GUIDE WAVE ANALYSIS AND FORECASTING - WMO

Energy (cm 2 /Hz)
Energy (cm 2 /Hz)
T p = 1.8 s
Hs = 0.2 m
S
bottom ωθ
Stations
g kh E
ω
, – Γ 2 ωθ , ,
sinh
( ) = ( )
(7.13)
where Γ is an empirically determined coefficient.
Tolman (1994) shows that this expression is very similar
in its effects to more complex expressions that have been
proposed.
7.7 Wave breaking in the surf zone
When a wave progresses into very shallow water (with
depth of the order of the wave height), the upper part of the
wave tends to increase its speed relative to the lower part.
At some point the crest attains a speed sufficiently high to
overtake the preceding trough. The face of the wave
becomes unstable and water from the crest “falls” along
the forward face of the wave (spilling). In extreme cases
the crest falls freely into the trough (plunging). In all cases
2
WAVES IN SHALLOW WATER 87
1 2 3 4 5 6
0.8 m 1:20
0,2 m
4.5 m
1:10
Station 1 Station 2 Station 3
––– Hs = 0.22 m
––––– Hs = 0.22 m
––– Hs = 0.23 m
––––– Hs = 0.22 m
Station 4 Station 5 Station 6
––– Hs = 0.19 m
––––– Hs = 0.19 m
––– Hs = 0.13 m
––––– Hs = 0.13 m
Frequency (Hz) Frequency (Hz) Frequency (Hz)
––– Hs = 0.23 m
––––– Hs = 0.21 m
––– Hs = 0.09 m
––––– Hs = 0.11 m
Figure 7.5 — Comparison of spectral observations and computations of wave breaking over a bar in laboratory conditions.
Solid lines indicate the computations and dashed lines the experiment (Battjes et al., 1993) (courtesy: Delft
University of Technology)
a high-velocity jet of water is at some point injected into
the area preceding the crest. This jet creates a submerged
whirl and in severe breaking it forces the water up again to
generate another wave (often seen as a continuation of the
breaking wave). This wave may break again, resulting in
an intermittent character of the breaker (Jansen, 1986).
Recent investigations have shown that the overall
effect of very shallow water on the wave spectrum can
be described with two processes: bottom induced breaking
and triad interaction. The latter is the non-linear
interaction between three wave components rather than
four as in deep water where it is represented by the
quadruplet interactions of Section 3.4.
The breaking of the waves is of course very visible
in the white water generated in the surf zone. It appears
to be possible to model this by treating each breaker
as a bore with a height equal to the wave height. The