{'fraction_non_alphanumeric': 0.021798365122615803, 'fraction_numerical': 0.004541326067211626, 'mean_word_length': 4.924731182795699, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Lagrangian Model for a Single Saltating Grain in the Near-Wall Region of an Open-Channel Flow

Abstract A mathematical model for the continuous saltation of a particle near the granular bed in an open-channel flow is developed in detail. The model is based on the Lagrangian equations governing particle motion, and it takes into account the following forces: drag, lift, gravitation, virtual mass and the force responsible for particle-particle interactions. A model of particle-particle collisions is developed and used to determine the mean impulsive force acting upon a particle flowing and rebounding from the channel bed. The model can simulate the continuous saltation trajectories of a single particle in the near-bed region of turbulent flows, in which particle motion is controlled by collisions. The model has been calibrated and verified with available published data in a rather wide range of grain sizes from 0.53 mm to 15 mm. All parameters, such as lift, drag, restitution, friction coefficients and roughness height, have been set on the basis of a reanalysis of these published data.