CFD simulation of the wind field over a terrain with sand fences: Critical spacing for the protected soil area

Sand fences are often erected to reduce wind speed, prevent aeolian soil erosion, and induce sand deposition and dune formation in areas affected by sand encroachment and desertification. However, the search for the most efficient array of fences by means of field experiments alone poses a challenging task given that field experiments are affected by weather conditions. Here we apply Computational Fluid Dynamic simulations to investigate the three-dimensional structure of the turbulent wind field over an array of fences of different sizes, porosity and spacing. Our goal is to perform a quantitative analysis of this structure in the absence of saltation or suspension transport, as first step toward the development of a continuum simulation of the aeolian soil in presence of the fences. We find that the area of soil protected against direct aerodynamic entrainment has two regimes, depending on the spacing $L_x$ between the fences. When $L_x$ is smaller than a critical value $L_{xc}$, the wake zones associated with each fence are inter-connected (regime A), while these wake zones appear separated from each other (regime B) when $L_x$ exceeds this critical value of spacing. The system undergoes a second order phase transition at $L_x = L_{xc}$, with the cross-wind width of the protected zone scaling with $\left[{1-{L}_x}/{L}_{xc}\right]^\beta$ in regime A, with $\beta \approx 0.32$. Our findings have implication for a better understanding of aeolian transport in the presence of sand fences, as well as to develop optimization strategies for measures to protect soils from wind erosion.