Singularities in Surface Waves - Selected Topics of Computational and Experimental Fluid Mechanics - page 218

Fig. 14 Graph of the wave amplitude obtained from numerical simulation. a Linear case and
b non linear case. Two dislocations appear outside the caustics both in linear and in nonlinear
waves. They are located inside the blue region of each figure

figure, they are symmetrically situated around x = 0. The dislocations are located

at ( 2.3, 28.9) and at (2.3, 28.9) for the linear wave. For the nonlinear wave the

dislocations are located at (

−

− 3, 29.5) and at (3, 29.5).

6 Conclusions

In this paper we have performed an experimental and numerical study of the wave
field having three types of singularities: caustics, wave breaking and dislocations.
The first one is a fictitious singularity appearing in the ray theory. It disappears when
wave properties are taken into account, but its position reveals bright regions. The
second kind of singularity (wave breaking) is produced by non linear interactions. In
our experiments the breaking is produced through spatial focusing over a distance of
some wavelengths. The wave breaking modify the shape of wave fronts and produces
a dissipation of the energy. Finally, the third kind of singularities are the dislocations,
which are defined as points of complete destructive interference. The singularity deals
with the fact that in a dislocation phase is undefined. The experiments and numerical
simulations were conducted to enhance the nonlinear effects. This research is in
the first stage. A more complete research of singularities requires, among others, a
detailed study of conditions of wave breaking, the determination of the amount of
energy dissipated and the study of dislocations both inside and outside the caustics.

Acknowledgments G. Ruíz Chavarría acknowledges DGAPA-UNAM by support for a sabbatical
period at IRPHE between September 2010 and August 2011. Additionally the authors acknowledge
support byDGAPA-UNAMunder project 116312, Vorticidad y ondas no lineales en fluidos. Authors
acknowledge also Eric Falcon fromUniversity Paris Diderot for his assistance in the implementation
of the Fourier Transform Profilometry.