Singing Dunes

The dune in section, the wind from the left: its steep lee side, the slip face, stands at sand's angle of repose, and each key sends an avalanche down it. The grains drawn slide at the avalanche's speed, slowed a hundredfold, and the face shakes with the song. In the layer's theory, the dashed line is the firmer sand under the dry layer, and the rays bounce in the layer between.

Each dot is a patch of sheared grains, placed round the circle by where it is in its cycle of pushes, with the circle turning at the note. Scattered, they push at random and the avalanche only rumbles; bunched, they push together and the dune sings. The arrow is their mean (Kuramoto's order parameter R): its length is how much of the song is in step.

The last six seconds of the focused avalanche: R, how much of it is in step (filled), and the coupling over its threshold (line), with the threshold dashed. The grains fall into step only once the line climbs past it, the harder the faster; as the avalanche stops, the line falls back and the song breaks up.

The grains' theory: the note against the grain size, f = 0.4·√(g/d), with the four dunes Douady and his colleagues measured (their grains, and the note each sang, ± its spread), and the sand classes along the bottom. The layer's theory: the note against the dry layer's depth, with the depths and notes Vriend's team found at Dumont Dunes. The ring is the key just played.