Singularities in Surface Waves - Selected Topics of Computational and Experimental Fluid Mechanics - page 213

0.6

0.4

0.2

0

−0.2

−0.4

30 25 20 15 10

Y (cm)

Fig. 6 Monochromatic wave of f = 7Hz produced by a parabolic wave maker along the symmetry
axis. Wave progresses from right to left . The asymmetry of the wave reveals that nonlinearities are
important

there is a change of sign of the wavefront curvature, so waves become divergent.
Consequently the further evolution leads to a decrease of the wave amplitude.
Taking into account that the maximal value of surface deformations occurs along

x 0, in Fig. 6 we show the curve h versus y along the symmetry axis. The maximal

amplitude occurs at y

=

27 cm, after passing the cusp, in agreement with results by
Pearcey. A key feature of Fig. 6 is the asymmetry of the wave. This is a signature
of a nonlinear behavior. For y

=

27 cm the wave amplitude decreases because wave
becomes divergent. In order to follow evolution of such divergent waves we have

>

0.06

0.04

0.02

0

−0.02

−0.04

−0.06

40 38 36 34 32

Y (cm)

Fig. 7 Wave field of a monochromatic wave of f = 10Hz produced by a parabolic wave maker. The
topography of the free surface was obtained with the synthetic Schlieren method. Wave progresses
from right to left .Aty = 40 the values of skewness and asymmetry are respectively 0.06 and − 0.02.
At y

=

34 cm these quantities take the following values A s =

.

16 and S =−

.

0 0 04