It’s been a while. Over the last week, I’ve been working on documenting the conservation laws via a weak formulation of the water-wave problem using some of the work of Sal (undergraduate research student). At this point, we can systematically derive the
8 7 conservation laws for the irrotational problem (the Hamiltonian is the 8th). We also have the system in place for constant vorticity.
Hopefully, we’ll have a really rough draft posted soon.