Role of wave breaking in the air–sea interaction - Breaking and Dissipation of Ocean Surface Waves - page 362

Thus, both mechanical and thermodynamic processes in the air filled by sea droplets
are most important. Some of them can be considered separately, some cannot, as the
mechanical-thermodynamic effects are often coupled. Vakhguelt ( 2007 ) and Chai &
Vakhguelt (2009), for example, suggest a model of pressure-wave propagating through
gas with liquid particles, and describe dissipation of the wave due to thermodynamic inter-
actions. While this is set up as a more general problem, compared to the water droplets
suspended in WBL where wave-induced pressure pulsations play the main role in the wave
growth by the wind, physically the problem is the same.
Generally speaking, in this regard oceanographers can learn a lot from the fields of
physics, technology and engineering where applications related to liquid particles
suspended in gas are abundant (e.g. Borisov & Vakhguelt , 1981 ). For example, such an
engineering problem as rocket combustion engines deals with liquid-fuel droplets in the
gas chamber, and this problem has at least a few decades' head start in theoretical and
practical terms, compared to detailed studies of tropical-cyclone physics which came into
the spotlight lately.
A range of geophysical applications, which oceanographers can relate and refer to, have
also been mentioned above in the context of suspended particles influencing the air/water
turbulence. For example, Kudryavtsev ( 2006 ) elaborated his stratification approach for
WBL, having started in general terms from the model of Barenblatt & Golitsyn ( 1974 )
for dust storms over the land (see also Goroch et al. , 1981 ). With respect to the other side
of the mechanical influence of spray, its momentum-balance impact on the surface stress,
analogies can be extended, for instance, to the effect of the rain in WBL (e.g. Caldwell &
Elliott , 1971 , 1972 ; Andreas , 2004 ).
Basic theory of tropical cyclones directly connects the mechanical and thermodynamic
processes, including those roles played by the spray. Emanuel ( 1986 ) showed that the
intensity of the cyclones depends both on the sea-drag coefficient C D and on the enthalpy-
transfer coefficient C k . Curiously enough, the large-scale modelling foreshadowed satu-
ration of C D magnitude at high wind speeds well before this topic exploded in the field
of wind-generated waves and small-scale air-sea interactions (see Section 9.1.3 ). That is,
according to Emanuel ( 1986 ), the maximal wind speed should be inversely proportional to
√ C D . Emanuel ( 1995 ) then concluded that, if the sea-drag parameterisations measured in
moderate winds were extrapolated into high winds (where they had not been measured),
the hurricanes would hardly be possible, certainly not beyond their lowest category.
This indirect-argument discussion of the sea-drag saturation is not free of controversy,
and the investigations and discussions still continue. Bister & Emanuel ( 1998 ) and Emanuel
( 2003 ) modified the previous approaches to stress that the enthalpy and drag coefficients
should become independent of the wind speed in extreme conditions. Makarieva et al.
( 2010 ), however, argued that previous derivations of the dissipative heating terms contra-
dict the fundamental thermodynamic laws.
The main problem here, as in most of the other theories and models related to hurricanes,
is the lack of direct measurements and observation-based estimates. Zhang et al. ( 2008 )
pointed out that, with respect to the ratio of C k /

C D , no such measurements have been