Creamer transform - a non-linear model for steep waves on deep water

Creamer, Henyey, Schult and Wright proposed a non-linear transform for linear Airy waves which reproduces the 2^nd order wave-wave interaction exactly and does well at higher order. Their transform captures the principal effects of short waves being subjected to a varying 'local gravity' field and transported by the velocity field of longer waves. In this paper an expansion of the Creamer transform is compared to Stokes 5^th order theory for regular waves for a single wave component. The Creamer transform does not capture the Stokes modification to the phase speed at 3^rd order but apart from this it is remarkably accurate, both for the shape of the surface and the velocity field. For each of the harmonics up to the 5^th, the leading order and the next order term in wave amplitude at each harmonic is correct - the results only differ from the exact Stokes results at 2 orders higher than the leading order term for each harmonic. The velocity field within the fluid can also accurately captured by the Creamer transform. For irregular waves no equivalent analytical theory to that of Stokes exists. Thus, the Creamer-transform can be used to generate good approximations for broad-banded and steep wave fields in a way not previously possible. Thus, the Creamer transform is a useful approach for problems where a locally accurate model of the nonlinear kinematics of water waves is required, such as modeling the 'ringing' of structures with surface piercing columns.