Numerical and experimental simulation of the wind velocity profile with a blowing sand cloud

Describing the wind velocity profiles modified by blown sand movement is one of the central issues in studying the wind-sand interaction in a blowing sand cloud. This paper develops the mathematical models of the wind-sand interaction, taking the saltating cloud as fluidized flow. The force exerting on the airflow by saltating particles is expressed in terms of the drag coefficient of the fluidized particle flow. The drag coefficient is introduced by modifying the expressions for the drag coefficient of the fluidized liquid-particle flow obtained by previous researchers with a correction factor. The saltation boundary layer is divided into an inner boundary layer in which the saltating particles exert significant force on the airflow, and an outer boundary layer in which saltating particles exert insignificant force on the airflow, but the out layer is affected by the inner boundary layer. Expressions for the wind velocity profiles of the inner and outer boundary layers are developed. The simulated wind velocity profiles based on the velocity and concentration profiles obtained from wind tunnel tests are compared to those directly measured. The both show reasonably good agreement. It is revealed that the wind profiles with saltation cloud are up-convex curves on the log-linear plot rather than the straight lines of the clean wind. The up-convexity of the curves increases as wind velocity increases. The wind velocity profiles above the saltation boundary layer approach the logarithmic law. Our results confirm the existence of the so-called Bagnold’s kink, which is found to be higher with increasing wind velocity and lower with increasing particle size. It is suggested that the wind shear velocity with a saltating cloud reflects the response of airflow to the ground surface and the saltation layer.