In this talk Professor Taylor will describe the canonical transformation of Creamer D.B., Henyey F., Schult R. and Wright J., from their 1989, Journal of Fluid Mechanics 205, paper “Improved linear representation of ocean surface waves”. The paper provides a transformation from the simplest linear wave model to a nonlinear approximation that is not only exact at 2nd order, but apparently captures much of the bound harmonic structure at all orders.

It also gives some information on what broad-banded spectral high tail forms are compatible with the water wave equations (Laplace and nonlinear free-surface boundary conditions) and which are not. There may also be a link between the possible limiting spectral tail shape, the onset of wave breaking and why the overturning crests of progressive breaking waves all tend to look similar, as discussed by Longuet-Higgins.