Numerical model of spherical particle saltation in a channel with a transversely tilted rough bed

This paper deals with the numerical simulation of spherical particle saltation in a channel with a rough transversely tilted bed. The numerical model presented is based on the 3D model of spherical particle saltation developed by the authors, which takes into account the translational and rotational particle motion. The stochastic method and the concept of a contact zone were used for the calculation of a particle trajectory and its dependence on the bed lateral slope, particle diameter, and shear velocity. The effect of the bed lateral slope results in a deviation of the particle trajectory from the downstream direction. Some examples of the calculation are presented. The trajectories of the saltating particles starting their movements from one point were calculated and it was shown that they are of random character and together create a bundle or fascicle of trajectories. It was found that the centrelines of the bundles can be approximated by the straight lines for low and moderate values of the bed transverse slope, i.e. slopes less than 20°. The angle of deviation of the centreline from the downstream direction increases when the bed lateral slope and/or the particle diameters increase. However, with increasing shear velocity, the deviation angle decreases. Due to the lateral bed slope the particles are sorted according to their size, and the criteria for sorting particles were defined. An example of the particle sorting was calculated and the separable and non-separable regions were determined.