Plant Streamlining and Hydraulic Resistance Model for Vegetated Flows Based on the Finite Element Method

When submerged during higher discharges, riparian vegetation affects the hydrodynamics and thus the sediment transport and morphodynamics of rivers. The fluvial drag on flexible riparian vegetation and the resulting hydraulic resistance depend on the plants’ deformation at the actual flow condition. Empirically derived relationships allowed the consideration of the streamlining of plants in existing models. However, if aiming for physics-based reconstruction of vegetated flows in hydrodynamic-numerical models, the mechanics related to plant deformation need to be adequately reconstructed.

We present a plant streamlining and flow resistance model for vegetated flows which is based on the finite element method and the first order structural analysis. The plant geometry and the mechanic properties are presented by cylindrical stem and branch elements of varying thickness and by the elastic modulus and shear modulus as functions of the stem or branch diameter. The coefficients of skin friction and form drag of the cylindrical elements are used as calibration parameters. The mechanical properties were measured in bending and torque experiments on branches/stems of different willow species (Salix alba, Salix purpurea, and Salix viminalis). The drag forces on individual plants were determined with a horizontal carriage with a force transducer. The use of a 5 m wide flume with a discharge up to 10 m³s^-1 allowed the installation and testing of 3 year old plants, which developed a shrubby growth habit after coppicing. Before the experiment, the plant geometry was measured photogrammetrically; branch and stem diameters were measured with a caliper. During the experiment, eventually emerging branches were surveyed with stereo-photogrammetry to assess their dislocation. The measured drag forces served for model calibration; measured dislocations were used for validation of the model.

Despite the application of the first order analysis the model could satisfyingly reproduce the measured drag forces and plant deformations. The model now enables the calculation of a plant’s flow resistance for different flow conditions and the definition of the flow resistance as a two-parametric function of water depth and flow velocity. This method is expected to allow the consideration of vegetation effects in a two-dimensional hydrodynamic-numerical model while maintaining reasonable computing times.