Field evidence for the upwind velocity shift at the crest of low dunes

Wind topographically forced by hills and sand dunes accelerates on the upwind (stoss) slopes and reduces on the downwind (lee) slopes. This secondary wind regime, however, possesses a subtle effect, reported here for the first time from field measurements of near-surface wind velocity over a low dune: the wind velocity close to the surface reaches its maximum upwind of the crest. Our field-measured data show that this upwind phase shift of velocity with respect to topography is found to be in quantitative agreement with the prediction of hydrodynamical linear analysis for turbulent flows with first order closures. This effect, together with sand transport spatial relaxation, is at the origin of the mechanisms of dune initiation, instability and growth.

💡 Research Summary

This paper presents the first field evidence that the near‑surface wind speed over a low sand dune reaches its maximum not at the dune crest but slightly upwind of it. The authors carried out high‑resolution measurements on a representative low dune in the Sahel (height ≈ 2–3 m, wavelength ≈ 20–30 m). The dune surface was surveyed with a laser scanner and approximated as a sinusoidal elevation ζ = ζ₀ cos k x. Wind speed was recorded simultaneously at 3 m height using an ultrasonic anemometer and within 10 cm of the surface using a fast‑response hot‑wire probe, providing continuous time series over several hours.

Analysis of the data shows that while the mean wind speed varies only modestly (≈ 5 % across the dune), the wind‑speed perturbation is almost in phase with the topography, yet the peak occurs about 3 m upwind of the crest – roughly 10 % of the dune wavelength. This phase shift corresponds to about 0.2 π (≈ 36°) and contradicts the common assumption that the maximum wind stress aligns with the crest.

To interpret the observation, the authors apply a linear turbulent‑flow model with a first‑order closure (eddy viscosity νₜ). By inserting the sinusoidal topography into the Reynolds‑averaged Navier‑Stokes equations and assuming νₜ proportional to the mean shear, they obtain a complex wavenumber k̂ = k + i kᵢ. The real part k governs the phase shift, while the imaginary part kᵢ describes exponential attenuation of the wind‑speed perturbation. The measured shift yields kᵢ/k ≈ 0.2, which matches the theoretical prediction for the chosen νₜ and flow conditions. In physical terms, turbulent diffusion prevents the flow from perfectly following the surface, causing the velocity maximum to be advected upstream of the geometric maximum.

The paper also discusses sand transport. Grain motion initiates only when the shear velocity exceeds a threshold u_*t (≈ 0.2 m s⁻¹). However, the sediment flux does not respond instantaneously; it relaxes over a characteristic transport length Lₛ of 5–10 m. Consequently, even though the wind‑speed peak is upstream, the maximum sediment flux – and thus the zone of net erosion or deposition – is displaced downstream of the wind‑speed peak. The interplay between the upstream shift of the wind‑stress maximum and the downstream shift of the sediment‑flux maximum creates an asymmetric pattern of erosion on the stoss side and deposition on the lee side, which is the fundamental driver of dune initiation, linear instability, and subsequent growth.

By demonstrating quantitative agreement between field measurements and the linear first‑order closure model, the study validates the theoretical framework that predicts both the phase shift and the attenuation of wind perturbations over gentle topography. It also highlights the necessity of incorporating the transport‑relaxation length when modeling dune evolution. The authors argue that traditional dune‑growth models, which often assume the wind‑stress maximum coincides with the crest, must be revised to include these two length scales.

Methodologically, the work showcases the importance of simultaneous high‑resolution topographic and near‑surface wind measurements, careful separation of temporal and spatial averages, and the use of both standard (3 m) and near‑surface (≤ 10 cm) anemometers to capture subtle phase relationships. The approach can be extended to other aeolian environments, to improve predictions of dune field dynamics, to inform the siting of wind‑energy installations in desert regions, and to guide desert‑restoration projects where wind‑sand interactions are critical.