# Optimal array of sand fences

## TL;DR

This study uses Computational Fluid Dynamics to determine the optimal design of sand fence arrays for soil protection, balancing material cost and effectiveness in reducing wind shear velocity.

## Contribution

It introduces a quantitative CFD-based approach to optimize sand fence arrays considering porosity, spacing, and height, advancing beyond empirical methods.

## Key findings

- Optimal fence height is around 50 cm for minimal material use.
- Fences of about 1.25 m height are most costly and less efficient.
- Flow profiles and wind shear reduction depend on fence parameters.

## Abstract

Sand fences are widely applied to prevent soil erosion by wind in areas affected by desertification. Sand fences also provide a way to reduce the emission rate of dust particles, which is triggered mainly by the impacts of wind-blown sand grains onto the soil and affects the Earth's climate. Many different types of fence have been designed and their effects on the sediment transport dynamics studied since many years. However, the search for the optimal array of fences has remained largely an empirical task. In order to achieve maximal soil protection using the minimal amount of fence material, a quantitative understanding of the flow profile over the relief encompassing the area to be protected including all employed fences is required. Here we use Computational Fluid Dynamics to calculate the average turbulent airflow through an array of fences as a function of the porosity, spacing and height of the fences. Specifically, we investigate the factors controlling the fraction of soil area over which the basal average wind shear velocity drops below the threshold for sand transport when the fences are applied. We introduce a cost function, given by the amount of material necessary to construct the fences. We find that, for typical sand-moving wind velocities, the optimal fence height (which minimizes this cost function) is around $50\,$cm, while using fences of height around $1.25\,$m leads to maximal cost.