischia and Vulcano in Italy and off Papua New Guinea. Living assemblages from the Gulf of California did not appear to show a response across a pH range of 7.55 – 7.88, although the species assemblage was impoverished in all locations and the dead assemblage was less diverse at the lowest pH sites where there was evidence of post mortem dissolution. At Vulcano, the small macroalga, Padina pavonica, did not protect calcareous foraminifera from the adverse effects of ocean acidification. Calcareous taxa disappeared from the assemblage and were replaced by agglutinated foraminifera as mean pH reduced from 8.19 to 7.71. Settlement of benthic foraminifera onto artificial collectors off Vulcano was adversely affected in the acidified water, with few species as pCO2 increased and evidence of post-mortem dissolution. The foraminiferal tests, collected off Papua New Guinea, had lower δ11B as mean pH decreased from 7.99 – 7.82 for small (250 – 500 µm) Amphistegina lessonii, but not for A. lessonii or Calcarina spengleri >500 µm. In the larger foraminifera, photosynthetic activity by symbionts may begin to dominate the boron isotopic signature. Overall, the responses of foraminiferal assemblages to ocean acidification are complex, but there was an overall reduction in species diversity in infaunal, epifaunal and epiphytic assemblages as pCO2 increased. This raises serious concerns for the survival of shallow water calcareous benthic foraminifera as the oceans continue to acidify, with implications for benthic ecosystems and inorganic carbon cycling.

Flood propagation over urban areas can cause an interaction between the free-surface flow and large underground pipe networks used for storm drainage and sewage, causing outflows and inflows at the bed. The associated waves may collide with each other and the surface waves. In this thesis the shallow water equations are used to model this type of wave interaction over dry or wet beds with bathymetry gradients and friction terms. The proposed shallow water scheme is solved based on finite volume high-resolution Godunov-type methods. The solver is well-balanced and can accurately balance the source terms and flux-gradients for the steady-state solutions. The solver also utilises a new type of Riemann wave speed to provide depth-positive results over nearly dry beds and dry states. Additionally a new type of source term is introduced in the continuity equation to model pipe inflow and outflow conditions at bed connections. For the standard one-dimensional shallow water equations the numerical results are validated with analytical solutions or other reference solutions provided in the literature. This includes the incipient Riemann problems for nearly dry and dry-states, steady flow over a hump in a rectangular channel and the wave propagation problem. Eventually, the generation of dry bed in the middle, over discontinuous topography is considered. Close agreement is achieved between the shallow water scheme and analytical or reference solutions for the above test cases. For the shallow water problems with influx/efflux source terms comparisons are made with STAR-CD, a commercial Navier-Stokes solver for general fluid flow prediction. The shallow water model is first used to simulate vertical flows through finite gaps in the bed. Next, the interaction of the vertical flows with a dam-break flow is considered for both dry and wet beds. An efflux number, En, is defined based on the vertical efflux velocity and the gap length. A parameter study is undertaken to investigate the effect of the one-dimensional approximation of the present model, for a range of non-dimensional efflux numbers. It is found that the shallow flow model gives sensible predictions at all times provided En<0.5, and for long durations for En>0.5. Dam break flow over an underground connecting pipe is also considered for the one-dimensional efflux problems. To solve two-dimensional problems the shallow water scheme uses the dimensional-splitting method which solves each one-dimensional Riemann problem in the x- and y-directions separately. The cross-derivative terms for second-order accuracy are incorporated by solving another Riemann problem in the orthogonal direction. For two-dimensional problems first the dam-break problems are considered over wet and dry beds. Then, flood propagation over complex terrain is demonstrated. Next, efflux discharge is modelled in isolation over a dry bed and then with dam-break interaction, comparing with STAR-CD results. Again very good agreement is shown between the two-dimensional shallow water model and STAR-CD for the efflux numbers of En<0.5. For modelling the inundation problem over an underground pipe network the solver is coupled with the general underground pipe network solver to calculate the efflux discharge as the flood waves pass through the pipe network. For analysing the pipe network with unknown effluxes an additional set of equations is incorporated into the solution of a general pipe network solver. The shallow water solver coupled to an underground pipe network is then used to simulate dam-break interaction with pipe networks with 9 and 25 nodes to demonstrate the versatility of the method.

The study of quasi-two-dimensional turbulent jets is relevant to chemical reactors, the coking process in oil refinement, as well as rivers flowing into lakes or oceans. In the event of a spillage of pollutants into a river, it is critical to understand how these agents disperse with the flow in order to assess damage to the environment. For such flows, characteristic streamwise and cross-stream dimensions can be much larger than the fluid-layer thickness, and so the flow develops in a confined environment. When the distance away from the discharge location is larger than ten times the fluid-layer thickness, the flow is referred to as a quasi-two-dimensional jet. From experimental observations using dyed jets and particle image velocimetry, we find that the structure of a quasi-two-dimensional jet consists of a high-speed meandering core with large counter-rotating eddies developing on alternate sides of the core. The core and eddy structure is self-similar with distance from the discharge location. The Gaussianity of the cross-stream distribution of the time-averaged velocity is due, in part, to the sinuous instability of the core. To understand the transport and dispersion properties of quasi-two-dimensional jets we use a time-dependent advection--diffusion equation, with a mixing length hypothesis accounting for the turbulent eddy diffusivity. The model is supported by experimental releases of dye in jets or numerical releases of virtual passive tracers in experimentally-measured jet velocity fields. We consider the statistical properties of this flow by releasing and then tracking large clusters of virtual particles in the jet velocity field. The probability distributions of two-point properties (such as the distance between two particles) reveal large streamwise dispersion. Owing to this streamwise dispersive effect, a significant amount of tracers can be transported faster than the speed predicted by a simple advection model. Using potential theory, we determine the flow induced by a quasi-two-dimensional jet confined in a rectangular domain. The streamlines of the induced flow predicted by the theory agree with experimental measurements away from the jet boundary. Finally, we investigate the case of a quasi-two-dimensional particle-laden jet. Depending on the bulk concentration of dense particles, we identify different flow regimes. At low concentrations, the jet features the same core and eddy structure observed without the particles, and thus quasi-two-dimensional jet theory can apply to some extent. At larger concentrations, we observe an oscillating instability of the particle-laden jet.

This work approaches the topic of modeling the atmospheric boundary layer in four research projects, which are summarized below. i) The diurnal cycles of near-surface meteorological parameters over Antarctic sea ice in six widely used atmospheric reanalyses were validated against observations from Ice Station Weddell. The station drifted from February through May 1992 and provided the most extensive set of meteorological observations ever collected in the Antarctic sea ice zone. For the radiative and turbulent surface fluxes, both the amplitude and shape of the diurnal cycles varied considerably among different reanalyses. Near-surface temperature, specific humidity, and wind speed in the reanalyses all featured small diurnal ranges, which, in most cases, fell within the uncertainties of the observed cycle. A skill score approach revealed the superiority of the ERA-Interim reanalysis in reproducing the observed diurnal cycles. An explanation for the shortcomings in the reanalyses is their failure to capture the diurnal cycle in cloud cover fraction, which leads to errors in other quantities as well. Apart from the diurnal cycles, NCEP-CFSR gave the best error statistics. ii) The accuracy of prediction of stable atmospheric boundary layers depends on the parameterization of the surface layer which is usually derived from the Monin-Obukhov similarity theory. In this study, several surface-layer models in the format of velocity and potential temperature Deacon numbers were compared to observations from CASES-99, Cardington, and Halley datasets. The comparisons were hindered by a large amount of scatter within and among datasets. Tests utilizing R2 demonstrated that the Quasi-Normal Scale Elimination (QNSE) theory exhibits the best overall performance. Further proof of this was provided by 1D simulations with the Weather Research and Forecasting (WRF) model. iii) The increasing number of physics parameterization schemes adopted in numerical weather forecasting models has resulted in a proliferation of inter-comparison studies in recent years. Many of these studies concentrated on determining which parameterization yields results closest to observations rather than analyzing the reasons underlying the differences. In this work, the performance of two 1.5-order boundary layer parameterizations was studied, the QNSE and Mellor-Yamada-Janjić (MYJ) schemes, in the Weather Research and Forecasting (WRF) model. The objectives were to isolate the effect of stability functions on the near-surface values and vertical profiles of virtual temperature, mixing ratio and wind speed. The results demonstrate that the QNSE stability functions yield better error statistics for 2-m virtual temperature but higher up the errors related to QNSE are slightly larger for virtual temperature and mixing ratio. A surprising finding is the sensitivity of the model results to the choice of the turbulent Prandtl number for neutral stratification (Prt0): in the Monin-Obukhov similarity function for heat, the choice of Prt0 is sometimes more important than the functional form of the similarity function itself. There is a stability-related dependence to this sensitivity: with increasing near-surface stability, the relative importance of the functional form increases. In near-neutral conditions, QNSE exhibits too strong vertical mixing attributed to the applied turbulent kinetic energy subroutine and the stability functions including the effect of Prt0. iv) In recent years, many eddy-diffusivity mass flux (EDMF) planetary boundary layer (PBL) parameterizations have been introduced. Yet, most validations are based on idealized setups and/or single column models. To address this gap, this study focused on the effect the mass flux part has on the performance in the QNSE-EDMF PBL scheme in the WRF model by comparing the results to observations from the CASES-97 field campaign. In addition, two refined versions, one introducing the parameterized clouds to the WRF radiation scheme, and the second adding a different entrainment formulation, were evaluated. The introduction of mass flux reduced errors in the average moisture profile but virtual temperature and wind speed profiles did not change as much. The turbulent flux profiles for modeled virtual potential temperature were little affected, with consistent reasonable agreement with observations, if one allows for biases in the observed data and modeled surface fluxes. However, the water vapor flux divergences from QNSE tend to be more negative than observed, while including the mass flux part tends to make the divergences more positive, the latter at least partially due to deeper model PBLs resulting from excessive model surface virtual temperature fluxes. Further, both virtual potential temperature and water vapor flux profiles display spurious spikes attributed to the way the non-local and local terms interact in the model. The influence of the mass flux schemes extends to 60 – 100-km scale circulation features, which were greatly modified by both the inclusion of mass flux and the new entrainment formulation. Adding mass flux based clouds to the radiation calculation improved the time and space averaged modeled incoming shortwave flux. The choice of the representation for entrainment/detrainment often affected the results to the same extent as adding mass flux did.

The MRS/MISS of the Makgabeng Formation encompasses sand cracks, wrinkle marks, mat fragments, mat chips and roll-ups and those of the Magaliesberg formation are wrinkle marks, petees/petee ridges, sand cracks, and multi-directional ripples. The sedimentary process that moderated the formational mechanism of the MISS of the Makgabeng Formation is (descriptively allochthonous) of high energy (inter-dune depositional setting) that eroded, transported and re-deposited mat bound sediments. The genetic mechanism of the MISS of the Magaliesberg Formation is descriptively authochthonous because of enhanced resistance of biostabilized sediments to being reworked. XRF (major and trace) and XRD analysis (qualitative and quantitative) was done on MISS bearing sedimentary rock layers (A) and underlying sedimentary sections (B) of Magaliesberg and Makgabeng samples. Result show high quartz content of all the analyzed samples compared to average sandstones. This premise suggests a relation of microbes (e.g. cyanobacteria) to phototrophy and/photoautotrophy because of the conduction properties of translucent quartz. Also plausible inference is that the intense chemical weathering that produced the quartz arenite was positively influenced by microbes, as noted in some Proterozoic basins. There is higher concentration of Ba in all A samples compared to B (Makgabeng and Magaliesberg) which might be emblematic of biogenicity. The Magaliesberg analyzed samples (MAG 101, 102, 103) exhibit homogeneity by the higher concentration of Al2O3, TiO2, K2O, and P2O5, and lower concentration of SiO2 in the A compared to the B subsamples of a particular sample. Also, Magaliesberg analyzed samples (MAG 101, 102, 103) exhibit homogeneity by the lower concentration of quartz and higher concentration of muscovite in the A compared to the B subsamples. This exact established negative correlation between the duo of SiO2 and quartz, and the quartet of Al2O3, TiO2, K2O, and P2O5, and muscovite as in Magaliesberg samples pertains also to a Makgabeng sample (MKG 102; roll-up). MKG 101 (mat fragment) deviates from this mineralogical and geochemical trend. Each of the A samples of MAG 101, 102, 103, are uniformly of higher concentration in Ce, Cr, Nb, Th, V, Y, Zn, Zr compared to the B version of that sample. MKG 101 and 102 are uniformly of lower concentration of Ce, Cr, Nb, Th, V, Y, Zn, Zr in A compared to the B version of that sample. The A of each of the samples MAG 101, 102, and 103 has higher concentration of Hf and Rb compared to its B; a character that is also exhibit in MKG 102, and MKG 101 is vice versa. Microscopy shows that A of all the samples is of smaller grain size compared to B, espousing affinity of microbes to fine-medium grained sandstones. Microscopy of the Magaliesberg Formation samples show Pseudo petee ridges and pseudo cross lamination which reflect biostabilization, and microscopy of the Makgabeng Formation show roll-ups, mat chips and composite mat chips. The MISS genetic difference of the two formations is related to energy, water residence time (emergence and inundation), Ph, and similarity is related to mutuality in shallow water environment. Mat types are inferred to be biologically, physically and chemically moderated adaptations of microbial communities to specific cum peculiar locally prevailing environmental conditions; factors that are premised on taphonomy and ecology. / Dissertation (MSc)--University of Pretoria, 2014. / tm2015 / Geology / MSc / Unrestricted

Shallow Tunneling through highly populated areas of big cities is a challenging task. Almost in all the tunneling projects of shallow tunnel some or the other types of tunneling problems have been encountered and are still being faced. The stability of shallow tunnel is also influenced by many factors, primarily the in situ stress, geological structures, groundwater, rock mass quality, shape of tunnel etc. The design of shallow tunnel in past was almost purely a matter of experience. During last decays computational methods have been introduced as powerful design aids tool to arrive at safe and economical shallow tunnel structure. The purpose of this thesis work is to provide technical criteria and guidance for the design, and stability of Norra Länken shallow tunnel in rock for civil works projects. The design of shallow tunnels in highly dense areas is an iterative process. A good starting point is essential to the process and facilitates safe and economic design. Currently there are many practical two and three-dimensional software tools available for carrying out the task. This master thesis provides an overview of a methodology being used by tunneling experts, which captures the three-dimensional essentials of tunnel behaviour with two-dimensional analysis tools, PLAXIS. Though it is not a full and final situation and conclusion, but there is a lot to learn from such conditions .

Detonation of an explosive charge, such as a mine or an improvised explosive device (IED) at the ground surface or buried at shallow depth in soil, can produce high airblast pressures and significant dynamic soil debris loads on an overlying or nearby structure, such as a vehicle passing over the explosive. The blast loading environment is a function of many factors including the explosive type, configuration, mass, and depth of burial, soil characteristics, and the distance between the ground surface and the structure or object. During the past several years, the US Army has focused considerable attention on developing improved methods for predicting this environment, particularly for use by vehicle/armor analysts, thereby, improving the survivability of these platforms. Research is needed to better understand the aboveground environment created by the detonation of a shallow-buried explosive in order to design adequate protective measures for an aboveground structure. Unfortunately, there is no accurate methodology for predicting these airblast and soil debris loads to support the designs. Development of the required prediction tools is hampered by lack of well controlled and documented experimental results for these complex loads. Without detailed experimental data, the numerical simulations of these loads cannot be adequately validated for the large deformation, stress, and motion gradients and the resulting interactions with structures. The focus of this research is to quantify the influence of soil properties on the aboveground environment from the detonation of a bare explosive charge resting on the soil surface or shallow-buried. In order to fully quantify the influence of soil parameters, well-controlled experiments were designed to directly measure soil debris and airblast loadings on an aboveground reaction structure due to the detonation of explosives at the surface of and shallow buried in three very different soils. The experiments were performed using specifications and strict quality controls that limited the influence of outside variables and ensured the experiments were repeatable. The experiments provided blast pressure, soil stress, and impulse data for each soil type. These data were analyzed to investigate the influence of the properties of the different soil types on the aboveground environment.

Accurate prediction of tsunami waves requires complete boundary and initial condition data, coupled with the appropriate mathematical model. However, necessary data is often missing or inaccurate, and may not have sufficient resolution to capture the dynamics of such nonlinear waves accurately. In this thesis we demonstrate that variational data assimilation for the continuous shallow water equations (SWE) is a feasible approach for recovering both initial conditions and bathymetry data from sparse observations. Using a Sadourny finite-difference finite volume discretisation for our numerical implementation, we show that convergence to true initial conditions can be achieved for sparse observations arranged in multiple configurations, for both isotropic and anisotropic initial conditions, and with realistic bathymetry data in two dimensions. We demonstrate that for the 1-D SWE, convergence to exact bathymetry is improved by including a low-pass filter in the data assimilation algorithm designed to remove scale-scale noise, and with a larger number of observations. A necessary condition for a relative L2 error less than 10% in bathymetry reconstruction is that the amplitude of the initial conditions be less than 1% of the bathymetry height. We perform Second Order Adjoint Sensitivity Analysis and Global Sensitivity Analysis to comprehensively assess the sensitivity of the surface wave to errors in the bathymetry and perturbations in the observations. By demonstrating low sensitivity of the surface wave to the reconstruction error, we found that reconstructing the bathymetry with a relative error of about 10% is sufficiently accurate for surface wave modelling in most cases. These idealised results with simplified 2-D and 1-D geometry are intended to be a first step towards more physically realistic settings, and can be used in tsunami modelling to (i) maximise accuracy of tsunami prediction through sufficiently accurate reconstruction of the necessary data, (ii) attain a priori knowledge of how different bathymetry and initial conditions can affect the surface wave error, and (iii) provide insight on how these can be mitigated through optimal configuration of the observations. / Thesis / Candidate in Philosophy

An integrated electromagnetic (EM) and seismic geophysical study was performed to evaluate non-invasive approaches to estimate depth to shallow groundwater in arid environments with elevated soil salinity where the installation of piezometers would be impractical or prohibited. Both methods were tested in two study areas (semi-arid and arid respectively), one in Palmyra, Utah, USA near the shore of Utah Lake where groundwater is shallow and unconfined in relatively homogeneous lacustrine sediments. The other area is Carson Slough, Nevada, USA near Ash Meadows National Wildlife Refuge in Amargosa Valley. The area is underlain by valley fill, with generally variable shallow depths to water in an ephemeral braided stream environment. The methods used include frequency domain electromagnetic induction allowing for multiple antenna-receiver spacings. High resolution compressional P-wave seismic profiles using a short (0.305 m) geophone spacing for common depth-point reflection stacking and first arrival modeling were also acquired. Both methods were deployed over several profiles where shallow piezometer control was present. The semi-arid Palmyra site with its simpler geohydrology serves as an independent calibration to be compared to the Carson Slough Site. EM results at both sites show that water surfaces correspond with a drop in conductivity. This is due to elevated concentrations of evaporative salts in the vadose zone immediately above the water table. EM and seismic profiles at the Palmyra site were readily correlated to depth to groundwater in monitoring wells demonstrating that the method is ideal under laterally homogeneous conditions. Interpreting the EM and seismic profiles at Carson Slough was challenging due to the laterally and vertically variable soil types, segmented perched water surfaces, and strong salinity variations. The high-resolution images and models provided by the seismic profiles confirm the simple soil and hydrological structure at the Palmyra site as well as the laterally complex structure at Carson Slough. The EM and seismic results indicate that an integrated geophysical approach is necessary for an area like Carson Slough, where continued leaching of salts combined with braided stream deposition has created a geophysically complex soil and groundwater system.