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

Depending on the wind regime, sand dunes exhibit linear, crescent-shaped or star-like forms resulting from the interaction between dune morphology and sand transport. Small-scale dunes form by destabilization of the sand bed with a wavelength (a few tens of metres) determined by the sand transport saturation length. 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 nonlinear interaction between small-scale superimposed dunes, is limited by the confinement of the flow within the atmospheric boundary layer. Aeolian giant dunes and river dunes form by similar processes, with the thermal inversion layer that caps the convective boundary layer in the atmosphere 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 nearbed 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 300 m 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. Aeolian dune fields generically present two well-separated length scales (Fig. 1). The smallest superimposed bed-forms have been explained by a linear aerodynamic instability the initial wavelength ls of which is related to the length needed for sand transport to reach equilibrium with the wind strength and are thus called ‘elementary dunes’. Tentative explanations for the formation of giant dunes have proposed specific dynamics associated with the different types of dunes, thought of as isolated objects. In contrast, we hypothesize that the emergence of giant transverse, longitudinal and star dunes results from collective processes, the symmetries of the different patterns resulting from those of the wind rose. Indeed, both smalland large-scale dunes share the same symmetries under a common wind regime (Fig. 1). Furthermore, the different types of giant dunes exhibit the same characteristic wavelength lg, of the order of a kilometre (Fig. 1), and feature superimposed structures the avalanche slip faces of which show separations on the same scale ls. These commonalities suggest that the key dynamical processes forming giant dunes are not to be looked for in the shape of the pattern but in the understanding of the characteristic time and length scales resulting from their formation. We propose a novel collective mechanism in which the average structure of the atmosphere determines the giant scale. The dryness of deserts results primarily from the overall stability of the atmosphere in anticyclonic regions. The stable stratification of the free atmosphere, characterized by the Brunt-Vaisala frequency N~ ffiffiffiffiffiffi g h dh dz q (where g is the gravity and h is the virtual potential temperature) for restoring vertically displaced air parcels, prevents the development of turbulence. The temperature gradient c~dh=dz<4 K km is largely independent of the location and the season (Supplementary Information 1). In winter, the heat flux from the surface is insufficient to produce convection, so the atmospheric boundary layer is stably stratified almost down to the ground (Fig. 2b). In warmer seasons, however, a convective (well-mixed) boundary layer forms, in which the temperature and the horizontal wind velocity are roughly homogeneous. A thermal inversion (capping) layer, characterized by a jump in air density Dr separates stable and unstable layers. The shear stress t decreases linearly with height in the well-mixed layer, vanishes at the capping altitude H and remains null in the free atmosphere. The base flow is thus similar to that in a river. Furthermore, gravity waves can propagate at a speed c on this atmospheric interface, as they do along the free surface of a river. Introducing the wavenumber k~2p=l, the surface-wave dispersion relation can be approximated by: