Olivier Rozier

Setting the length and time scales of a cellular automaton dune model from the analysis of superimposed bed forms

[1] We present a new 3-D cellular automaton model for bed form dynamics in which individual physical processes such as erosion, deposition, and transport are implemented by nearest neighbor interactions and a time-dependent stochastic process. Simultaneously, a lattice gas cellular automaton model is used to compute the flow and quantify the bed shear stress on the topography. Local erosion rates are assumed to be proportional to the shear stress in such a way that there is a complete feedback mechanism between flow and bed form dynamics. In the numerical simulations of dune fields, we observe the formation and the evolution of superimposed bed forms on barchan and transverse dunes. Using the same model under different initial conditions, we perform the linear stability analysis of a flat sand bed disturbed by a small sinusoidal perturbation. Comparing the most unstable wavelength in the model with the characteristic size of secondary bed forms in nature, we determine the length and time scales of our cellular automaton model. Thus, we establish a link between discrete and continuous approaches and open new perspectives for modeling and quantification of complex patterns in dune fields.

Sediment flux from the morphodynamics of elongating linear dunes

Although dunes are very common bedforms in terrestrial sand seas, the description of linear dune growth, either by extension or lateral accretion, is still hindered by our limited understanding of the underlying mechanisms. Therefore, sand flux estimates from remote imagery rely essentially on the migration speed of barchan dunes, but not on the dynamics of linear dunes. Here we use ∼50 yr of high-resolution aerial and satellite imagery of the Tenere desert (Niger), the worlds largest source of mineral aerosols, to demonstrate that linear dunes can elongate in the direction of the resultant sand flux with no lateral migration. As they elongate from topographic obstacles in a zone of low sediment availability with multimodal winds, these elongating lee dunes are ideal to isolate and quantify linear dune growth only by extension. Using similar conditions in a numerical model, we show how deposition downstream of low hills may result in nucleation and development of bedforms. From elongation we derive the local sand flux parallel to the linear dune crests. This study shows that the morphodynamics of linear dunes under complex wind regimes can also be used for assessing sediment flux and wind conditions, comparably to the more-established method of using sand flux estimates perpendicular to the barchan dune crests in zones of unidirectional wind.

Development and steady states of transverse dunes: A numerical analysis of dune pattern coarsening and giant dunes

We investigate the development and steady states of transverse dunes for ranges of flow depths and velocities using a cellular automaton dune model. Subsequent to the initial bed instability, dune pattern coarsening is driven by bed form interactions. Collisions lead to two types of coalescence associated with upstream or downstream dominant dunes. In addition, a single collision-ejection mechanism enhances the exchange of mass between two adjacent bed forms (throughpassing dunes). The power law increases in wavelength and amplitude exhibit the same exponents, which are independent of flow properties. Contrary to the wavelength, dune height is limited not only by flow depth but also by the strength of the flow. Superimposed bed forms may propagate and continuously destabilize the largest dunes. We identify three classes of steady state transverse dune fields according to the periodicity in crest-to-crest spacing and the mechanism of size limitation. In all cases, the steady state is reached and maintained through the dynamic equilibrium between flow strength and dune aspect ratio. In the limit of low flow strength, where it becomes the primary factor of size limitation, the bed shear stress in the dune trough regions is close to its critical value for motion inception. Comparisons with natural dune fields suggest that many of them may have reached a steady state. Finally, we infer that the sedimentary patterns in the model may be used to bring new constraints on the development of modern and ancient dune fields.

Phase diagrams of dune shape and orientation depending on sand availability.

New evidence indicates that sand availability does not only control dune type but also the underlying dune growth mechanism and the subsequent dune orientation. Here we numerically investigate the development of bedforms in bidirectional wind regimes for two different conditions of sand availability: an erodible sand bed or a localized sand source on a non-erodible ground. These two conditions of sand availability are associated with two independent dune growth mechanisms and, for both of them, we present the complete phase diagrams of dune shape and orientation. On an erodible sand bed, linear dunes are observed over the entire parameter space. Then, the divergence angle and the transport ratio between the two winds control dune orientation and dynamics. For a localized sand source, different dune morphologies are observed depending on the wind regime. There are systematic transitions in dune shape from barchans to linear dunes extending away from the localized sand source, and vice-versa. These transitions are captured fairly by a new dimensionless parameter, which compares the ability of winds to build the dune topography in the two modes of dune orientation.

Mean sediment residence time in barchan dunes

When a barchan dune migrates, the sediment trapped on its lee side is later mobilized when exposed on the stoss side. Then sand grains may undergo many dune turnover cycles before their ejection along the horns, but the amount of time a sand grain contributes to the dune morphodynamics remains unknown. To estimate such a residence time, we analyze sediment particle motions in steady state barchans by tracking individual cells of a 3-D cellular automaton dune model. The overall sediment flux may be decomposed into advective and dispersive fluxes to estimate the relative contribution of the underlying physical processes to the barchan shape. The net lateral sediment transport from the center to the horns indicates that dispersion on the stoss slope is more efficient than the convergent sediment fluxes associated with avalanches on the lee slope. The combined effect of these two antagonistic dispersive processes restricts the lateral mixing of sediment particles in the central region of barchans. Then, for different flow strengths and dune sizes, we find that the mean residence time of sediment particles in barchans is equal to the surface of the central longitudinal dune slices divided by the input sand flux. We infer that this central slice contains most of the relevant information about barchan morphodynamics. Finally, we initiate a discussion about sediment transport and memory in the presence of bed forms using the advantages of the particle tracking technique.

Controls on and effects of armoring and vertical sorting in aeolian dune fields: A numerical simulation study

Unlike ripples, there are only few numerical studies on grain size segregation at the scale of dunes in aeolian environments. Here we use a cellular automaton model to analyze vertical sorting in granular mixtures under steady unidirectional flow conditions. We investigate the feedbacks between dune growth and the segregation mechanisms by varying the size of coarse grains and their proportion within the bed. We systematically observe the development of a horizontal layer of coarse grains at the top of which sorted bed forms may grow by amalgamation. The formation of such an armor layer controls the overall sediment transport and availability. The emergence of dunes and the transition from barchan to transverse dune fields depend only on the grain size distribution of the initial sediment layer. As confirmed by observation, this result indicates that armor layers should be present in most arid deserts, where they are likely to control dune morphodynamics.

Unravelling raked linear dunes to explain the coexistence of bedforms in complex dunefields

Raked linear dunes keep a constant orientation for considerable distances with a marked asymmetry between a periodic pattern of semi-crescentic structures on one side and a continuous slope on the other. Here we show that this shape is associated with a steady-state dune type arising from the coexistence of two dune growth mechanisms. Primary ridges elongate in the direction of the resultant sand flux. Semi-crescentic structures result from the development of superimposed dunes growing perpendicularly to the maximum gross bedform-normal transport. In the particular case of raked linear dunes, these two mechanisms produces primary and secondary ridges with similar height but with different orientations, which are oblique to each other. The raked pattern develops preferentially on the leeward side of the primary ridges according to the direction of propagation of the superimposed bedforms. As shown by numerical modelling, raked linear dunes occur where both these oblique orientations and dynamics are met.

Morphodynamic mechanisms for the formation of asymmetric barchans: improvement of the Bagnold and Tsoar models

Asymmetric barchan dunes exhibit a marked asymmetry, this morphology develops from the combined effects of two dominant winds, with different directions and relative strengths, and can be described based on Bagnold’s and Tsoar’s models. In Bagnold’s model, the limb nearest to the strongest wind extends and is sustained and enhanced by a gentler wind nearly parallel to the barchan. Tsoar’s model expects that the limb farthest from the gentler wind extends in a manner similar to the evolution of seif dunes and that the limb closest to the gentler wind is eroded. To know which model will emerge with variations of the wind, we did some numerical simulations, and found that there exists a critical angle between orientations of the two winds, which decide the formation model of asymmetric barchans. When the angle is greater than this critical value, the effect of the bi-directional winds agrees with Tsoar’s model. When the angle is less than the critical value, the evolution of the two horns contradicts Tsoar’s model and agrees with Bagnold’s model. The critical value for this angle depends on the transport ratio of two winds.

Morphodynamics of barchan and dome dunes under variable wind regimes

Dome dunes are traditionally interpreted as a transient or an independent class of bedforms because of their rounded and smooth shape without slipfaces. Here we show that they can also reach a steady state and form dome dune fields, which entail the same interactions between flow, bed topography, and moving sediment as other dune types in the absence of grain-size segregation and vegetation. We study the transition from barchan to dome dunes by increasing the standard deviation of a normal distribution of sand flux orientation in a numerical model. We find that, under steady-state conditions, barchan and dome dunes exhibit the same relationships between their height and migration rate. As shown in Earth’s deserts, dome dune shape and migration rate can then be used to estimate sand flux properties, including the variability in transport directionality.