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Conditions for aeolian transport in the Solar System

Abstract

Sand dunes, which arise wherever loose sediment is mobilized by winds that exceed threshold speed and grains are sufficiently strong to survive collisions1, are ubiquitous in the Solar System2. However, current threshold theories usually neglect physical processes that become relevant under exotic conditions3,4, and are in disagreement when extrapolated to extraterrestrial planetary bodies5,6,7,8,9. Here we draw on results in contact10, rarefied gas11, statistical12 and adhesion13 mechanics to present a theory for the fluid and impact thresholds of aeolian transport that encompasses the various conditions present in Solar System bodies. Our theoretical predictions are consistent with available experimental threshold observations and indicate that these thresholds strongly depend on local environmental conditions everywhere but Earth. Our results suggest, among other things, that Titan’s dunes are locally sourced4 and that Mars’s high threshold makes its dunes more resistant to motion14. This work highlights the role of dunes in understanding atmospheric dynamics and surface sediment. Further studies are needed to include hitherto neglected and still poorly understood processes.

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Data availability

All data are available in the Supplementary Data files. Source data are provided with this paper.

Code availability

The code used to produce this paper can be accessed at https://doi.org/10.5281/zenodo.6480898.

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Acknowledgements

We thank P. Claudin, B. Andreotti, C. Thom, A. Seiphoori and B. Ferdowsi for insightful discussions. D.J.J. acknowledges support from the Army Research Office, grant 569074. Acknowledgement is made to the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research through grant 61536-ND8 to D.J.J.

Author information

Authors

Contributions

Conceptualization, data curation, formal analysis, investigation, software, validation, visualization, writing—original draft, A.G.; methodology, project administration, writing—review & editing, A.G. and D.J.J.; resources, funding acquisition, supervision, D.J.J.

Corresponding author

Correspondence to Douglas J. Jerolmack.

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The authors declare no competing interests.

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Nature Astronomy thanks Ping Wang and Hezi Yizhaq for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Wind profiles.

(a) Mean horizontal wind speed with elevation for a fixed friction velocity (u* = 0.3 m/s) and grain size (d = 100μm) for the six bodies of interest using the empirical relation in Supplementary Information Text S4. The grain center is denoted with a black line. (b) Dimensionless presentation of (a), where $${u}_{x}^{+}=u/{u}_{* }$$ and z+ = zu*/υ.

Extended Data Fig. 2 Fluid threshold prediction comparison to data.

Four methods for predicting the fluid threshold are compared to observed data, where the vertical axis is u*,observed/u*,predicted − 1 (for the labelled prediction) and the horizontal axis is the Galileo number, $${{{\mathcal{G}}}}$$. References for the observations are given on the right, where markers with shaded interiors signify experiments not using standard Earth conditions. The correlation coefficient (r2) for each log-log comparison of u*,observed versus is u*,predicted (that is Fig. 2c) is annotated. (a) The prediction in the main text, where A=1. (b) The prediction except $${{{\mathcal{A}}}}$$ is a free-parameter. (c) The prediction using the empirical relation of Iversen & White (1982). (d) The prediction using the semiempirical theory of Shao & Lu (2000).

Extended Data Fig. 3 Fluid threshold prediction comparison to each other.

The relative error between the alternative predictions of Shao & Lu (2000) (S&L) and Iversen & White (1982) (I&W) with the prediction in the main text for the fluid threshold for average conditions on each body. Each sediment candidate is given for (a) Earth, (b) Mars, (c) Titan, (d) Venus, (e) Pluto and (f) Triton.

Extended Data Fig. 4 Restitution mechanics and empirical fit.

References for the observations are given on the bottom right, where markers with shaded interiors signify experiments not using standard Earth conditions or field data, markers with solid interiors signify explicit measurements of the restitution coefficients outside wind tunnels. Magenta and yellow markers are from studies where the restitution coefficient is measured or noted, values for the vertical-axes of markers with other colors are inferred from simulated trajectories. All horizontal-axes are the Galileo number $${{{\mathcal{G}}}}$$. (a) The ratio of the ejection to impact velocity of a characteristic saltating grain, that is the restitution coefficient e. (b) The angle the grain impacts the bed, with the theoretical fixed ejection angle denoted (cyan line). (c) The restitution coefficient normalized such that it impacted the bed at a fixed angle (θ = − 10), e10, with the empirical relationship used in the main text relating the two axes (cyan line) (Methods).

Extended Data Fig. 5 Impact threshold prediction comparison to data.

Four methods for predicting the impact threshold are compared to observed data, where the vertical axis is u*,observed/u*,predicted − 1 (for the labelled prediction) and the horizontal axis is the Galileo number, $${{{\mathcal{G}}}}$$. References for the observations are given on the right, where markers with shaded interiors signify experiments not using standard Earth conditions or field data. The correlation coefficient (r2) for each log-log comparison of u*,observed versus is u*,predicted (that is Fig. 3c) is annotated. (a) The prediction in the main text. (b) The prediction using the semiempirical theory of Kok (2010) (note: the vertical axis bounds are extended in the inset to show the full data extent). (c) The prediction using the semiempirical theory of Pähtz & Durán (2018). (d) The prediction using the semiempirical theory of Claudin & Andreotti (2006).

Extended Data Fig. 6 Impact threshold prediction comparison to each other.

The relative error between the alternative predictions of Kok (2010) (K), Pähtz & Durán (2018) (P&D) and Claudin & Andreotti (2006) (C&A) with the prediction in the main text for the impact threshold for average conditions on each body. Each sediment candidate is given for (a) Earth, (b) Mars, (c) Titan, (d) Venus, (e) Pluto and (f) Triton.

Extended Data Fig. 7 Trajectory analysis example.

(a-c) Each point on the lines with color corresponding to the colorbar on the left are for a trajectory of a 1 mm quartz grain at average Earth conditions leaving the bed with an ejection velocity of v from the horizontal axis. The solid black line denotes the impact threshold friction velocity, while the black dot and the corresponding dashed black lines denote the unique pair of the friction velocity and ejection velocity at the impact threshold. (a) The ratio of the ejection to impact speeds for a trajectory. (b) The impact angle for a trajectory, with the cyan line indicating the ejection angle. (c) The ratio of the ejection to impact speeds for a trajectory, normalized as if the impact angle was fixed (θ = − 10), e10 (Methods). The green line (also in (d)) is the ‘target’ restitution coefficient for this case using the empirical relation found in Extended Data Figure 4c. (d) The minima for each line in (c) plotted against the friction velocity. We define the impact threshold as the intersection of the trend and the green line.

Extended Data Fig. 8 Contrasting trajectory examples.

Trajectories like Extended Data Figure 7c for Basalt grains at average Mars conditions of size (a) d = 1 mm and (b) d = 10μm. The green lines are the ‘target’ restitution coefficient for each case using the empirical relation found in Extended Data Figure 4c. The qualitatively different behavior in the neighborhood of the solution shows how this formulation of the impact threshold loses meaning for small grains. The minima for each successive curve of fixed friction velocity in (a) are close and transition smoothly, and u* and v are not extremely different. This is in contrast with (b), where the minima close to the target restitution rapidly diverges as u* changes, and v is extremely small at the minima relative to u*.

Extended Data Fig. 9 Trajectory diagnostics.

Predictions for the characteristic saltator trajectory at the impact threshold with varying grain diameter for (a) impact speed, (b) impact angle, (c) hop height and (d) hop duration. Bands show the range for different candidate and known sediments on each planetary body (see legends in (c) and (d)) based on known temperature and pressure variability.

Supplementary information

Supplementary Information

Supplementary Sections 1–6, Tables 1–3 and Figs. 1 and 2.

Supplementary Data 1

Fluid threshold measurements. All collated data used in the fluid threshold fit for each measurement (Methods). Additionally, the phrase used to explain the threshold in the literature is given, as is the wind-tunnel name and height. Note that some of the values in this spreadsheet are assumed and not explicitly stated in the paper in which the threshold measurements are reported; see Methods for an explanation of how these are calculated.

Supplementary Data 2

Impact threshold measurements. All collated data used in the impact threshold fit for each measurement (Methods). Additionally, the phrase used to explain the threshold in the literature is given, as is the wind-tunnel name and height. Note that some of the values in this spreadsheet are assumed and not explicitly stated in the paper in which the threshold measurements are reported; see Methods for an explanation of how these are calculated.

Supplementary Data 3

Restitution coefficient measurements. All collated data used in the impact threshold fit for each measurement (Methods). A cell entry of ‘−9999’ denotes a parameter that does not exist for that experiment (wind-tunnel name and height, for example). Note that some of the values in this spreadsheet are assumed and not explicitly stated in the paper in which the measurements are reported; see Methods for an explanation of how these are calculated.

Source data

Source Data Fig. 2

Data for panels bd.

Source Data Fig. 3

Data for panels c and d.

Source Data Extended Data Fig. 2

Data for all panels.

Source Data Extended Data Fig. 4

Data for all panels.

Source Data Extended Data Fig. 5

Data for all panels.

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Gunn, A., Jerolmack, D.J. Conditions for aeolian transport in the Solar System. Nat Astron (2022). https://doi.org/10.1038/s41550-022-01669-0

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• DOI: https://doi.org/10.1038/s41550-022-01669-0