How Is Wavenumber Calculated for Large Topography Disturbances in Steady Waves?

[rsq_a]

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?

 

[gtoguy97]

Is there a technique for solving the wavenumber analytically or numerically without linearizing the topography?This is a difficult question to answer without more specifics, but some techniques that may be helpful include using analytical solutions from potential flow theory, numerical methods such as finite element analysis, and a variety of other numerical methods for solving partial differential equations. Additionally, linear perturbation theory can also be used to find exact solutions to the wave equation.