Quantifying geometry-induced resistance asymmetry in a Tesla-type horizontal weir using the braid index

A series of horizontally deployed structures was designed instead of a vertical dam or weir to control flows in open channels. Conventional vertical dams and weirs have been employed to prevent saltwater from intruding into the channel bottom layer and stormwater from flooding river–estuary systems. We used the geometry of the Tesla valve to induce and enhance directional flow asymmetry in the open channel, designating this structure as a Tesla-type horizontal weir. A bidirectional pattern index (BPI) was designed by modifying a braid index to quantify the deployment patterns and arrangements of structures for practical design. Based on the BPI, a series of numerical simulations was performed with the k−ω shear stress transport model to solve the governing equations. The efficiency of generating flow asymmetry was quantified by the mean difference in the water level between the upstream and downstream areas over one cycle, a metric we termed the asymmetric flow efficiency index. By comparing the indices, we observed a significant linear relationship. Therefore, the proposed asymmetric index can be a practical quantitative measure for generating asymmetric flows, along with a design index for assessing the morphological patterns of a channel.