Application of Boundary Element Method for Determination of the Wavemaker Driving Signal

Abstract

A method for the generation of steep nonlinear broad-banded wave trains having an arbitrary prescribed shape is developed. It is shown that the second-order contributions to the velocity field are negligible in deep water, while the second-order bound components of the surface elevation are significant. This fact allows improvement of an iterative method of the wavemaker driving signal adjustment that increases the accuracy of excitation of wave train with the prescribed free waves’ spectrum. The decomposition of the complex amplitude spectrum of the surface elevation into free and bound components is based on the approach adopted in the derivation of the Zakharov model. The iterative adjustment of the driving signal is carried out using the numerical wave tank based on the boundary element method. It is demonstrated that accurate wave train excitation is attained for different values of the wave steepness. The method allows decreasing the number of iterations needed for the driving signal adjustment. The surface elevation values measured in the laboratory wave tank agree closely with those obtained in the numerical simulations. The measured and the simulated frequency spectra are in agreement as well.