Geoscience Reference
In-Depth Information
The impact of the helicopter forcing in the frequency spectrum is clearly visible at fre-
quencies
f
2 Hz. Note that the tail rise at the high end of the frequency range is not
physical, it is noise caused by the wire probes averaging the surface elevations over an
area exceeding its diameter several times (e.g.
Cavaleri
,
1979
). In the frequency range
2Hz
>
<
f
<
7 Hz, the helicopter response is rather flat and the corresponding level
α
is
10
−
3
α
helicopter
≈
24
.
5
·
,
(7.29)
that is
α
helicopter
α
Phillips
≈
1
.
9
.
(7.30)
For reference, the
f
−
4
trend is also shown in the bottom panel. It is interesting to point
out that
23 was found as a level corresponding to the 'limiting' wave spectrum
derived by
Stiassnie
(
2010
) for maximal wave steepness of
α
=
0
.
=
.
0
4 for waves across the
spectrum.
We should realise, of course, the limits of this exercise where the wind-wave interaction
pattern was anything but natural. Yet, it provides an instructive insight into wave breaking/
dissipation in extreme weather conditions. In response to such extreme wind forcing, the
waves of all scales grow to the breaking point within less than one period and a 100%
breaking-rate situation is observed. Once the breaking rate can no longer be increasing, the
wave system must, apparently, react with a more intensive breaking dissipation, in order to
balance the wind energy input in conditions when the spectrum level does not (or cannot)
grow any more.
Indeed, the wave spectrum responding to the helicopter forcing by the spectral-density
increased less than two times. If the dependence of the wind-energy input at those scales
is approximately quadratic in terms of the wind speed (
Donelan
et al.
,
2006
), and if we
presume an upper-limit wind speed
U
10
=
20m
/
sfor
α
Phillips
and a lower-limit
U
10
=
30m
/
s for the measured
α
helicopter
, then
U
helicopter
U
Phillips
2
=
2
.
25
,
(7.31)
quite close to the ratio
(7.30)
. If we choose more realistic midrange values of
U
10
=
10m
/
s
for
α
Phillips
and
U
10
=
40m
/
sfor
α
helicopter
, then the ratio becomes
U
helicopter
U
Phillips
2
=
16
.
(7.32)
This is an enormous gap between the increased wind-input rate and the spectral-power
response. This gap should be filled in with the greatly increased dissipation which, in such
a scenario, should be a function of the growing wind forcing or of the wind speed directly,
as was suggested in
Sections 5.3.4
and
6.2
.
Quantitatively, we should remember that estimates
(7.30)
-
(7.32)
are only a guide. As
emphasised already, the helicopter experiment does not fully reflect real hurricane-like
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