Comparison of hydrodynamics simulated by 1D, 2D and 3D models focusing on bed shear stresses

Abstract

For centuries, scientists have been attempting to map complex hydraulic processes to empirical formulas using different flow resistance definitions, which are further applied in numerical models. Now questions arise as to how consistent the simulated results are between the model dimensions and what influence different morphologies and flow conditions have. For this reason, 1D, 2D and 3D simulations were performed and compared with each other in three study areas with up to three different discharges. A standardized, relative comparison of the models shows that after successful calibration at measured water levels, the associated 2D/1D and 3D/1D ratios are almost unity, while bed shear stresses in the 3D models are only about 62-86% of the simulated 1D values and 90-100% in the case of 2D/1D. Reasons for this can be found in different roughness definitions, in simplified geometries, in different calculation approaches, as well as in influences of the turbulence closure. Moreover, decreasing 3D/1D ratios of shear stresses were found with increasing discharges and with increasing slopes, while the equivalent 2D/1D ratios remain almost unchanged. The findings of this study should be taken into account, particularly in subsequent sediment transport simulations, as these calculations are often based on shear stresses.