Department of Applied Mathematics

Permanent URI for this community

https://scholar.sun.ac.za/handle/10019.1/96341

Browse

Browsing Department of Applied Mathematics by browse.metadata.advisor "Diedericks, Gerhardus Petrus Jacobus"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Analysis of Extreme Events in the Coastal Engineering Environment
    (Stellenbosch : Stellenbosch University, 2015-12) Stander, Cornel; Diedericks, Gerhardus Petrus Jacobus; Fidder-Woudberg, Sonia; Stellenbosch University. Faculty of Science. Department of Mathematical Sciences (Applied Mathematics)
    ENGLISH ABSTRACT : Coastal zones are subject to storm events and extreme waves with certain return periods. The return period of such events is defined as the average time interceding two independent, consecutive events, similar in nature, i.e., with the same return level. Coastal structures have to be designed to provide sufficient protection against flooding or erosion to a desired return level associated with a particular return period, for example 100 years. Statistical analyses of measured wave data over a time series are used for these estimations. In this study, wave data, measured by a Datawell Waverider buoy, is analysed by means of extreme value analyses. This dataset covers only approximately 18 years. Extreme value theory provides a framework that enables extrapolation in order to estimate the probability of events that are more extreme than any that have already been observed. It can, for example, be used to estimate wave return levels over the next 100 years given only an 18 year history. Different methods for making these estimations are implemented and evaluated. Datasets containing periods where data values are absent (i.e., gaps in a dataset), as well as the effects these missing values have on the estimation of extreme values, are also investigated. Methods for the treatment of gaps are evaluated by using NCEP (National Centre for Environmental Prediction) hindcast data, containing no missing values, and creating incomplete datasets from this data. Estimations are then made based on these incomplete sets. The resulting estimations are compared to the estimations made based on the complete NCEP dataset. Finally, recommendations are made for conducting optimal extreme value analyses, based on this study.
  • Thumbnail Image
    Item
    Modelling the dispersion and deposition of solid wastes from fish farming with a continuum approach
    (Stellenbosch : Stellenbosch University, 2022-04) Fourie, Samantha-Kerry; Goosen, Neill; Diedericks, Gerhardus Petrus Jacobus; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)
    ENGLISH ABSTRACT: The sustainability of the environment in coastal ecosystems is of great concern due to aquaculture. There are many unknowns and constraints in the predictive modelling of fish farm waste due to the limitations of obtaining information in the farming area. By understanding the gaps in the information, the necessary research projects can be established, therefore improving the predictive modelling. This project presents an academic case for Delft3D-FLOW to predict the dispersion and deposition of organic mariculture waste using a continuum approach. The continuum approach allows us to model the waste interaction with the seabed as a cohesive sediment, which can be done using Delft3D-FLOW. More information is needed on how the wastes interact with the seabed as it has been observed that the erosion and deposition of the waste is sensitive to the cohesive properties. Delft3D-FLOW was used for the simulation as it includes modules of multi-dimensional hydrodynamic flows and transport phenomena, including the transport of cohesive and non-cohesive sediments. The simulation represents a growth cycle of six months for Atlantic salmon within a simple rectangular grid, using the background currents of a fjord in the Faroe Islands. A six month simulation period was chosen due to time constraints, allowing for a feasible simulation time and time to conduct a sensitivity analysis on the interaction of the waste with the seabed. The growth data of the simulation period was gathered from existing data in order to determine the amount of feed used, therefore representing the growth cycle of the Atlantic salmon. Using the feed cycle and information from literature, the corresponding waste output of the farm was calculated. Observing the output from the simulations, the waste has been completely dispersed from the grid at the end of the cycle, indication a highly dispersive site. These results correlates with the high currents that were calculated within the fjord. Further, an investigation was conducted into the critical deposition and erosion stresses in order to observe the affect the stresses have on the resultant deposition and dispersion of the waste at the seabed. The results of the sensitivity analysis of the shear stresses result in validation that low critical shear stresses were chosen
  • Thumbnail Image
    Item
    Time series analysis of data measured in the nearshore area
    (Stellenbosch : Stellenbosch University, 2016-03) Mphasha, Rosa; Diedericks, Gerhardus Petrus Jacobus; Fidder-Woudberg, Sonia; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)
    ENGLISH ABSTRACT : Factors that lead to the generation of currents in the nearshore area within the Natal Bight were investigated. The investigation was carried out on data that spans from the 6th June 2012 to the 16th January 2013. The data comprised current measurements, wave measurements, water level measurements, as well as wind measurements. The measurements were decomposed into different direction components in order to study their impacts on corresponding current measurements. Current measurements were resolved into tidal currents and non-tidal currents through the use of harmonic analysis. Stokes drift was estimated using a monochromatic spectrum to obtain the wave induced current. The effect of the wind on the currents was analysed through the use of wind roses and duration analysis. The study was completed with an exploration of the contribution of the Agulhas current. It was found that the waters are characterized by a semi-diurnal, micro-tidal system and tides have a limited contribution to the generation of currents. The contribution of Stokes drift to the overall currents is less than that of tides. Wind is the most significant generator of the nearshore currents.