Nonlinear wave generation by a wavemaker in deep to intermediate water depth

A new analytical method to calculate the nonlinear correction to the wavemaker motion needed for the accurate generation of steep waves is suggested. It is developed taking advantage of the existing models of nonlinear water waves, such as Zakharov, Dysthe, or Schrödinger equations. The limitations of the method in terms of the order of nonlinearity and spectral width are determined by the wave model used, thus allowing its extension to the 3^rd and higher orders, beyond the limits of the existing wavemaker theories. Application of the nonlinear water waves models allowed significant simplification of the procedure of determination of the nonlinear correction to the wavemaker driving signal. The suggested method was carefully validated against the theory of Schäffer, fully-nonlinear numerical simulations and wave flume experiments. The advantages of the method were exploited to carefully investigate different regimes of wave generation. An appreciable deviation of the actual value of the linear transfer function from the theoretical predictions was found in agreement with the earlier experimental investigations. The mean current arising at the 2^nd order due to finite displacements of the wavemaker surface was suggested as one of the reasons for that deviation.