Megaripple mechanics: bimodal transport ingrained in bimodal sands

Abstract

Aeolian sand transport is a major process shaping landscapes on Earth and on diverse celestial bodies. Conditions favoring bimodal sand transport, with fine-grain saltation driving coarse-grain reptation, give rise to the evolution of megaripples with a characteristic bimodal sand composition. Here, we derive a unified phase diagram for this special aeolian process and the ensuing nonequilibrium megaripple morphodynamics by means of a conceptually simple quantitative model, grounded in the grain-scale physics. We establish a well-preserved quantitative signature of bimodal aeolian transport in the otherwise highly variable grain size distributions, namely, the log-scale width (Krumbein phi scale) of their coarse-grain peaks. A comprehensive collection of terrestrial and extraterrestrial data, covering a wide range of geographical sources and environmental conditions, supports the accuracy and robustness of this unexpected theoretical finding. It could help to resolve ambiguities in the classification of terrestrial and extraterrestrial sedimentary bedforms.

Fig. 1. Bimodal grain transport creates delicate intermediate-sized megaripples via sand sorting.

Background photo (Sossusvlei, Namibia): dunes (top), megaripples (middle) and ripples (bottom) emerge due to aeolian (wind-driven) sand transport. a Grain-size distributions (GSDs) found on megaripple crests exhibit a characteristic, yet variable bimodal structure; GSDs are from Nahal Kasuy, Israel; Sanshan Desert, China; Sossusvlei, Namibia (Supplementary Fig. S7); Ladakh, India (Fig. S8) and wind tunnel. b Fine-grain saltation drives coarse-grain reptation. c Grain-size modes (locations of peak maxima), mode(d^(f)) and mode(d^(c)), in the bimodal crest GSDs appear to be poorly correlated even within the range of terrestrial conditions; data are from refs. ^,,,,,–,,, (Table S3), with mean ratio mode(d^(c))/mode(d^(f)) ≈ 4.59 (solid line, coefficient of determination R² = 0.13).

Fig. 2. Aeolian transport phase diagram for perfectly bidisperse sand (terrestrial conditions).

Here, the sand bed is idealized as consisting of two grain species with diameters d^(f) and d^(c). The coarse grains can be incrementally kicked forward by the fine grains, resulting in a creeping motion known as reptation, if the wind shear stress τ falls within the bimodal transport regime (green-shaded area). It is delimited by the saltation thresholds τ_t(d^(f)) and τ_t(d^(c)) (dashed and dotted lines) of the fine and coarse grains, respectively, and the coarse-grain reptation threshold τ_r(d^(c)) (solid line). The thresholds are calculated from a physical grain-scale model (Methods) for typical terrestrial conditions (kinematic viscosity ν_a ≈ 1.6 × 10⁻⁵ m² s⁻¹, atmospheric density ρ_a ≈ 1.2 kg m⁻³, grain density ρ_p ≈ 2650 kg m⁻³ and fine-grain size d^(f) ≈ 491 μm, corresponding to Galileo number Ga^(f) ≈ 100 and density ratio s ≈ 2200). The transport regimes map directly onto dynamical regimes of sand sorting and megaripple evolution, as summarized in Table 1. To generalize this framework to more realistic continuous GSDs, as measured in the field, d^(f) is equated to the coarsest saltating grain size, $\max \left(d^{\left(\mathrm{f}\right)}\right)$, at a given wind strength τ. Thereupon, the transport phase diagram collapses onto the thick green line where ${\tau }_{\mathrm{t}}\left(\max \left(d^{\left(\mathrm{f}\right)}\right)\right)=\tau$.

Fig. 3. Bimodal surface GSD and projected transport modes.

The projection of the phase diagram for bidisperse grain transport from Fig. 2 is intimately linked to the (continuously) bimodal surface GSD found on megaripples (see Fig. S1 for another visual representation of the connection). While the left peak comprises the saltating fine grains and maps to the saltation regime (blue), the right peak comprises the reptating coarse grains and maps to the reptation regime (green). The transition between them corresponds to the minimum of the GSD, where one finds the coarsest saltating fine grains, whose saltation threshold ${\tau }_{\mathrm{t}}\left(\max \left(d^{\left(\mathrm{f}\right)}\right)\right)=\tau$ is equal to the prevailing wind stress and constantly adjusts, accordingly (dotted line). Likewise, the transition to stagnation (solid line) defines the coarsest grain size at the right margin of the coarse-grain peak via its reptation threshold ${\tau }_{\mathrm{r}}\left(\max \left(d^{\left(\mathrm{c}\right)}\right)=\tau \right)$. The displayed representative surface GSD was obtained from a megaripple crest located in Nahal Kasuy, Israel (see Fig. 1 in ref. ).

Fig. 4. Solution of the transcendental equations predicting the max-size ratio (general atmospheric conditions).

For given environmental conditions, parametrized in terms of the dimensionless Galileo number Ga^(f) and grain-atmosphere density ratio s, reptation is only possible in a specific range of coarse-grain diameters d^(c), as encoded in the width of the coarse-grain peak of the surface GSD. For sufficiently large fine grains (s^1/4Ga^(f) ≳ 200), the analytical scaling function in Eq. (1) (solid line), implicitly predicting the max-size ratio $\max \left(d^{\left(\mathrm{c}\right)}\right)/\max \left(d^{\left(\mathrm{f}\right)}\right)$, provides a perfect match to the full theory (symbols) for various combinations of Ga^(f) and s. Note the higher numerical sensitivity to s rather than Ga^(f) (inset) and the breakdown of the scaling for s^1/4Ga^(f) ≲ 200. Also, H depends on the planetary conditions primarily via s and the dimensionless settling velocity V_s.

Fig. 5. Comparison between data and predictions.

The coarsest grain sizes $\max \left(d^{\left(\mathrm{f}\right)}\right)$ and $\max \left(d^{\left(\mathrm{c}\right)}\right)$ are extracted from the left and right margins, respectively, of the coarse-grain peaks of the empirical GSDs (Methods). For a given measurement site, with a given measured size $\max \left(d^{\left(\mathrm{f}\right)}\right)$ of the coarsest saltating grains, the theoretically predicted size $\max \left(d^{\left(\mathrm{c}\right)}\right)$ of the coarsest reptating grains is plotted against its measured value. The solid line corresponds to perfect agreement with the idealized model, and the dashed lines indicate a relative error of 20%. See main text for plausible origins of the scatter in the data and suggestions for more accurate measurement protocols. The displayed data is from megaripples located at Nahal Kasuy, Ktora and Yahel in the southern Negev, Israel (filled circles)^,, (Figs. S4–6); Wadi Rum in southern Jordan (open squares); Sanshan Desert in western China (filled diamonds)^,; Antarctica (filled pentagons); Sossusvlei in Namibia (crossed circles) (Fig. S7); Ladakh in India (crosses) (Fig. S8); New Mexico (open triangles); and Mars (stars) (Methods). Wind tunnel data are from ref. .

Fig. 6. Relation between bidisperse and monodisperse saltation thresholds.

Comparison of fine-grain saltation thresholds based on the periodic saltation model for bidisperse, ${\mathrm{\Theta }}_{\mathrm{t}}^{\left(\mathrm{f}\right)}\left(d^{\left(\mathrm{c}\right)}/d^{\left(\mathrm{f}\right)}\right)$, and monodisperse, ${\mathrm{\Theta }}_{\mathrm{t}}^{\left(\mathrm{f}\right)}\left(d^{\left(\mathrm{c}\right)}=d^{\left(\mathrm{f}\right)}\right)$, sand for different atmospheric conditions parametrized by the Galileo number Ga^(f) and density ratio s.