Experiments on nonlinear gravity-capillary waves

Benjamin-Feir instability of nonlinear gravity-capillary waves is studied e xperimentally. The experimental results are compared with computations perf ormed for values of wavelength and steepness identical to those employed in the experiments. The theoretical approach is based on the Zakharov nonline ar equation which is modified here to incorporate weak viscous dissipation. Experiments are performed in a wave flume which has an accurately controll ed wavemaker for generation of the carrier wave, as well as an additional i ndependent conical wavemaker for generation of controlled three-dimensional disturbances. The approach adopted in the present experimental investigati on allows therefore the determination of the actual boundaries of the insta bility domain, and not just the most unstable disturbances. Instantaneous s urface elevation measurements are performed with capacitance-type wave gaug es. Multipoint measurements make it possible to determine the angular depen dence of the amplitude of the forced and unforced disturbances, as well as their variation along the tank. The limits of the instability domains obtai ned experimentally for each set of carrier wave parameters agree favourably with those computed numerically using the model equation. The numerical st udy shows that application of the Zakharov equation, which is free of the n arrow-band approximation adopted in the derivation of the nonlinear Schrodi nger (NLS) equation, may lead to qualitatively different results regarding the stability of nonlinear gravity-capillary waves. The present experiments support the results of the numerical investigation.