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.
Highlights
Good agreements with average differences below 1 cm between measurements and simulations were obtained for C.1 (Figure 2a—solid lines) for all numerical models excluding the inlet area between distance 10.5 m and 9.5 m, where maximum differences of 3 cm occurred, which are related to issues of the physical model setup
Comparable results were found in the case of 3D models, where similarities occur between the profiles of the near-wall tangential flow velocities and bed shear stresses, with a maximum (10.2 Nm−2 ) on the left bank and a minimum (0.4 Nm−2 ) on the right bank
The application of numerical models in hydraulic engineering has become routine over recent decades, resulting in numerous published studies
Summary
The interaction between gravity and flow resistance is the mechanism underlying both fundamental hydraulic processes and river morphological changes [1,2].Following Powell [2], flow resistance is composed of the boundary resistance, vegetation resistance [3,4,5,6,7], channel resistance [8,9,10,11,12], spill resistance [13,14,15,16,17,18] and sediment transport resistance [19,20,21,22,23,24,25]and affects bed shear stress and energy dissipation. The challenge in river hydraulics is to achieve the complexity of flow resistance through physical relationships and engineering approaches to gain knowledge about flow velocities, water depths, bed shear stresses and energy losses in channels [2]. Classical approaches for the calculation of flow variables under the influence of flow resistance are the equations of Darcy–Weisbach, Chezy and Manning–Strickler [26,27,28]. These are empirical methods, which were developed from observations in channels in which the flow resistance was determined almost exclusively from the boundary of the flow—much like a block sliding down a plane [29].
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