Pattern Formation

The role of edge waves in sand transport into beaches and pattern formation (cusps)

Edge waves (also called trapped waves) were discovered theoretically by G. G. Stokes (one of the two names in Navier-Stokes equations) in 1846 [1]. These are inviscid, irrotational, three dimensional travelling wave solutions representing surface waves propagating parallel to a coast, the wave amplitude decaying exponentially in the direction of increasing ocean depth. These waves have been under intense study in the past few decades where it was understood that they play a crucial role in cusp formation (sand patterns on beaches) through complex instability mechanisms [2,3].