Focusing of Surface Waves

Abstract

In this chapter we present some original experimental results of the process of focusing of surface waves in a fluid. To this end, monochromatic waves of frequencies in the range 5–15 Hz are produced in a water layer of 10 cm depth using a parabolic wave maker. Experiments remain in the deep water approximation and both gravity and surface tension influence the evolution of waves. We find that, as in optics, the wave field exhibits phenomena such as diffraction, interference and the presence of two caustics intersecting at one point and forming a cusp. To investigate the properties of surface waves, the synthetic Schlieren method is used. Nonlinear behavior emerges during the process of focusing even for small amplitude waves. For example the peak amplitudes are more pronounced that the amplitude of the troughs. Some non expected results emerge from our experiments. The first is that the position of the maximum amplitude of the wave is dependent on the amplitude of the initial parabolic wave front, but in any case, is always in the vicinity of the origin of Huygens’ cusp. Second, the predictions for linear waves are only in partial agreement with our experimental data. And finally, due to the fact that the ratio of the size of wave maker to the wavelength does not tend to infinity some finite size effects are observed.