Steep unidirectional waves: experiments and modeling

Abstract

We demonstrate the possibility to obtain experimentally a single steep unidirectional wave at а prescribed cross-section of the wave tank. It is shown that the evolution of wave groups with moderate to high maximum steepness is accompanied by notable nonlinearity. The spatial version of the Zakharov equation that was obtained by the authors recently was used as а theoretical model. The equation describes nonlinear spatial evolution of unidirectional wave groups with wide spectra. Good agreement was obtained between the experimental results and the model computations for wave groups with moderate steepness. For wave groups with very high steepness, а good qualitative agreement was observed. It is suggested that bound waves affect the wave envelope shape as well as the location of the focusing. Lack of the quantitative agreement between the numerical computations and the experiments for very steep wave groups is partially attributed to the inability of the conservative Zakharov model to describe the non-conservative effects like the wave breaking.