# SAND FLUX EMITTED BY DUNES

Jean Verité, C Narteau, L Barrier, O Rozier, S Courrech Du Pont

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Jean Verité, C Narteau, L Barrier, O Rozier, S Courrech Du Pont. SAND FLUX EMITTED BY DUNES. 8th International Planetary Dunes Workshop, May 2025, Alghero (Sardaigne), Italy. hal-05491933

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
**SAND FLUX EMITTED BY DUNES.** J. Verité¹, C. Narteau¹, L. Barrier¹, O. Rozier¹, S. Courrech du Pont².
¹Institut de Physique du Globe de Paris, Université Paris Cité, CNRS, Paris, France (narteau@ipgp.fr). ²Laboratoire Matière et Systèmes Complexes, Université Paris Cité, CNRS, Paris, France.

**Introduction:** Dunes do not usually act as pure sediment traps. Instead, as they grow, migrate or elongate on consolidated beds, they exchange sediment with their surrounding environment (Figure 1). The associated transport is not only of great significance for understanding the morphodynamics of the dune populations and quantifying dust emission, but also critical for the evolution of the interdune areas where smaller bedforms can develop (Rambert et al., 2025) or plants can grow (Alkalla et al. 2025). However, a standard form has yet to be developed to describe the sand flux emitted by dunes. In this study, we utilize a numerical dune model in which these output sand fluxes occur as a result of a self-organizing process to assess their magnitude according to the divergence angle between the orientation of the dune crest and the wind direction, in comparison with the sand flux at the crest and on a flat sand bed away from any topography.

**Method:** The ReSCAL dune model combines two cellular automata to simulate sediment transport and turbulent flow (Narteau et al., 2009). While these automata can operate independently, the strength of the model lies in their coupling, which ensures continuous feedback between the evolving topography, the flow, and the sediment transport rate. Thus, there is no predefined relationship between the topography and the bed shear stress, allowing transport rates to spontaneously establish according to the interaction dynamics between the constituent parts of the system over time.

The model is constructed from a finite number of states distributed on a cellular grid. At the elementary length scale $l_0$ of a cubic lattice, a cell is a real-space representation of the physical environment. The dynamical system is based on the evolution of pairs of nearest-neighbor cells called doublets. Each individual physical process (i.e., erosion, transport, deposition) is associated with a set of doublet transitions and a characteristic transition rate expressed in units of $t_0^{-1}$, where $t_0$ is the characteristic time scale of the model (Narteau et al., 2001, 2009; Rozier and Narteau, 2014).

A infinite symmetric linear dune of triangular shape with height H and base 2L is placed at the center of the domain on a flat non-erodable bed (Figure 2a). This dune of orientation $\alpha$ is subjected to an uni-directional flow of constant strength with orientation $\Theta$ for a short period of time, such that its triangular shape is not significantly altered during the simulation. To determine the sediment flux at the crest, $Q_{\text{crest}}$, we

average the horizontal transport transitions per unit time $t_0$ that occur in a vertical section of width $3l_0$ on either side of the top of the dune. To determine the sediment flux emitted by this dune, $Q_{\text{out}}$, we average the same transitions in a vertical section of width $3l_0$ located on the non-erodable at the bottom of its lee face. In both cases, transport transitions associated with avalanches are not counted.

<figure><img src="image_2.png" /><figcaption>Figure 1: Sand flux emitted by dunes. (a) Schematic illustration of sediment flux from barchan and linear dunes. (b) Sand flux from linear dunes submitted to a bimodal wind regime in the Ténéré Desert (Niger). (c) Flux from defrosting dome dunes on Mars.</figcaption></figure>

**Results:** Figure 2 shows how $Q_{\text{crest}}$ and $Q_{\text{out}}$ vary according to the apparent dune slope,

$$ \tan(\phi_a) = H/L |\sin(\Theta-\alpha)|, \quad (1) $$
i.e., the dune slope experimented by the wind on both sides. When the wind tend to blow in the direction of the dune crest, $Q_{crest}$ and $Q_{out}$ approach $Q_{flat}$, the saturated flux on a flat sand bed away from any topography. As the wind becomes more perpendicular to the dune, $Q_{crest}$ increases under the effect of the wind speed-up (Figure 2b), while $Q_{out}$ decreases due to a shielding effect associated with the negative dune slope, and the development of a recirculation zone (Figure 2c). The sand flux at the crest shows a linear dependence on the apparent aspect dune ratio,

$$Q_{crest} = Q_{flat}(1 + \beta \tan(\phi_a)), \quad (2)$$

where $\beta=3.80\pm0.1$ is a dimensionless constant that fully determine the fractional flux-up ratio, $(Q_{crest}-Q_{flat})/Q_{flat}$.

The output transport rate decreases exponentially with respect to the apparent aspect ratio of the dune,

$$Q_{out} = Q_{flat} \exp(-\tan(\phi_a)/\tan(\phi_{th})) \quad (3)$$

where $\tan(\phi_{th})=0.094$ (i.e., $\phi_{th}=5.4^\circ$) is the threshold dune aspect ratio at which the transition from the linear to the non-linear phase of the dune instability has been observed by Lü et al. (2021). Considering sinusoidal bedforms, $\tan(\phi_{th})$ can also be described as the ratio between amplitude and wavelength at which flow detachment occurs and avalanche faces emerge in the field.

**Concluding remarks:** We show that sand fluxes emitted by the dune can be modeled by an exponential relationship, whose only parameter is a critical slope commonly used to describe the dune instability. Sand fluxes in the interdune areas can now be estimated from surface wind data to investigate how they contribute to the formation of bedforms (sand patches, nebkhas) and dust emissions.

**Acknowledgments:** We acknowledge financial support from the French National Research Agency (ANR-23-CE56-0008/EOLE), and the UnivEarthS LabEx and IdeX programs of Université Paris Cité (ANR-10-LABX-0023 and ANR-18-IDEX-0001).

References:

Alkalla, J., Narteau, C., Rozier, O., Vérité, J., Courrech du Pont, S. (2025). *Steady-state dune morphodynamics through the barchan-parabolic transition*, in review in Journal of Geophysical Research: Earth Surface.

Lü, P., Narteau, C., Dong, Z., Claudin, P., Rodriguez, S., An, Z., Fernandez-Cascales, L., Gadal,

C., Courrech du Pont, S. (2021). *Direct validation of dune instability theory*, Proc. Nat. Acad. Sc. USA, **18**, e2024105118.

Narteau, C. et al., M. (2001). *On a small scale roughness of the core-mantle boundary*, Phys. Earth Planet. Int., **191**, 49–61.

<figure><img src="image_3.png" /><figcaption>Figure 2: Sediment flux in the ReSCAL dune model. (a) Schematic view of the model. (b) Sand flux at the dune crest. (c) Sand flux emitted by dunes. The slopes of these two relationships give independent estimates of the values of $\beta$ and $\tan(\phi_{th})$, the only unknown variables in Equations 2 and 3.</figcaption></figure>

Narteau, C., Zhang, D., Rozier, O., Claudin, P. (2009). *Setting the length and time scales of a cellular automaton dune model from the analysis of superimposed bed forms*. Journal of Geophysical Research: Earth Surface, **114**, F03006.

Rambert, C., Nield, J., Narteau, C., Delorme, P., Wiggs, G., Baddock, M., Best, J., Christensen, M. and Claudin, P. (2025), *Modeling the dynamics of aeolian meter-scale bedforms induced by bed heterogeneities*, in review in Proc. Nat. Acad. Sc. USA.

Rozier, O. and Narteau, C. (2014). A real-space cellular automaton laboratory, Earth Surface Processes and Landforms, **39**, 98–109.