Barchan Dune Migration: Saltation Flux Simulator

Wind & Grain

Shear velocity u* 0.45 m/s

Grain diameter D 0.25 mm

Dune height H 4.0 m

Time acceleration 2.0e5×

below threshold — no transport

Live Readouts

Threshold u*t

0.20 m/s

Sand flux q

0 kg/m/yr

Celerity c

0 m/yr

Migrated

0.0 m

Elapsed (sim)

0 yr

Saltating grains

0 / s

How it works

Wind drags grains along the bed once the shear velocity u* exceeds a threshold set by gravity and grain weight (Bagnold 1941, Shields-type threshold):

u*t = A · √[((ρs/ρa) − 1) · g · D]
  A ≈ 0.1,  ρs ≈ 2650 kg/m³ (quartz),  ρa ≈ 1.2 kg/m³

Above threshold, grains hop downwind in ballistic arcs (saltation) and the volumetric mass flux follows an empirical cubic law in shear velocity (Bagnold / Lettau & Lettau):

q = C · (ρa/g) · √(D/D₀) · u*² · (u* − u*t),   u* > u*t
  C ≈ 1.8,  D₀ = 0.25 mm (reference grain size)

Saltating grains climb the gentle windward slope (~10–15°) and avalanche down the steep lee slip face once it reaches the angle of repose (~34°) — this asymmetric erosion/deposition cycle is what pushes the whole dune body downwind. Its bulk migration speed (celerity) follows Bagnold's dune-speed relation:

c = q / (ρs · H)

Taller dunes hold more sand per unit of migrating flux, so — for the same wind — they crawl slower than small ones; this is why barchan swarms fan out with big dunes trailing behind small ones. Real migration is centimetres to metres per year, so the clock here runs at a large, labelled time acceleration to make it visible.

Shear velocity u* — wind strength at the bed; raise it past threshold to start transport.
Grain diameter D — coarser sand needs faster wind to move (higher u*t) but each grain carries more mass once moving.
Dune height H — taller dunes migrate slower for the same sand flux (c = q / ρsH).
Time acceleration — compresses years of real migration into seconds of simulated time.

Saltating grains Reference stakes

wind → downwind (+Z)

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