# Incipient bedforms in a bidirectional wind regime

## TL;DR

This study extends linear stability analysis to bidirectional wind regimes, predicting bedform patterns and wavelengths, validated by water flow experiments, enhancing understanding of dune formation in seasonal wind conditions.

## Contribution

It introduces a three-dimensional model for bedform formation under bidirectional winds, expanding previous unidirectional analyses and including experimental validation.

## Key findings

- Transition from transverse to oblique or longitudinal patterns depends on transport ratio and divergence angle.
- Predicted pattern wavelength varies with flow strength and angle, decreasing near transition angles and increasing at low winds.
- Experimental data supports the model for transverse bedforms but shows discrepancies for longitudinal ones.

## Abstract

Most terrestrial sand seas form at `horse' latitudes, where the wind direction exhibits seasonal variation. Here, we extend the two-dimensional linear stability analysis of a flat sand bed associated with a unidirectional wind to the three-dimensional case in order to account for multidirectional wind regimes. Focusing on the simplest case of bidirectional flow regimes, we show that the transition from transverse to oblique or longitudinal patterns is controlled by the transport ratio and the divergence angle between the two flows. Our predictions agree with previous results for dune orientation, and also provide a wider range of possible alignments depending on flow strength, especially when the two winds are perpendicular, at which the transition occurs. This analysis also predicts the selected pattern wavelength, which either decreases close to the transition angle for strong winds, due to a geometric effect, or increases at low winds, when the bed slope affects the transport. This theoretical analysis is complemented by analogous subaqueous experiments, where bedforms are submitted to alternate water flows. For transverse bedforms, the experimental data validate the model at strong flows, providing evidence for the predicted geometric effect, but also for the increase of the wavelength close to the transport threshold. For longitudinal bedforms, a discrepancy is observed, which we interpret as the sign of enhanced nonlinearities induced by the development of slip faces when the flow alternately blows on both sides of the dune.