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]. This remains an active area of current research [4].

This project aims to understand and improve the theory behind edge waves, simulate them using open source codes like Gerris/Basilisk and understand sediment transport due to these. Please apply for this project up if you enjoy mathematics and physics and would like to also learn CFD.

1. Stokes, G. G. 1846 Report on recent researches in hydrodynamics. Rep. 16th Brit. Assoc. Adv. Sei., pp. 1-20.

2. Edge Waves and beach cusps, Guza & Inmam, J. Geophys. Res., vol. 80, 1975

3. Field observations of edge waves, Nature 243, 349–365

4. Can edge waves be generated by wind? V. Shrira et al, J. Fluid Mechanics, vol. 934, 2022