Fully nonlinear analytical theories for surface waves and numerical simulations of wave breaking - Breaking and Dissipation of Ocean Surface Waves - page 133

30 U/Cp=1.0

U/Cp=1.5
U/Cp=2.0
U/Cp=2.5
U/Cp=3.0
U/Cp=3.5
U/Cp=4.0
U/Cp=4.5
U/Cp=5.0
U/Cp=5.5
U/Cp=6.0
U/Cp=6.5
U/Cp=7.0
U/Cp=7.5
U/Cp=8.0
U/Cp=8.5
U/Cp=9.0
U/Cp=9.5
U/Cp=10.0
U/Cp=10.5
U/Cp=11.0

25

20

U/Cp=1

15

10

U/Cp=11

5

0

0.18 0.20 0.22 0.24 0.26 0.28 0.30

AK

Figure 4.7 Numerical simulations, number of wave lengths to breaking versus IMS = ak , different
wind forcing U / c . Chalikov (2007, personal communication)

significantly, i.e. U 0, such a wave will only break after 31 wavelengths. Under

the same wind forcing, the wave will break faster if its IMS is greater. That is, at a forcing
of U

/ c = 3 .

/ c = 3 . 0, but IMS = 0 . 26, it will take 15 wavelengths to reach the point of breaking,

and at IMS 27 only nine. Quantitative application of these strictly two-dimensional

numerical results may be limited, but as will be shown in Section 5.1.1 , qualitatively this
picture agrees well with the experiment.

= 0 .