Rill flow velocity and resistance law: A review

Rills caused by runoff concentration on erodible hillslopes generally have very irregular longitudinal profiles and cross-section shapes. Rill erosion directly depends on the hydraulics of flow within the rills which may differ greatly from that in larger and regular channels like streams or rivers. At first, in this paper, a review of the two different approaches to estimate rill flow velocity, based on flow regime and flow resistance laws, is presented. Recent advances in measurements of rill geometry by the three-dimensional photo-reconstruction (3D-PR) technique, which allows one to obtain a Digital Terrain Model (DTM) by low-altitude aerial and terrestrial photogrammetry, are also discussed. Indeed, information on rill geometry is also necessary to estimate flow velocity and depth using flow resistance equations. Then, the results of related laboratory and field investigations carried out from 1984 to 2022 are reported. In particular, the review was developed considering the studies conducted investigating the different components of rill flow resistance due to grain resistance, morphological resistance (step-pool), and sediment transport. Moreover, a brief mention of the slope threshold, equal to 18%, determining differences in hydraulic and sediment transport variables, is done. Also, an analysis is developed to demonstrate that a theoretical rill flow resistance law has been erroneously presented as an example of spurious correlation. Finally, some research needs on rill flow hydraulics are highlighted.