Pattern Formation

The vast majority of flows in our daily experience are turbulent and yet we see patterns all around us. Ordered arrays of cloud streets, (turbulent) wind-driven waves with distinct wavelengths, and---for a more exotic example---Jupiter's red spot all testify to the ability of ordered patterns to arise and persist amidst turbulent fluctuations. A well-known, yet still unexplained, example from the laboratory is the ghost vortices in turbulent Taylor-Couette flow. 

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].