Last week, Salvatore Calatola-Young presented his Senior Synthesis project: “A Method for Deriving Conservation Laws for Water Waves”. In this talk, he presented the culmination of 3 years of research with me during his time as an undergraduate.
It wasn’t easy work, but he nailed it.
In summary, Sal showed how Olver’s conserved densities for the water-wave problem can be derived directly from a weak formulation without using the Lie Symmetries. Of course, Sal didn’t stop there! He extended the work for waves traveling over linear shear (constant vorticity), as well as multilayer flows. There’s a lot left to be explored here – and we’re working to bring it all together.
You can find the first in a series of papers available on the ArXiV (https://arxiv.org/abs/2105.07580).