A semi coupled shallow water model for vertical velocity distribution in an open channel with submerged flexible vegetation

Flow-vegetation interactions modify the instream roughness and flow characteristics in the river and estuaries. This study proposes a new quasi three-dimensional hydrodynamic framework to compute the vertical velocity profile in an open channel having submerged flexible vegetation. A modified form of two-dimensional depth-averaged shallow water equations coupled with vegetal drag forces is derived and applied in the simulation. The explicit second-order accurate TVD McCormack predictor-corrector finite difference method with operator splitting technique is used to solve the governing equations in MATLAB. The TVD approach is robust and gives accurate results free from numerical oscillations. The bending profile of the flexible stems under various flow events is calculated from the cantilever beam theory. The vertical velocity profile in the vegetation layer and the free water layer is estimated from Reynold's stress equation and Shannon's entropy theory. The present model is used to replicate some popular experimental test cases. Results indicate a conservative and robust model performance under different flow conditions and patch density. Quantitative analysis of the predicted results is carried out using two statistical indices and found satisfactory.