Singularities in Surface Waves - Selected Topics of Computational and Experimental Fluid Mechanics - page 212

dislocations. Attention is paid to the growth of wave amplitude in the vicinity of the
Huygens cusp, because in this region these singularities occur. On one side a non
linear wave cannot rise indefinitely, at certain time the wave breaking begins. On the
other side diffraction is capable to produce dislocations on the dark side of caustics.
Some comments will be addressed to the decay of wave field far from the Huygens
cusp and the recovery of the linear behavior far from caustics. In most of experiments
the topography of the free surface is recovered with the method of Fourier Transform
Profilometry. The images recorded by the digital camera cover only a fraction of the
fringe pattern, but in any case we consider regions around the Huygens cusp. On the
other side, experiments with synthetic Schlieren method were conducted covering
an area of 20 cm × 11.2 cm. Images were taken at 4 different positions in the range

10 50. The area covered in a position of the camera overlap with the next

one, so we have a complete set of data in a region of 20 cm

< y <

40 cm. In some cases
it is best the use of synthetic Schlieren method. For instance, in a previous work this
method has been successfully used to prove that for small amplitude waves (Ruiz-
Chavarria et al. 2014 )( h

×

10 − 4 m) the nonlinearities are already relevant. Another
case were synthetic Schlieren method is suitable deals with the study of divergent
waves because amplitude decreases as they progress. This happens in our system
after passing the cusp.
Figure 5 shows the wave field as measured by the FTP method for a driving
frequency of 7Hz in the area delimited by

<

32 cm.
As in all figures in this paper, wave progresses from right to left. The Huygens cusp
is located inside this region. Otherwise, the focusing becomes evident by two facts:
(a) the size of wave front decreases from right to left and (b) the wave amplitude
(represented by colors) grows when approaching the cusp. At the left border of figure

− 11 < x < 11 cm and 7 < y <

Fig. 5 Wave fie ld of a
monochromatic wave of
f 7Hz produced by a

parabolic wave maker. Wave
progresses from right to left .
In the figure the maximal
amplitude occurs after
passing the cusp

=