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

The linear stability analysis of the equations governing the evolution of a flat sand bed submitted to a turbulent shear flow predicts that the wavelength $\lambda$ at which the bed destabilises to form dunes should scale with the drag length $L_{\rm drag} = \frac{\rho_s}{\rho_f} d$. This scaling law is tested using existing and new measurements performed in water (subaqueous ripples), in air (aeolian dunes and fresh snow dunes), in a high pressure CO$_2$ wind tunnel reproducing conditions close to the Venus atmosphere and in the low pressure CO$_2$ martian atmosphere (martian dunes). A difficulty is to determine the diameter of saltating grains on Mars. A first estimate 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 and viscosity on the dynamic and static transport thresholds. It confirms that the small grains visualised by the rovers should be grains experiencing saltation. Finally, we show that, within error bars, the scaling of $\lambda$ with $L_{\rm drag}$ 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.