Giant aeolian dune size determined by the average depth of the atmospheric boundary layer

Depending on the wind regime(1,2), sand dunes exhibit linear(3,4), crescent-shaped or star-like forms(5) resulting from the interaction between dune morphology and sand transport(6-8). Small-scale dunes form by destabilization of the sand bed(9-11) with a wavelength (a few tens of metres) determined by the sand transport saturation length(11-13). The mechanisms controlling the formation of giant dunes, and in particular accounting for their typical time and length scales, have remained unknown. Using a combination of field measurements and aerodynamic calculations, we show here that the growth of aeolian giant dunes, ascribed to the non-linear interaction between small-scale superimposed dunes(4,10,14,15), is limited by the confinement of the flow within the atmospheric boundary layer(16,17). Aeolian giant dunes and river dunes form by similar processes, with the thermal inversion layer that caps the convective boundary layer in the atmosphere(18) acting analogously to the water surface in rivers. In both cases, the bed topography excites surface waves on the interface that in turn modify the near-bed flow velocity. This mechanism is a stabilizing process that prevents the scale of the pattern from coarsening beyond the resonant condition. Our results can explain the mean spacing of aeolian giant dunes ranging from 300m in coastal terrestrial deserts to 3.5 km. We propose that our findings could serve as a starting point for the modelling of long-term evolution of desert landscapes under specific wind regimes.