3D mathematical model of spherical particle saltatory movement in open channel with rough bed

Abstract eng:
One of the main modes of bed load transport is saltation when particles hop up from the bed and follow ballistic-like trajectories. Mathematical models of saltation are mostly two-dimensional although the particle motion is actually three- dimensional. The aim of the present study is development of the 3D mathematical model of solid particle saltatory motion over rough bed in an open channel. The motion of the particle is described by the equation of motion of particle mass centre and by equation of the particle rotation around particle centre. Gravitational force, buoyancy force, drag force, Basset history force, Magnus force and forces due to added mass and fluid acceleration are taken into account together with the mean velocity profile for turbulent flow in open channel with rough boundary. The model allows calculating 3D trajectories of the particle, statistical characteristics of saltation, such as mean length and height of the trajectory, longitudinal velocity and also the lateral dispersion of the particles.

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