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.

An analytical and numerical study of a vertically discretized multi-paddle wavemaker for generating free surface and internal waves

“…Extensive work has focused on deriving analytical wavemaker solutions (e.g. Flick and Guza, 1980;Schäffer, 1996;Aknin and Spinneken, 2017;Khait and Shemer, 2019;Veloso Lima et al, 2019). Flick and Guza (1980) developed the solution applicable to the piston and flap type wavemakers by dividing the solution into harmonic free wave and harmonic Stokes (forced) wave components to exclude spurious errors originated from sub-and super-harmonic wave components.…”

“…Compared to experimental data, however, notable deviations in amplitude and phase were observed (Aknin and Spinneken, 2017). Recently, Khait and Shemer (2019) presented the nonlinear formulation using higher-order spectral method (e.g. Houtani et al, 2018) for improved predictions.…”

“…Chwang (1983) and Chwang and Li (1983) studied porous piston type wavemakers to reduce wave paddle pressure. Hybrid type wavemakers were also developed to eliminate the second harmonic waves induced by the aforementioned dissimilarity between the 'classical' wavemaker motions and resulting velocity profiles (Fontanet, 1961;Flick and Guza, 1980;Schäffer, 1996;Khait and Shemer, 2019). This wavemaker engages both piston and flap types by changing the bottom position of the paddle in the 'classical' flap type wavemaker and functions as a piston type if paddle is infinitely long.…”