Part I : <Emphasis Type="Italic">a priori</Emphasis> study of erosion and deposition with large eddy simulation of turbulent flow over multiple 2D sandy Gaussian hills

The micro-scale prediction of sand trapping or take-off over hilly terrains is a crucial issue in semi-arid regions for soil depletion. In this context, large eddy simulations around one or several hills are performed in order to provide statistical parameters to characterize the flow at micro-scales and provide data for mesoscale modelling. We focus on the determination of recirculation zones since they play an important role in solid particle erosion or entrapment. A new wall modeling adapted from Huang et al. (J Turbul 17:1–24, 2016) for rough boundary layers is found to improve the prediction of the recirculation zone length downstream of an isolated hill and is used for all the numerical cases presented here. A geometrical parameterization of the recirculation zones is proposed. When the recirculation region is assumed to have an ellipsoidal shape, the total surface of the recirculation can be obtained from this new parameterization and easily extrapolated to more general dune configurations. Numerical results are compared with experiments performed in our laboratory (Simoëns et al. in Procedia IUTAM 17:110–118, 2015) and good agreement is achieved. We explore general aerodynamic cases deduced from the urban canopy scheme of Oke (Energy Build 11:103–113, 1988). In this scheme the momentum and mass exchange between the upper layer and the space between hills is sorted according to the streamwise hill spacing within three basic cases of skimming, wake or isolated flow. The study of the recirculation zones, the mean velocity and Reynolds stress profiles around an isolated or two consecutive hills with different distances shows that the double hill configuration with 3H separation behaves as much as a whole to the upcoming flow. The vortex formed between the crests does not strongly affect the overall evolution of the outer flow. By an a priori prediction of the preferential zones of erosion and accumulation of fictive particles, it is shown that isolated dunes present more deposition and less erosion than two-hill configurations. The results presented in this study will be discussed in the presence of Lagrangian transport of sand particles above 2D Gaussian hills in future work.