Geoscience Reference
In-Depth Information
In Babanin et al. ( 2007b ), b t was taken as 2.5 throughout the analysis. This choice of b t
will be proved below.
In Figure 8.3 d, the synchronous instantaneous energy flux p t is plotted, where p is the
instantaneous pressure detected just above the moving surface and ∂η
is the partial time
t
derivative of the elevation
η
. The wave-height signal, which in this measurement was sam-
pled at f s =
50 Hz, was smoothed using a 5 Hz low-pass filter. Again, the bursts are evident,
but require a formal averaging procedure to quantify the integral enhanced-pressure effect.
This is done in the last panel, Figure 8.3 e. To highlight the enhancement effect, this
subplot shows the running average of the energy flux, based on the same averaging interval
of 0
f p as above. It is clear that the flux is enhanced over the second and third breakers,
somewhat enhanced over the first one, but hardly at all over the last breaker.
Thus, the approach adopted by Babanin et al. ( 2007b ) was based on measuring the flux
over breaking waves, the breakers being detected on the basis of the acoustic noise emitted.
The capability of the breakers to emit noise, however, depends strongly on the phase of the
wave breaking (not to be confused with the phase angle of the wave). Classification of these
phases was proposed by Liu & Babanin ( 2004 ) and discussed in detail in Chapter 2 . There
are four phases: incipient breaking, developing breaking, subsiding breaking and residual
breaking. At the incipient stage, the water surface becomes unstable and the breaking starts,
but little if any whitecapping is produced and therefore the acoustic or visual methods will
not detect such a breaker. They will detect it at the developing and subsiding stages when
the whitecaps are actively formed, the latter stage being characterised by the originally
steep waves having lost much of their height and their steepness having dropped below
the mean-steepness level. During the last, residual, stage of breaking, whitecaps are left
behind, and this stage is not relevant here. Obviously, the first three breakers in Figure 8.3 a
are developing while the last one is subsiding, its steepness being no different to that of
non-breaking waves.
The enhancement effect is expected to be due to flow separation over the steep breakers
and hence will exhibit itself at the incipient and developing breaking stages, but not at the
subsiding and residual stages. Therefore, it is not unexpected that there is no enhancement
evident over the fourth breaker in Figure 8.3 e. This kind of breaker will, however, be rou-
tinely detected by means of the acoustic-based technique and will tend to lower the overall
enhancement value compared to the integrated energy flux over the entire wave-breaking
set. Additionally, the acoustic technique will not detect the incipient breakers that may or
may not produce a separated flow. If they do, energy fluxes over such waves will be inte-
grated into the contribution of non-breaking waves and thus will lead to underestimation
of the breaking-induced enhancement. Therefore, estimates made here have to be regarded
as a lower bound.
The basis for the choice of the bottom-pressure threshold b t for registering breaking
events is justified in Figure 8.4 . The data sets used to illustrate this are from three dif-
ferent wind-speed cases of Table 8.1 : U 10
.
25
/
=
6
.
6m
/
s (record 4, circles), 8
.
1m
/
s (record
10, x-symbols) and 11
s (record 8, plus-symbols). The bottom-pressure signal was
processed as described above.
.
9m
/
 
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