Attraction and repulsion of dunes under reversing winds

Abstract

Linear dunes are easily recognizable in the field due to their periodic pattern. In zones of high sand availability, this periodicity results from  the initial wavelength at which a sand bed destabilize, via a coarsening mechanism induced by migration and collision during dune growth. In zones of low sand availability, linear dunes may however exhibit a periodic pattern despite a non-erodible bed in the interdune areas. This property may be inherited from the conditions of formation at the edges of dune fields (Gadal et al., 2020), but it can also be controlled by flow perturbation induced by dune topography. To illustrate this mechanism, we focus here on how dunes interact with each other over long distances through their feedback on flow.We use the ReSCAL dune model (Narteau et al., 2009, Rozier and Narteau, 2014), which couples a cellular automaton model of sediment transport and a lattice gas model of turbulent fluid flow. To eliminate the contribution of transverse flows, migration and sediment exchanges between dunes, we work in 2D with a pair of isolated dunes under perfectly symmetric reversing wind conditions. Whatever the initial spacing between the dunes, simulations show they either attract or repel each other, to eventually converge towards the same interdune distance, λD. This distance increases with the period, ΔT, of wind reorientation with a dependence on dune size and wind strength. We demonstrate that the relative dune migration (i.e., attraction or repulsion) is primarily governed by dune shape during the wind cycle. This shape  modulates the cumulative shear stress on the stoss slope of the downwind dune located in the turbulent wake of the upwind one. As a consequence, three regimes can be observed according to ratio between the wind period, ΔT, and the characteristic dune time, Tc. For small  ΔT/Tc-values, the shape of the dune remains almost unchanged, the crest reversal distance is small and there is almost no migration during a single wind period. For high ΔT/Tc-values, there is a complete crest reversal, with fully established slip face and significant migration during a single wind period. In between, an intermediate regime is dominated by crest reversal.Our results show that dunes can interact over long distances through their feedback on the flow. This has implications for all wind regimes, for modulating dune migration and collisions under unidirectional wind regimes but also under multidirectional wind regimes in order to select the dune wavelength under conditions of low sand availability.