On the representation of bottom shear stress in z-layer models

F. Platzek, G.S. Stelling, J.A. Jankowski, R. Patzwahl

Abstract. Bottom friction plays an important role in modelling river flows. In three-dimensional (3D) models, the vertical discretization is commonly based on σ-layers or z-layers. In this paper we focus on a well-known problem encountered when applying z-layers: local truncation errors in the computation of bottom shear stress and near-bed turbulence along a sloping bottom as e.g. in the case of 3D river simulations. This problem stems from the ‘staircase’ representation of the bottom and results in difficulties in the computation of morphological changes. We consider uniform channel flow and analyze the influence of variations in near- bed layer thickness on the local truncation errors in the vertical diffusion term. Application of both an algebraic turbulence model, based on a prescribed mixing-length and the standard k-ε turbulence model to compute the eddy viscosity is investigated. We consider two approaches that reduce the local truncation errors and inspect their applicability for more general flow situations.

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Reference: F. Platzek, G.S. Stelling, J.A. Jankowski, R. Patzwahl (2012) On the representation of bottom shear stress in z-layer models In: Proceedings of HIC 2012 – 10th International Conference on Hydroinformatics, Hamburg, Germany, July 14-18, 2012.