Role of wave breaking in the air–sea interaction - Breaking and Dissipation of Ocean Surface Waves - page 353

for long-term climate prognosis, which predicts an increasing frequency of such events.
It is felt, however, even in moderate-wind conditions as some parts of the continuous wave
spectrum are always subject to strong forcing and thus further contribute to uncertainties
and scatter of C D estimates ( Donelan et al. , 2006 ; Kudryavtsev & Makin , 2007 ; Tsagareli
et al. , 2010 ).
Parameterising C D in terms of mean wind speed U 10 bears further deficiencies. The
mean wind speed U 10 does not define the wave properties unambiguously. For example, the
mean or dominant wave height and length, the saturation level of the wave frequency spec-
trum and its directional spread, all are contributors to the sea drag and all can vary greatly
for the same wind speed as a function of other properties and phenomena in the air-sea
system, even in ideal wave-development situations. Depending on the duration of the wind
action and on the wave fetch, the waves will evolve from short young seas into much longer
old seas. Young waves are on average much steeper compared to the old ones, break more
frequently and most of the other wave characteristics evolve too. This is known as the sea-
state dependence, with U 10 /

c p usually being the sea-state (or inverse wave age) parameter.
A sea-state dependence in C D has long been foreshadowed (e.g. Stewart , 1974 ), but only
relatively recently has it been observed in field measurements. Some support has been
found in a number of data sets (e.g. Smith et al. , 1992 ; Donelan et al. , 1993 ; Oost et al. ,
2001 ; Drennan et al. , 2003 ), but notably not in others (e.g. Yelland et al. , 1998 ). Another
effort at reconciling this fundamental issue has been on the basis of the dominant wave
steepness (e.g. Oost et al. , 2001 ; Taylor & Yelland , 2001 ). The dominant sea waves, how-
ever, are known to play a relatively small direct role in determining the wind stress, except
possibly for very young wind seas. Unless the waves are young, dominant waves are fast
and their interaction with the wind is weak, but the effect of the dominant waves on the
sea drag may be indirect - by means of modulating the shorter waves ( Kudryavtsev &
Makin , 2002 ; Hara & Belcher , 2002 ) or due to air-flow separation from breaking or non-
breaking dominant waves ( Makin & Kudryavtsev , 2002 ; Donelan et al. , 2006 ; Babanin
et al. , 2007b ). This highlights the need to understand more completely the basic physics of
the sea-surface wind stress, including the wave-breaking effects, in order to parameterise
it reliably in the form of a drag coefficient.
Many other effects can contribute significantly to the wind stress. The gustiness of the
wind, which is always a feature of real wind fields, is accommodated in a number of the-
ories ( Janssen , 1986a ; Miles & Ierley , 1998 ) and may result in either reduction of the
stress or its enhancement, but certainly in increasing the scatter of C D dependences if not
accounted for ( Babanin & Makin , 2008 ). The effects of the gustiness, however, are very
difficult to take into account, even if parameterisation of C D for these effects were avail-
able. Indeed, most of the measurements and the majority of models produce wind-speed
variations at temporal scales which average the gustiness out, and therefore it remains
unknown. Babanin & Makin ( 2008 ) suggested a way to bypass this difficulty. They esti-
mated the minimal relative gustiness, which is approximately constant, and produced an
experimental dependence for the maximal gustiness as a function of mean wind speed. That
is, at each value of U 10 , the maximal and minimal magnitudes of gustiness are known, and