A scaling law for aeolian dunes on Mars, on Earth and subaqueous ripples

The linear stability analysis of equations governing the evolution of a flat sand bed submitted to a shearing flow predicts that the wavelength $\lambda$ at which the bed destabilises to form dunes should scale with the drag length $L_{drag} = \frac{\rho_s}{\rho_f} d$. We tested this scaling law using measurements performed in water (subaqueous ripples), in air (aeolian dunes) and in the CO$_2$ martian atmosphere (martian dunes). The main difficulty is to determine the diameter of saltating grains on Mars. A first estimation comes from photographs of aeolian ripples taken by the rovers Opportunity and Spirit, showing grains whose diameters are smaller than on Earth dunes. In addition we calculate the effect of cohesion on the saltation threshold. It confirms that the small grains visualised by the rovers should be (or have been) grains experiencing saltation. Finally, we show that, within error bars, the scaling of $\lambda$ with $L_{drag}$ holds over almost five decades. We conclude with a discussion on the time scales and velocities at which these bed instabilities develop and propagate on Mars.