Comparison and Analysis of Flow Hydrodinamics Through a Meander Using a Langrangian and Eulerien Formulation in Flow 3D

The evolution of a meander in a river course results from an erosion process due to the shear forces created by a transverse secondary flow. The characteristics of such flow are three dimensional, may involve a density current and are associated with sediment transport and mobilization. Such a situation may impact greatly dwellings located along a river floodplain. La Dorada, Caldas has been affected by such problematic. In order to design mitigation measures for the erosion process occurring in the region, two field campaigns were completed on January and May 2018 including topographical and bathymetric surveys using Topcon GR5 DGPS and Sontek River Surveyor ADCP over 5km of the River. In addition, river bed samples were retrieved in order to characterize the channel roughness. Using a digital elevation model (DEM) and the field data, a three dimensional flow model was prepared and calibrated. The modelling process was intended completed to determine maximum critical velocity and flow depth. In fluid dynamics, Eulerian conceptualization of the flow is determined through the evaluation of a control volume or frame of reference, while Lagrangian formulation follows displacement of fluid particles along its flow path determining the overall flow field. In principle both formulations should yield similar results. The Flow 3D commercial software allows for both Lagrangian and Eulerian simulation based on a finite difference scheme. This specific study strived to compare the two mathematical formulations in 3 dimension with a RAN turbulent turbulence model considering equivalent conditions, observing its impact on channel depth and maximum simulated velocities. The results confirmed the presence of anticipated secondary flow through the meander and quantified the differences between the simulated hydraulic variables in both formulations. Furthermore, the study established the result differences and limitations between the Lagrangian and Eulerian mathematical formulations and hypothesis.