TABLE OF CONTENTS As described in Chapter 3 the linear water wave theory also called "sinusoidal wave theory" due to the shape of the waves assumes that the wave height to wave length ratio H/ L (the wave steepness) is so small that the nonlinear terms in the free surface boundary conditions can be neglected.
Although we found that the linear theory in many respects yields meaningful results, there are also situations where it is insufficient. This, of course, applies to cases where one wants to study wave properties that originate from the neglected nonlinearity of the waves. Some of these phenomena will be discussed in the following. It also applies to situations where the wave steepness is so large that linear wave theory becomes too inaccurate. And third, it is relevant to realize that the confidence in linear wave results, where they are known to suffice, essentially comes from comparing with more accurate higher order wave theories.
The more accurate wave theories all include the effects of the nonlinear terms in some form. Hence, all such wave theories are nonlinear and therefore also more complicated than the linear wave theory.
The nonlinear wave theory most widely used today was developed by Stokes (1847) (who by the way at the same time invented the perturbation method which still is the most powerful mathematical tool for solving (weakly) nonlinear problems in all areas of physics), and for that reason, the theory is know as Stokes' wave...
