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Treating the whitecap coverage W (3.5) as a direct indicator, or even as a property
directly proportional to the dissipation S ds (3.9) and (3.10) , however, is a significant over-
simplification which is quite poorly justified. While the S ds
U 3 relationship for steady
U 3 , even if the depen-
dence of the bubble lifetime on environmental conditions does not play its role. Dominant
waves, if they break, provide a major contribution to whitecapping. For mature seas, how-
ever, they do not break (e.g. Banner et al. , 2000 ; Dulov et al. , 2002 ), and for developing
seas a combined effect of frequency of their occurrence and severity of their breaking
is not necessarily proportional to U 3 (e.g. Babanin et al. , 2009a , 2010a ). Also there is
multiple evidence that the bulk of energy flux to the waves is supported by short waves
(e.g. Terray et al. , 1996 ) which bulk is also lost through dissipation at high frequencies
(e.g. Babanin et al. , 2007c ). Such short-wave breaking has a strong connection with the
dominant waves, rather than directly with the wind, and the energy-containing waves
appear to strongly modulate the respective whitecapping which is physically located near
the dominant crests. At the spectral end of very short waves, furthermore, their breaking
produces little or no whitecapping (see Section 2.8 ).
With this in mind, let us review the theoretical argument based on the assumption that
coverage W is proportional to the wind energy flux (3.6) . If the drag coefficient
wind-wave fields is true, it does not necessarily imply that W
C D =
constant
,
(3.11)
we arrive at p
3 assumed in (3.3) and similar dependences. It is, however, not constant.
There is a great variety of experimental parameterisations of C D versus U , and none of
them suggests that the drag coefficient is independent of wind speed. Wu ( 1979 ), based on
Wu ( 1969 ) and Garratt ( 1977 ), used
=
U 1 / 2
10
C D
(3.12)
=
.
and obtained p
75 in (3.2) and (3.9) . Most experimental dependences are much steeper
than (3.12) . We refer to Babanin & Makin ( 2008 ) for a recent review and to their 'ideal-
condition' parameterisation of
3
10 7 U 10 +
C D =
1
.
92
·
0
.
000953
.
(3.13)
3 was assumed, cannot be
expected to remain general. Whichever power p is chosen or fitted, however, deviations
from fit are still observed at high wind speeds (e.g. Monahan , 1971 ; Wu , 1979 ; Stramska &
Petelski , 2003 , and others), particularly as in a very strong wind the sea drag C D indeed
saturates (see Section 9.1.3 ). The explanation of such an effect seems obvious. At high
wind speeds, whitecap coverage can no longer characterise the balance (3.6) between the
wind input and wave dissipation. As Munk ( 1947 ) puts it, for 'fresh breeze' “spume tends
to be blown from the breaking wave crests”. According to Munk ( 1947 ), the fresh breeze
is winds in excess of 8
In any case, (3.3) and similar approximations where p
=
s. The blown spume should create an enhanced foam coverage,
in addition to the coverage due to the strength of the wave breaking, and the respective bias
of the W versus U dependences. Therefore, any such parameterisations should be treated
.
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