Third-order generation of narrow-banded wave trains by a wavemaker

Abstract

Analytic method for nonlinear wave generation by a wavemaker that is free of 2nd order limitation inherent to existing wavemaker theories is proposed. The method is based on the Nonlinear Schrödinger (NLS) equation and the nonlinear boundary condition at the wavemaker. Advantages offered by the NLS model allowed simplification of the expressions for determination of the wavemaker driving signal and thus made them easily applicable in practice. The 2nd and the 3rd-order corrections to the wavemaker driving signal are calculated from the complex surface elevation envelope obtained as a solution of the NLS equation at the prescribed location in the wave flume. The domain of applicability of the generation method was determined on the basis of numerous experiments in the wave flume as well as numerical simulations using a fully-nonlinear Numerical Wave Tank (NWT). A very good generation of the required wave train shape was obtained for sufficiently narrow-banded spectra in both deep-water and intermediate depth conditions. The generation of the sheared current due to oscillatory wavemaker motion has been discussed.