Mean sediment residence time in barchan dunes

Abstract

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.

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

“…It may be different for crescentic barchan dunes for which the same types of collision and coalescence dynamics have been observed [ Hersen and Douady , ; Katsuki et al , ; Vermeesch , ; Hugenholtz and Barchyn , ; Bo and Zheng , ; Génois et al , ]. Indeed, the lateral slope of these isolated dunes may significantly increase the transverse component of transport [ Zhang et al , ] and promotes the slow disappearance of the impacting dune. These lateral fluxes are likely to be much smaller on transverse dunes, and our results indicate that impacting dunes may be resilient to an increase in slope of the longitudinal topographic profiles.…”

“…All transitions are incorporated into a continuous time stochastic process to produce a global dynamical system devoted to the formation and evolution of bed forms. In addition, to take into account avalanching, we impose an angle of repose for the granular material [ Zhang et al , ].…”

“…At any given time step in the model, we can save the topography built by the immobile sedimentary cells, the flow field, and the state of the 3‐D cellular space (i.e., state of all cells, position and orientation of the velocity vector of fluid particles). In addition, we can record all the transitions of doublet and the corresponding physical mechanism (see Figure a) to track sedimentary cells or locally estimate sand flux [ Zhang et al , ]. All these sources of information are used to quantify dune morphodynamics in the model.…”

“…τ 1 / τ 0 =0, except when 2 × 10 5 < t / t 0 <3 × 10 5 where τ 1 / τ 0 =20. For visibility, note that the dependency of the t 0 value on the τ 1 values is not taken into account (see Narteau et al [] and Zhang et al [, Table 2]). Basically, it would have expanded the timescale when 2 × 10 5 < t / t 0 <3 × 10 5 .…”

“…Third, the three‐dimensional cellular space can be used for the tracking of individual particles and the mapping of sedimentary structures. Hence, in addition to the morphodynamics features, it is possible to bring new insights into the migration history of sediment particles [ Zhang et al , ] and into changes in stratification patterns [ Zhang et al , ]. This is particularly important to distinguish interaction bounding surfaces from other types of sedimentary structures [ Brookfield , ].…”