  The first-order and the second-order wave generation theory is studied in
this paper. The theory is based on the fully nonlinear water wave equations.
The nonlinear boundary value problem (BVP) is solved using a series expansion
method. Using this method, the problem becomes a set of linear, signalling
problems according to the expansion order. The first-order theory leads to a
homogeneous BVP. It is a system with the first-order steering of the wavemaker
motion as input and the surface wave field with propagating and evanescent
modes as output. The second-order theory leads to a nonhomogeneous BVP. It is a
system where the second-order steering of the wavemaker motion is prescribed in
such a way that the second-order part of the surface elevation far from the
wavemaker contains only the bound wave component and the free wave component
vanishes. The second-order surface wave elevation consists of a superposition
of bichromatic frequencies.

Fluid Dynamics