This study explored two-dimensional (2D) numerical hydrodynamic model simulations of Lake Victoria. Several methods were developed in Matlab to build the lake topography. Old depth soundings taken in smaller parts of the lake were combined with more recent extensive data to produce a smooth topographical model. The lake free surface numerical model in the COMSOL Multiphysics (CM) software was implemented using bathymetry and vertically integrated 2D shallow water equations. Validated by measurements of mean lake water level, the model predicted very low mean flow speeds and was thus close to being linear and time invariant, allowing long-time simulations with low-pass filtered inflow data. An outflow boundary condition allowed an accurate simulation to achieve the lake’s steady state level. The numerical accuracy of the linear measurement of lake water level was excellent.

This study explores by a vertically integrated tracer transport model, hydro-meteorologicalevent characteristics and their influence on solute transport. Changes in Hydro-meteorologicalprocesses and increasing frequency of extreme weather events are responsible for changingthe lake water balance, influencing streamflow variations, and lake tracer transport. Wecompare historical data over a long time with model data from a vertically integrated modelin COMSOL Multiphysics. We consider water balance, sources of data uncertainty, correlations,extreme rain and inflow years, and seasonal variations. The lake transport model has estimatedsoluble loading and transportation. The results showed there are strong correlations betweentributary inflows and precipitation, and between lake outflow and water level. It was found that“events” influence lake level fluctuations. The solute transport was shown to vary more in wetperiods. Modeled transportations were higher in Kenya and Uganda lake zones than inTanzanian zones. The major inflow, from the Kagera river, appears to strongly influence lakesolute transportation, so the composition of this river must be considered.

Lake Victoria is the world’s largest tropical lake and the third-largest water body, providing significant water resources for surrounding environments including the cultural, societal, and livelihood needs of people in its basin and along the White Nile. The aim of this study was to use decade-long time series of measured lake flow in the lake system and phosphorus deposition to develop a suitable numerical model based on shallow water equations (SWE) for assessing water quality in Lake Victoria, an increasingly important tool under climate variation. Different techniques were combined to identify a numerical model that included: i) a high-resolution SWE model to establish raindrop diffusion to trace pollutants; ii) a two-dimensional (2D) vertically integrated SWE model to establish lake surface flow and vertically transported wind speed flow acting on lake surface water by wind stress; and iii) a site-specific phosphorus deposition sub-model to calculate atmospheric deposition in the lake. A smooth (non-oscillatory) solution was obtained by applying a high-resolution scheme for a raindrop diffusion model. Analysis with the vertically integrated SWE model generated depth averages for flow velocity and associated changes in water level profile in the lake system and showed unidirectional whole lake wind blowing from the southwest to northeast. The atmospheric phosphorous deposition model enabled water value assessment for mass balances with different magnitudes of both inflows and outflows demonstrating annual total phosphorus at 13,500 tons concentrating at mid-lake western and eastern parts. The model developed here is simple and suitable for use in assessing flow changes and lake level changes and can serve as a tool in studies of lake bathymetry and nutrient and pollution transport processes. Our study opens towards refining models of complex shallow-water systems.

The lake surface water directly influenced by wind force, named the surface boundary layer, is where most pollution release and mixing occurs. The dynamical process of wind force matches the speed of the surface currents and a wind shear is generated over the lake depth. This paper used measurements and numerical modeling of Lake Victoria and the Murchison Bay (MB) to assess the transport of pollutants focusing on nearshore phenomena characterized through wind stress hydrodynamics. Singular value decompositions of wind speed and wind directions were used for pattern analysis considering data from three Tanzania and one Uganda locations at multiple temporal scales. Results showed that strong winds blow typically at midday for daily wind patterns and at mid-year for seasonal wind patterns. Further analysis of the daily, monthly, and yearly wind speeds showed there was a significant periodical trend over these temporal scales. Based on these wind data, a vertically integrated shallow water equations model was applied to explore the potential role of wind for water and pollution movement for the MB surface water. Results showed that the MB wind stress would need to move the whole water column and that would occur much too slowly for the wind to be a dominant factor in the transport of pollutants. Further, we discovered that the depth-resolved hydrostatic model considered required artificial dissipation for stability. Based on the wind patterns and our modeling results, it appears that full Navier-Stokes equations resolved with depth would be required to accurately model the role of wind on lake hydrodynamics. As such, further analysis would be needed to ascertain the true role of wind on mixing and transport in MB and Lake Victoria. 

The development work focuses on the numerical simulations of free body movement in viscous fluid. The aim is to make the simulation of very slow motion of the small body in viscous fluid. We developed bodies’ immersed dynamics simulations in viscous fluid by seeking numerical solutions for appropriate field variables. We developed the methods for vertically and spherically cylindrical objects’ motions, the forces on bodies close to a plane stationary wall are computed from the velocity and pressure fields using the Stokes equation through COMSOL Multiphysics finite element software. The Navier-Stokes equation is reduced to Stokes equation there is independence of time which means object will have an effect only on the motion and the slightly compressible flow assumption is made in order to obtain smooth solution numerically. The forces on an object in slightly compressible Stokes flow have been exerted on the falling objects. The resulting forces have compared with analytical results from the Reynolds Lubrication Theory, and achieved significant results from the development method in Matlab and achieved significant numerical simulations in COMSOL. In addition, an investigation has been madeto an object swimming at low Reynolds number. At low Reynolds number moving is possible when object scale is small and flow pattern is slow and sticky. We have developed a system for a thin two-dimensional (2D) worm-like object wiggle that is passing a wave along its centreline and its motion has simulated by the Ordinary Differential Equations (ODE) system and by the Arbitrary Lagrangian-Eulerian (ALE) moving mesh technology. The development method result shows that it is possible for the small object to have a motion from one position to another through small amplitudes and wavelengths in viscous fluid.

This study examines how hydrodynamic processes in the catchment area of Lake Victoria are affected by climate change. A methodology was developed using numerical modelling and long-term geospatial mapping methods to understand the influence of climate change on hydro-meteorological processes in Lake Victoria, utilising satellite and climatic data from 1900 to 2020. The methodology enables the examination of how hydrodynamic processes, like the inflow of water to the lake and responses to water level variations, are impacted by climate variables. The resulting model demonstrates the crucial interdependence between hydrodynamic processes and climatological factors. Long-term rainfall variation shows a linear positive correlation, which explains the increase in the lake’s overall water level. With respect to the bathymetry as well as the areal coverage, the presence of nutrients in the lake water helps to identify pollution patterns and water quality. Given the regional importance of shallow freshwater lakes across the world, Lake Victoria provides an exceptional case study and the study shows how numerical modelling can improve understanding of the relationship between the physical features of shallow lakes and their hydrodynamics. This includes analysing flow patterns, hydro-meteorological processes, transport of pollutants, and the impact of eutrophication. These factors are crucial in determining water levels and water quality, especially in face of climate change.