Aeolian sand transport: Scaling of mean saltation length and height and implications for mass flux scaling

TL;DR

This study investigates the scaling laws of saltation length and height in aeolian sand transport, revealing insensitivity to wind speed and grain size, and challenges existing theoretical models and scaling assumptions.

Contribution

It demonstrates that a rebound-based saltation model aligns with measurements and suggests splash ejection does not significantly influence saltation kinematics.

Findings

Saltation length and height are insensitive to wind speed and grain size.

Rebound-only saltation model matches experimental data.

Supports flux scaling models that ignore splash ejection effects.

Abstract

Wind tunnel measurements of the mean saltation length $L$ and of different proxies of the mean saltation height $H$ in saturated aeolian sand transport indicate that $L$ and $H$ are relatively insensitive to both the wind speed and grain diameter $d$. The latter result is currently unexplained and contradicts the theoretical prediction $L\propto H\propto d$. This prediction is based on the assumption that the characteristic velocity $\sqrt{\tilde gd}$ of bed grains ejected by the splash of an impacting grain controls the average saltation kinematics. Here, we show that a recent analytical saltation model that considers only rebounds of saltating grains, but neglects splash ejection, is consistent with the measurements. The model suggests that the buffer layer of the inner turbulent boundary layer, which connects the viscous sublayer with the log-layer, is partially responsible for the insensitivity of $L$ and $H$ to $d$. In combination, the measurements and model therefore indicate that splash ejection, though important to sustain saltation, does not significantly affect the average saltation kinematics. This finding represents a strong argument against the Ungar and Haff (1987)-scaling and in favor of the Dur\'an et al. (2011)-scaling of the saturated saltation mass flux, with implications for ripple formation on Mars. Furthermore, it supports the recent controversial claim that this flux is insensitive to soil cohesion.