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.
Dune pattern for multidirectional wind regimes in (a) the Namib Desert, Angola (16°27'S 11°58'E), and (b) the Taklamacan Desert, China (37°25'N 81°50'E). The flow roses are calculated from the wind data of the ERAInterim project. Simple arrow: direction of the resulting flow. Double arrow: prediction of the initial orientation of the dunes by linear stability analysis. © DigitalGlobe
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.
Dune pattern formed from a flat bed of sediment in underwater experiments, from a bidirectional wind regime. The angle between the winds is (a) 30°, forming dunes transverse to the resulting flow, and (b) 150°, forming dunes aligned with the resulting flow. © Sylvain Courrech du Pont and Cyril Gadal
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