Aeolian transport over polydisperse granular beds with a novel splash model

We present a splash model that explicitly accounts for arbitrary particle size distributions on polydisperse granular beds. This model enables a direct investigation of how bed size heterogeneity governs particle rebound and ejection dynamics. We find that increasing size dispersion suppresses horizontal momentum transfer during rebound while enhancing vertical rebound efficiency, leading to steeper rebound trajectories. For ejection, higher dispersion reduces the number of particles dislodged per impact but increases their launch velocities, reflecting a trade-off between entrainment frequency and individual particle energy. When integrated into a transport model, these effects are translated into macroscale changes in sand flux, causing both the flux coefficient and the dynamic threshold to vary systematically with bed dispersion. By altering the characteristic diameter into an airborne equivalent, we find a nearly constant threshold across different beds, providing a physically intrinsic threshold for saltation initiation. Meanwhile, we demonstrate that the 90th percentile diameter of bed particles is a superior scaling parameter while discussing the coefficient of the flux, yielding a direct link from the particle rebound dynamics to the transport law. The absence of a universal characteristic diameter implies a non-single-diameter-parameter transport law for polydisperse beds. A semi-empirical model for the flux law is then proposed, which incorporates the effects of bed dispersion.