January 2025
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Windblown sand creates multiscale bedforms on Earth, Mars, and other planetary bodies. According to conventional wisdom, decameter-scale dunes and decimeter-scale ripples emerge via distinct mechanisms on Earth: a hydrodynamic instability related to a phase shift between the turbulent flow and the topography, and a granular instability related to a synchronization of hopping grains with the topography. Here, we report the reproducible creation of coevolving centimeter and decimeter-scale ripples on fine-grained monodisperse sand beds in ambient-air and low-pressure wind-tunnels, revealing two adjacent mesoscale growth instabilities. Their morphological traits and our quantitative grain-scale numerical simulations authenticate the smaller structures as impact ripples but point at a hydrodynamic origin for the larger ones. This suggests that the aeolian transport layer would have to partially respond to the topography on a scale comparable to the average hop length, hence faster than previously thought, but consistent with the phase lag of the inferred aeolian sand flux relative to the wind. Hydrodynamic modelling supports the existence of hydrodynamic aerodynamic ripples on Earth, connecting them mechanistically to megaripples and to the debated Martian ripples. We thereby propose a unified framework for mesoscale granular bedforms found across the Solar System.
![Multiple growth instabilities in ambient air wind tunnel measurements
Grain size d ≈ 90 µm and wind friction velocity u* ≈ 0.184 m s⁻¹. a–d, Amplitude A (a, blue) and wavelength λ (b, red and yellow) of decimetre-scale ripples (c) and wavelength of the superimposed centimetre-scale ripples (b, green), emerging simultaneously from an initially flat sand bed under a constant wind (d). The inset (c) is a spatio-temporal plot showing the emergence of decimetre-scale ripples along a transect in the central section of the wind tunnel (λ shown in b, yellow), while the time-lapse photos in d show the full evolution of both ripple scales (λ shown in b, red and green). The notion of two distinct linear growth instabilities is supported by the initial exponential growth of the larger ripples’ amplitudes (dashed line in a), as inferred from an empirical fit of the whole time series (dotted line; Methods), at well-separated, invariable initial ripple wavelengths (b), in accord with the predicted initial wavelengths (dashed lines) from our aeolian impact ripple numerical simulations (Fig. 1f, Methods and Supplementary Methods) and from the hydrodynamic ripple model (Fig. 4). Extracted wavelengths (amplitudes) are noisy for the large ripples at early times (≲10min\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lesssim 10\,\min$$\end{document}) because of the superimposed small ripples (Methods) and for the small ripples at late times (≳40min\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gtrsim 40\,\min$$\end{document}) because of disturbances due to the emerging larger ripples, which may even cause their partial flattening (d). The wrinkles at t = 0 min in the time-lapse photos (d) are minor (inconsequential) imperfections in the initial bed preparation.
Source data](https://www.researchgate.net/publication/377239107/figure/fig2/AS:11431281217010714@1705032096993/Multiple-growth-instabilities-in-ambient-air-wind-tunnel-measurements-Grain-size-d90-m_Q320.jpg)
![Estimating the subscale saturation length under ambient air conditions
a, Exemplary bed elevation profile h(x), experimentally inferred sand flux perturbation δq(x) (Methods) and calculated bed shear stress perturbation δτ(x) (Methods), all normalized by their maximum values during the initial formation of large ripples in the centre of the ambient air wind tunnel (t = 11 min; Fig. 2). b, The sand flux is shifted relative to the bed shear stress by a well-defined lag distance, quantified by the maximum of the cross-correlation function Cδq,δτ (Methods). This lag is about 50 times smaller than previous estimates obtained on much coarser scales53–56 and is thus indicative of a partial, subscale saturation over a length ℓsatsub\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ell }_{{{{\rm{sat}}}}}^{{{{\rm{sub}}}}}$$\end{document} on the order of the average hop length ℓ¯hop≈0.8cm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{\ell }}_{{{{\rm{hop}}}}}\approx 0.8\,{{{\rm{cm}}}}$$\end{document} (calculated from grain-scale simulations; Supplementary Methods).
Source data](https://www.researchgate.net/publication/377239107/figure/fig3/AS:11431281217066965@1705032097319/Estimating-the-subscale-saturation-length-under-ambient-air-conditions-a-Exemplary-bed_Q320.jpg)
![Model predictions for ambient air conditions
Integrating an additional subscale relaxation process into a state-of-the-art morphodynamic model¹⁴ (Methods) leads to a new dispersion relation σ(λ) (solid line). For terrestrial conditions, it predicts a hydrodynamic ripple mode in addition to the classical dune mode associated with the overall saturation process in good agreement with our experimental data for incipient large ripples (◊, t≲15min\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t\lesssim 15\,\min$$\end{document}; Fig. 2 and Methods) and field measurements of incipient sand dunes⁵⁶, corrected for the different grain sizes and wind speeds (Methods). Experimental data are presented as mean values ± s.d. (sample size is 120). The dotted and dashed lines indicate two limiting scenarios considering merely one sand flux relaxation process: conventional large-scale saturation (ℓsat ∼ 0.4m) or the newly postulated subscale saturation (ℓsatsub~0.8cm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ell }_{{{{\rm{sat}}}}}^{{{{\rm{sub}}}}} \sim 0.8\,{{{\rm{cm}}}}$$\end{document}) alone. Their linear combination (solid line) involves, as the only free parameter, the fraction γ ≈ 0.1 of the total sand flux that is modulated at the smaller scales. It is adjusted to fit the measured growth rate of the large ripples (Fig. 2a and Methods).
Source data](https://www.researchgate.net/publication/377239107/figure/fig4/AS:11431281217066966@1705032097502/Model-predictions-for-ambient-air-conditions-Integrating-an-additional-subscale_Q320.jpg)
