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Higher-than-predicted saltation threshold wind speeds on Titan

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Abstract

Titan, the largest satellite of Saturn, exhibits extensive aeolian, that is, wind-formed, dunes1,2, features previously identified exclusively on Earth, Mars and Venus. Wind tunnel data collected under ambient and planetary-analogue conditions inform our models of aeolian processes on the terrestrial planets3,4. However, the accuracy of these widely used formulations in predicting the threshold wind speeds required to move sand by saltation, or by short bounces, has not been tested under conditions relevant for non-terrestrial planets. Here we derive saltation threshold wind speeds under the thick-atmosphere, low-gravity and low-sediment-density conditions on Titan, using a high-pressure wind tunnel5 refurbished to simulate the appropriate kinematic viscosity for the near-surface atmosphere of Titan. The experimentally derived saltation threshold wind speeds are higher than those predicted by models based on terrestrial-analogue experiments6,7, indicating the limitations of these models for such extreme conditions. The models can be reconciled with the experimental results by inclusion of the extremely low ratio of particle density to fluid density8 on Titan. Whereas the density ratio term enables accurate modelling of aeolian entrainment in thick atmospheres, such as those inferred for some extrasolar planets, our results also indicate that for environments with high density ratios, such as in jets on icy satellites or in tenuous atmospheres or exospheres, the correction for low-density-ratio conditions is not required.

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Figure 1: Titan Wind Tunnel with important components labelled.
Figure 2: Experimentally derived threshold fiction wind speeds on Titan.
Figure 3: Derived parameters from Titan threshold fiction speeds.

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Acknowledgements

This research was supported by grants from NASA's Planetary Geology and Geophysics Program and the Outer Planets Research Program. We dedicate this manuscript to our colleague R. Greeley, who was the motivating force behind the construction of the Planetary Aeolian Laboratory at the NASA Ames Research Center and used it over several decades to make fundamental and long-lasting contributions to understanding aeolian processes on other bodies.

Author information

Authors and Affiliations

Authors

Contributions

D.M.B. is the principal investigator on the NASA grants that funded this work. She conceived the work, defined the objectives, oversaw the wind tunnel refurbishment, oversaw and participated in the data collection, analysis and reduction, and led the writing of the manuscript. N.T.B. contributed fundamental ideas and calculations during wind tunnel refurbishment, participated in the data collection, analysis and reduction, and contributed to writing the manuscript. The Titan Wind Tunnel is housed in the Planetary Aeolian Laboratory at the NASA Ames Research Center. J.R.M. and J.K.S. provided practical assistance, in conjunction with NASA personnel, to complete the wind tunnel refurbishment and calibration. J.K.S., the engineer at the Planetary Aeolian Laboratory, provided sieved sediments for the experiments, maintained and operated the wind tunnel during all runs, and provided data logs from all runs. B.R.W. contributed ideas during project design, wind tunnel refurbishment and data collection. J.P.E. provided assistance in data reduction and analysis, and contributed to writing the manuscript.

Corresponding author

Correspondence to Devon M. Burr.

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Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Flow chart of methodology showing the steps used in this work.

The results are threshold friction wind speed on Titan, u*tTitan, and freestream wind speed at height z, u(z)tTitan, as a function of particle density (ρp) and diameter (Dp), and the shear stress at the surface at threshold (τtTitan). Upright font denotes calibration data or informational text. Italic font indicates measured wind speeds or parameters derived from measured wind speeds.

Extended Data Figure 2 A view into the test section with the test plate inserted.

In this photo, the test plate is prepared for an experimental run with silica sand.

Extended Data Figure 3 Close-up views of some wind tunnel elements.

a, View of the downwind end of the test section rolled out from the wind tunnel, showing the single upwind viewing port (far left) and the three downwind viewing ports (top of third port visible on far side of test section). The downwind end of the calibration plate is seen within the test section (lower right), with walnut shell and pneumatic lines visible (traversable pitot tube within test section not visible). b, Oblique view of downstream end of test plate after partial removal from the test section (opening visible at far left) showing the traversable pitot tube assembly (in centre of photo). 100-grit (125 μm-diameter grains) sandpaper, for ensuring development of a representative boundary layer, is visible to the left (upwind side) of the pitot tube assembly.

Extended Data Figure 4 Example plot (at 60% of the maximum rated fan motor speed) of boundary layer data collected with the traversable pitot tube.

a, Data showing that the boundary layer is fully developed with a freestream wind speed, u(z), of 3.35 m s−1 at a height of 1.9 cm. b, Linearized data illustrating how values of roughness height (z0) are derived. Fitting a straight line to the data gives the equation y = 0.00187x − 5.7669 in centimetres. Comparison with equation (5) shows that ln(z0) = −5.7669, such that z0 = 0.003 cm.

Extended Data Figure 5 Plots of experimentally derived threshold fiction wind speeds in the TWT for the Iversen–White and Shao–Lu models.

For each plot, the dashed line represents the nominal model, the solid line shows the model matched to the data using the density ratio term of ref. 8, and the dotted line shows the model fitted to the data (χ2 minimization). For the modified Iversen–White model, we use K = 0.055 g s−2 and n = 2 (following ref. 8; see Extended Data Table 4). This modification makes the interparticle force (Ip) proportional to Dp as in the Shao–Lu model7, thereby facilitating comparison between the two models. The modified Iversen–White model6 is plotted for their equations 5 (0.03 ≤ Re*p ≤ 10) and 6 (10 ≤ Re*p) (see equations (7) and (8) here), with the transition between the two particle friction Reynolds number regimes at 200 μm. The Shao–Lu model7 is plotted for their nominal value for AN (0.0123) and for their lowest value for γ (1 × 10−4 kg s−2) to optimize the fit. The proximity of the models with the density ratio term (solid lines) and the models fitted to the data (dotted lines) indicates the power of the density ratio term to match the models to the data. Horizontal bars indicate the range of grain sizes (Extended Data Table 2). Vertical bars show the standard deviation uncertainty in speed for the number of data points indicated in Extended Data Table 2; see Methods for calculation of uncertainties.

Extended Data Figure 6 Plot of the u*t ratios used for converting the u*tTWT to u*tTitan.

See Methods (‘Comparison of u*tTitan with models’) for details.

Extended Data Table 1 Conditions necessary to achieve similitude of kinematic viscosity with the Titan near-surface atmosphere
Extended Data Table 2 Experimental matrix of sediments with 23 unique combinations of particle diameter (Dp) and density
Extended Data Table 3 Description of each stage of grain motion during data collection
Extended Data Table 4 Values for the interparticle force parameters in various formulations of the models used here

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Burr, D., Bridges, N., Marshall, J. et al. Higher-than-predicted saltation threshold wind speeds on Titan. Nature 517, 60–63 (2015). https://doi.org/10.1038/nature14088

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