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Wind
Transport only starts above the threshold shear velocity.
Sand and dune
Changing height or width restarts the dune.
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The science
Sand transport
Wind lifts grains once the shear velocity u* exceeds a threshold, hopping them downwind (saltation). The saturated flux follows the Bagnold-Owen law:
qs = C √(d/D) (ρa/g) u*3 (1 - u*t2/u*2) u*t = A √((ρs-ρa) g d / ρa)with C = 1.8, A = 0.1, reference grain D = 250 micrometres. Vegetation raises the threshold.
Dune evolution
The real flux relaxes towards qs over a saturation length Ls (dq/dx = (qs - q)/Ls). Sand piles up where the flux falls and erodes where it rises (Exner equation):
(1 - φ) ∂h/∂t + ∂q/∂x = 0The wind speeds up over the crest, so the crest erodes faster than the stoss slope, and a lee-side shadow zone (grey) gets no transport, so sand avalanches down the slip face at the 34 degree angle of repose. A heap therefore steepens its lee side and migrates downwind; smaller dunes move faster than big ones.
Honest simplifications
- 1-D cross-section: no sideways flow, so real barchan horns and dune fields are not captured.
- The speed-up over the crest is a simple empirical fit, not a solved boundary layer.
- Time is accelerated (days per second); real storms are intermittent.
What to try
- Strong storm: flux grows with the cube of u*, so migration speeds up dramatically.
- Bidirectional winds: the dune barely moves and grows taller.
- Vegetated: the threshold rises and the dune stops moving.
- Compare a tall narrow dune with a low wide one: the smaller dune moves faster.