Accurate vertical profiles of turbulent flow in z‐layer models

Three-dimensional hydrodynamic z-layer models, which are used for simulating the flow in rivers, estuaries, and oceans, suffer from an inaccurate and often discontinuous bottom shear stress representation, due to the staircase bottom. We analyze the governing equations and clearly show the cause of the inaccuracies. Based on the analysis, we present a new method that significantly reduces the errors and the grid dependency of the results. The method consists of a near-bed layer-remapping and a modified near-bed discretization of the k-epsilon turbulence model. We demonstrate the applicability of the approach for uniform channel flow, using a schematized two-dimensional vertical model and for the flow over a bottom sill using the Delft3D modeling system. Key Points Analyzing discretization errors in z-layer models (staircase bottom problem) Near-bed layer remapping for adequate discretization of vertical diffusion Modified near-bed discretization for vertical k-epsilon turbulence model