Detection and measurement of wave breaking - Breaking and Dissipation of Ocean Surface Waves - page 57

if the relative breaking duration (in terms of the wave period) does not change, the abso-
lute duration (3.17) will grow. If so, dependence (3.17) should be used with caution, as,
for the same wind speed U 10 , under-developed or over-developed (by comparison with the
average stage of development in measurements of Bortkovskii ( 1987a )) estimates based on
(3.17) will be biased.
Bortkovskii ( 1987a ) also produced a number of other statistics and dependences which
are worth noting. Among them, dependence of the duration t B of the existence of pas-
sive whitecapping on water temperature, and long-wind extent of passive whitecaps as
a function of temperature and wind speed. For active whitecaps, he obtained the rate of
lateral spreading of the active whitecaps versus U 10 , an expression for the geometrical
proportion of the longitudinal and lateral whitecap dimensions, and histograms of these
dimensions and of their product (active whitecap area). For this area, he suggested sepa-
rate dependences for the tropical regions and for the Southern Ocean and concluded that
the number of whitecaps per unit area does not depend on the wind in the range of speeds
10m

s, among other interesting findings.
Coming back to the classification of whitecaps into active and passive, they are gener-
ally accepted now, as was re-introduced later by Monahan ( 1993 ), to be named stage A and
stage B whitecaps respectively. It is apparent that, even if both stages are connected with
the breaking probability and breaking strength, the diffusive stage B depends to a great
extent on the lifetime of the residual bubble clouds. This lifetime, as was already known
from earlier observations, is an environmental characteristic rather than a property of wave
breaking or dissipation. Monahan ( 1971 ) compared diffusion rates of oceanic whitecaps
with those in fresh water ( Monahan , 1969 ) and found that the fresh-water whitecap area
decays approximately 1.5 times faster. Thus, an essential variation of the whitecap cov-
erage, in similar meteorological conditions and similar wave fields, is expected for water
bodies with different salinity.
It is interesting to note that there is considerable controversy in the literature regarding
further roles played by salinity in this regard. While some researchers find that the bub-
bles are smaller in salt water (e.g. Haines & Johnson , 1995 ), others claim they are not
(e.g. Cartmill & Su , 1993 ; Wu , 2000 ). Wu ( 2000 ), in particular, found rather that,

/ s ≤ U 10 ≤ 20m /

“a greater volume of air is entrained in salt than in freshwater to generate many more bubbles”.

If this was true, salt-water breaking would have to be more severe which is difficult to
justify physically.
From early observations, it was also known that the lifetime of whitecap foaming L t
depends on the water temperature ( Miyake & Abe , 1948 ). Laboratory experiments of
Miyake & Abe ( 1948 ) produced a rather strong dependence:

L t ∼ exp ( − T

w /

25 ) (3.18)

where T w is the water temperature. Mention of the temperature effect is scattered around
later studies ( Wu , 1979 ; Monahan & MacNiocaill , 1986 ; Monahan & O'Muircheartaigh ,
1986 ; Bortkovskii , 1987a , b , 1997 ; Wu , 1988 ; Bortkovskii & Novak , 1993 ; Stramska &