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Supporting data for sediment transport due to streaming

The sediment transport module of REEF3D is used to calculate the scour and the deposition pattern for abutment, pier and contraction under constant discharge and for pier under waves. The time development of scour for all these cases is also observed. To this effect, the Reynolds Averaged Navier Stokes (RANS) equations are solved in all three dimensions, making it fully three dimensional. The location of the free surface is represented using level set method. The eddy viscosity in the RANS equation is determined by the use of the two-equation k-ω model and k-ε model. Using the conservative finite-difference framework on a structured-staggered grid, convective terms of RANS equation is discretized with the fifth-order WENO scheme. The pressure gradient term in the RANS equation is modelled using Chorin ́s projection method on a staggered grid. For implementation of waves, the CFD code is used as a numerical wave tank. For the representation of the moveable sediment bed, the level set method is used. Kovacs and Parker and Dey formulations of bed shear stress reduction due to the sloping bed is implemented along with the sand slide algorithm to take care of erosion of individual bed cells.In the first case, the numerical model results are validated against the experimental findings of the abutment scour study done at Politecnico di Milano, Dept. I.I.A.R., Milan, Italy.. This test case is used as a benchmark for validation of sediment transport module of REEF3D. The effect on numerical results upon variation of grid size, turbulence model, time discretization scheme, formulations of critical shear stress for sloping bed and porosity was observed and compared against the experimental results. In the second configuration, the numerical model is used to predict the scour pattern around a pier. The scour pattern around the pier is compared against the numerical result of the hydraulic laboratory of the Technical University Darmstadt. The performance of turbulence model and formulations of critical shear stress for sloping bed was observed. The numerical model is then tested for predicting a general contraction scour. The result is compared against the physical experiments of the contraction case conducted at the laboratories of the BAW (Federal Waterways Engineering and Research Institute), Karlsruhe, Germany. For the above mentioned three cases, a constant discharge at the boundary is used. The numerical model in above configurations predict the general evolution (geometry, location and maximum scour depth) and time development of the scour hole accurately.In the final configuration, 3D local scour around a vertical pile under waves is modelled using sediment transport module of REEF3D. The numerical result is first compared to the theoretical observations and then validated against the pier scour experiments conducted in the Department of Hydrodynamics and Water Resources (ISVA), Technical University of Denmark by Sumer and Fredsoe. The effect of variation of the sediment time stepping with the decoupling of the hydrodynamic and the morphodynamic time step is tested. The numerical model shows good agreement with the experiment and theoretical erosion and deposition pattern. The de-coupled approach for simulation of hydrodynamic and sediment transport processes is found to be a reasonable assumption.

Vortex formation is one of the fundamental modes in fluid mechanics and it can develop in almost every realization of fluid motion. Studying its fundamental dynamics and interactions is of great interest for engineering applications; the vortex shedding behind slender cylindrical structures with various cross sections like pipelines, risers, bridges, buildings and wind turbine blades, can cause fluctuating drag and lift forces, which lead to the vortex-induced vibration (VIV), causing the material subjected to periodic bending stresses, which eventually can lead to fracture; the vortex shedding behind the offshore pipeline placed on/close to the seabed determines the gentle slope of the downstream scour hole. In order to understand the complex physics underpinning the vortex dynamics, some classical flow problems, i.e. oscillatory lid-driven cavity flows, cavity flows with an inserted cylinder and wake behind an elliptic cylinder translating above a wall, which are dominated by the vortex flow have been investigated numerically in the present thesis. Flow in a two-dimensional oscillatory lid-driven rectangular cavity with a depth-to-width ratio 1:2 is investigated, covering a wide range of Reynolds numbers (based on the velocity amplitude and the cavity depth) and Stokes numbers (based on the lid oscillation angular frequency and the cavity depth) where this flow is known to be in the two-dimensional regime. Effects of these two parameters on vortex dynamics, vertical and horizontal centerline velocities and the drag force on the lid are presented and discussed. Four different flow patterns are classified based on the vortex dynamics. Moreover, the corner singularity effect on the flow patterns is also presented and discussed. Effects of an inserted circular cylinder on a steady lid-driven cavity flow are investigated and discussed for different Reynolds numbers (based on the lid motion velocity and the cavity depth), depth-to-width ratios, cylinder radii and locations. An immersed boundary method is applied to treat the circular cylinder surface. Numerical results concerning the vortex structures and pressure distribution around the cylinder are presented and discussed. For the depth-to-width ratio of 1:2, seven flow patterns have been classified based on the vortex structures and their distributions are presented as a function of the Reynolds numbers and the cylinder radii for a given cylinder location. Wake behind an elliptic cylinder translating above a plane wall is investigated numerically for Reynolds numbers less than 150 and gap ratios from 0.1 to 5 (i.e., the ratio between the gap and semi-major axis length of the elliptic cylinder). Numerical results concerning the steady and unsteady wake structures Karman vortex street, the two-layered wake and the secondary vortex street), the hydrodynamic forces and the onset location of the two-layered wake are presented and discussed. Four flow patterns are classified based on the wake structure and their distributions are given in the space of the Reynolds number and the gap ratio. Numerical simulations of the oscillating boundary layer on a plane wall have been conducted for = 500 and 1120 (based on the boundary layer thickness and the amplitude of the oscillation velocity), and the present results for the wall shear stress and instantaneous vorticity contours are in a good agreement with previous numerical and experimental results.

The Arctic coastal zone is characterized by high erosion rates, which are on average 0,5 m/year but can reach up locally to 25 m/year and therefore endanger coastal infrastructure. Additionally, the global warming takes place twice as fast in the Arctic than in the rest of world, resulting in an expected increase of the erosion rates and a further acceleration of the climate change. Furthermore, warmer temperatures and a retreat of sea ice cover favour human activities in the Arctic regions. Therefore, it is very important to develop reliable ways to model and forecast coastal erosion in the Arctic. This thesis provides a new approach in simulating the thermodenudation erosion process using the geotechnical software Plaxis. The developed Thermodenudation Model is a combination of a thermo-hydraulic model, which considers the cryogenic suction as an important process within frozen soil, coupled with a mechanical model via Python program codes to allow the analysis of slope stability and coastal retreat rates. Additionally, a separate Excel sheet was developed to determine the volume of eroded soil. This model was then calibrated and partly validated to the situation at Baydara Bay a coastline in west Russia, obtaining good results, which are very close to measured data. To investigate the effects of climate change on Baydara Bay until the end of this century a temperature increase was simulated with the Thermodenudation Model in several scenarios, whereby the calculated results regarding the active layer thickness, the coastal retreat rate and the volume of eroded soil are reasonable and comply with predicted developments. Additionally, investigations regarding the bearing capacity of the bluff and coastal protection measures and a parameter variation were conducted.