Modelling turbulence in stably stratified flows
as part of cohesive sediment transport simulations in estuaries


Technical University Berlin , Hermann-FÖTTINGER-Institute for Fluid Mechanics
Department of Hydraulic Turbomachinery and Fluid Mechanics


In estuaries fine and mainly cohesive sediments have the tendency to gather in turbidity zones where they are frequently deposited and resuspended by the tidal movement. To manage siltation, numerical simulation is used as a tool of planning. Yet unresolved differences between numerical simulation and reality diminish the value of numerical results for this task. This study progresses in quantifying the part of the turbulence model in these differences, which is only one out of four empirical models in cohesive sediment transport simulation. Stable density stratification, caused by dissolved salt and suspended sediments, damp turbulence and may result in a complete collapse of mixing in some estuarine conditions (according to WINTERWERP).

In this study a 3D hydrostatic numerical algorithm based an the ideas of CASULLI et al. was coded. In addition to literature proposals unstructured meshes and the k-eps -turbulence model was implemented. The source code and the test cases can be downloaded from the authors webpage (

A first set of calculation is used to test the base-model. The known properties (mass conservative, fast and stable dry and rewet) were reproduced. A momentum loss due to streamline curvature is described for the first time. In a second step, a set of test cases is created that verifies all terms of the turbulence model with a chain of analytical solutions. 

The performance of the k-eps model in stable stratified fluids was tested by comparison with laboratory experiments. The zero pressure gradient wall boundary layer was compared with cooled bottom wind tunnel experiments. For the layer where the MONIN-OBUKHOV-similarity hypothesis applies, the model results can be improved by supplementing the turbulence model with a stability function. The standard k-eps model is able to reproduce the turbulence collapse, when applied to the free and plain shear layer. Free shear layers are very sensible to inflow conditions, therefore the relevance of this comparison has to be judged carefully.

In a final step the model is applied to flow situations that are typical for erosion and deposition in the estuary. For the erosion process an estimate of accuracy is found by comparing calculations with and without stability function. In combination with the erosion model an error of 15% in the bottom friction results in a ca. 40% error in the erosional mass flux. The flow deposits sediment when slowing down around slack water. In the test case a transient formation of turbulence bubbles is calculated. The frequency of this bubbling is lower than the tidal frequency. This flow is no longer comparable with existing experiments, especially stationary channel flows. The calculated re-ignition of turbulence starting from the rough bottom would explain the episodic nature of deposition observed in the Weser estuary.