Wavenumber of steady waves
This is an ultra vague question, but I'm hoping to bump into an expert who might know.
Consider the steady flow of water over a polygonal surface (like a step, for instance -- something that can be easily conformally mapped). The wavenumber of the far field (large x) gravity waves can be found by linearizing both in wave amplitude (small waves) and the topography height (small disturbance). It's something like,
[tex]\epsilon k = \tanh(k\pi)[/tex]
where epsilon is the Froude number. This can be easily done using Fourier transforms.
The question I have is, how is the wavenumber found WITHOUT assuming a small disturbance?