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1
0.8
0.6
0
2
4
6
8
10
12
1
0.8
0.6
0
2
4
6
8
10
12
0
−0.2
−0.4
0
2
4
6
8
10
12
U/c
Figure 4.11 Simulations of incipient breaking. (top panel) Steepness 2 (1.1) ; (middle panel) skew-
ness S k (1.2) ; (bottom panel) asymmetry A s (1.3) -versus U / c for IMS = 0 . 20 (dash-dotted line),
0.24 (dashed line) and 0.28 (solid line)
the wave grows to the limiting steepness almost instantaneously - within 1-3 periods (see
Figure 4.7 ). Note that the simulation was again run for a limited number of wave periods.
As a result, in the case of IMS
=
0
.
20, for example, the waves do not have enough time to
break if U
5.
Apart from the relatively weak growth of the limiting steepness as a function of wind in
the top panel (as previously noted), the skewness (middle) and asymmetry (bottom) pan-
els exhibit another marginal feature. For the critical initial steepness of IMS
/
c
<
28, both
skewness and asymmetry magnitudes at breaking are, for all wind forcing cases, greater
than the respective values at less steep initial conditions.
Thus, numerical simulations of the breaking onset reveal some marginal effects which
wind forcing and initial-steepness conditions have on the onset of breaking. Some of these
effects are only noticeable at extreme winds and critical initial steepness.
Therefore, the wind plays a dual role in this process. Firstly, it accelerates the growth
of individual wave steepness. In the simulations shown in Figure 4.2 , doubling the wind
speed resulted in the wave growing to its critical height almost four times faster. Secondly,
the wind can push the wave over and thus reduce the critical steepness, but this reduction
=
0
.
 
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