Improved analytical model for the relaxation process of aeolian sand transport

The process from the initial sand movement to sand flux saturation is described as the relaxation of aeolian sand transport. For this relaxation process, most existing models distinguish the conditions with and without upwind sand flux, therefore lacking in generality. An improved analytical model is proposed in this paper, which incorporates the phenomena of "overshoot" and "equilibrium" and the concept of the region of initiation by fluid, and is able to unify the cases with and without upwind sand flux. Within the proposed model, a new definition of the saturation length is proposed based on the analogy between two damping oscillation models, and its constancy is physically interpreted and verified with wind tunnel experimental data. In comparison with the existing models, the proposed model agrees better with the measurements of the process of sand transport, thereby shedding light on the understanding of aeolian sand transport under complex circumstances.