Influence of Eddy Viscosity on Velocity and Sediment Concentration Profiles

Abstract

Estuaries are economically and ecologically important regions, hence understanding its fluid and sediment dynamics is essential. One factor that influences the dynamics is turbulence. This physical phenomenon occurs in the Navier-Stokes equations, which are notoriously difficult to solve. Various methods exist to include the effect of turbulence, one of them is to parametrize the effects of turbulence via a model parameter called the eddy viscosity. The objective in this thesis is to study the effect of the choice of eddy viscosity on the resulting velocity and concentration profiles. Three choices for the eddy viscosity formulations are examined: a prescribed viscosity model that is constant in space and time, a prescribed parabolic viscosity model that is constant in time and the k-ε model, which is the most advanced model that is widely used in computational fluid dynamics and depends on the local physics of the flow, and is not constant in time. Special emphasis is given to systems with high concentrations. To reproduce some of the complex dynamics in these systems, two processes are essential: hindered settling of particles and stratification, i.e. the distinct layering of water due to density differences. Hindered settling is included for each model, and stratification is studied separately by analyzing both stratified and non stratified cases. The effect of the three models is investigated by implementing a vertical one dimensional water column model and examining resulting velocity and concentration profiles. This is done for a constant water level gradient, resulting in steady-state profiles. Newton's method is implemented with a non-uniform grid to ensure converged solutions.

Neglecting stratification effects, the parabolic viscosity model and k-ε viscosity model yield similar velocity and sediment concentration profiles. In contrast, the constant eddy viscosity model produces weaker flow and higher sediment concentrations. When stratification is included, all eddy viscosity formulations give qualitatively the same results. The suppression of turbulence leads to damped eddy viscosity profiles and sediment settles more easily. When the concentration at the bed is higher than a critical concentration, the concentration where hindered settling attains its maximum, a lutocline may form. This is a sharp transition between a clear upper layer and dense lower layer. All three viscosity profiles show the presence of this lutocline for certain parameter regimes. If the lutocline is present, the location is near the region where the turbulence is most strongly suppressed. Furthermore, the concentration where the lutocline forms can be approximated by the value where the hindered settling term reaches its maximum.