The expansion parameter ka is known as the wave steepness.

This is only noticeable when the wave steepness k A is large.

Depends on wave steepness and bottom bathymetry.

Here, ka is the wave steepness, with k a characteristic wavenumber and a a characteristic wave amplitude for the problem under study.

A Hazardous Seas Warning is issued by the National Weather Service of the United States when wave heights and/or wave steepness values reach certain criteria.

Consequently, the wave steepness ka in terms of wave amplitude is not a monotone function up to the highest wave, and Schwartz utilizes instead kH as the expansion parameter.

Soon after, in 1847, the linear theory of Airy was extended by Stokes for non-linear wave motion - known as Stokes' wave theory - correct up to third order in the wave steepness.

Next, a solution for the non-linear wave problem (including the Taylor series expansion around the mean or still surface elevation) is sought by means of a perturbation series - known as the Stokes expansion - in terms of a small parameter, most often the wave steepness.

The linear dispersion relation - unaffected by wave amplitude - is for nonlinear waves also correct at the second order of the perturbation theory expansion, with the orders in terms of the wave steepness k A (where A is wave amplitude).