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I have been working on a simulation to approximate the formation process of dunes. I understand that their formation is a result of saltation and aeolian processes, but I don't understand the exact small scale mechanisms which contribute to their shape.

Diagram of a dune

The leeward side of most dunes is steep and straight because the sand slips down it and it exceeds the angle of repose. So what exactly contributes to the gentle curve of the windward side?

  • Is more sand removed on steeper parts of the dune?
  • Does the distance of saltation change over the dune?
  • What does the sand flux look like across the surface?
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    $\begingroup$ Discussed here. $\endgroup$
    – J.G.
    Commented Feb 27, 2022 at 16:37

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Saltation cannot proceed up a steeper slope under the wind conditions that prevail in the particular dune's formation. Dunes are basically traffic pile ups for wind driven sand grains, the slip face of a dune is defined almost entirely by the angle of repose of the grains that make up it's structure. The windward side is where new grains join the pile up and the important factor is how far off the ground, on average, the wind is capable of lifting the grains that compose the dune.

Saltation is effectively wind assisted grain skipping; on a smooth flat surface the wind could push an individual grain an unlimited distance, with it bouncing off the surface every so often, without it being obstructed in it's forward progress. On flat ground the likelihood of a grain impacting another on the surface that stops it is higher but on a slope an individual grain will encounter another grain, and quickly, because saltating grains do not rise high above the ground.

Dunes usually form around an original obstruction and while they may move across the landscape and even sweep aside would-be barriers when they are larger they are then themselves barriers that perpetuate the blockage of sand grains.

To answer the questions at the end of your query:

  • Is more sand removed on steeper parts of the dune?
    Yes but no; most of the individual grains in a dune actually rotate through from windward-to-leeward-to-basement of the dune, not a lot of sand is removed from the dune in any area. There is a much greater rate of vertical motion for grains on the leeward edge of the dune however.
  • Does the distance of saltation change over the dune?
    Yes saltation distance is a function of wind strength and "average distance to stop" the steeper the slope of the dune is the shorter the distance to stop becomes because saltation is effectively a horizontal flow and the slope of the dune intercepts the very flat ballistic of the grains before they would otherwise hit the ground.
  • What does the sand flux look like across the surface?
    In terms of grain numbers moving across a given metre grid square pretty even. In terms of movement across the surface area of the dune also very even over time but with movement of the windward slope being slow and steady while movements on the lee slope tend to be more variable and characterised by irregular slips of large areas. In terms of grains joining and leaving the dune that is a matter of how you define a grain as being part of the dune or not but I'd be inclined to go with a model that showed a trickle of new grains on the windward edge with an even smaller number of grains lost at the leeward toe with most of the outgoings being concentrated at the crest.
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    $\begingroup$ You need more paragraph breaks. $\endgroup$
    – Spencer
    Commented Feb 26, 2022 at 14:46
  • $\begingroup$ Thank you so much. I think this helped explain almost everything I didn't understand. But I still don't get why the crests tend to be more flat than the rest of the windward slope. $\endgroup$
    – Ale Kid
    Commented Feb 27, 2022 at 7:52
  • $\begingroup$ @Spencer I tried, and I tried to do so without changing the spirit of the answer. $\endgroup$ Commented Feb 27, 2022 at 10:57
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    $\begingroup$ @AleKid Vertical lift during saltation is a function of impact speed when a grain hits the surface it is moving over, the higher the wind speed the more upward deflection is possible. $\endgroup$
    – Ash
    Commented Feb 28, 2022 at 10:27
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    $\begingroup$ @DavidHammen Thanks that is a lot clearer, I'll try to remember that trick in future. $\endgroup$
    – Ash
    Commented Feb 28, 2022 at 11:16

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