A study on the initiation of saltation in the model of wind-blown sand transport considering the effect of turbulence

Turbulence plays an important role in the transport of wind-blown sand. If the model of wind-blown sand transport considering the effect of turbulence is to be established, the influence of turbulence needs to be introduced into the four sub-processes of saltation, namely (1) aerodynamic entrainment, (2) the subsequent trajectories of saltating particles, (3) the collision of particles with the soil surface and the subsequent splashing of surface particles into the fluid stream, and (4) the modification of the wind profile through momentum transfer between the wind flow and saltating particles. In this paper, turbulence is introduced into two models predicting the first and the third sub-processes of saltation by the aerodynamic drag force and the creep velocity of surface particles respectively. The effects of turbulence on the two sub-processes are discussed. Our results show that turbulence has an important effect on aerodynamic entrainment. That is, when the wind velocity exceeds the threshold velocity, about 20% of all surface particles are unable to lift-off from the bed surface. The effect of turbulence on aerodynamic entrainment is mainly caused by large-scale turbulent motions. The model of number of lifting sand particles caused by aerodynamic drag force is modified by introducing a lift-off rate sigma\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\sigma$$\end{document} (i.e., the ratio of the number of actually lifting sand particles judged by our theory to the total number of lifting sand particles judged by existing theory), which is N-a = sigma x zeta rho(mu(2)(tau)- mu(2)(c)), where sigma is defined as the lift-off rate, u(tau) is the friction wind velocity, u(c) is the threshold velocity, rho is the air density, and zeta is the empirical constant. In addition, the results show that the cumulative distribution of creep velocity under the direct action of turbulence (which can be characterized by the SGompertz distribution) has little effect on the velocity distributions of rebound particles and ejected particles.