Role of wave breaking in the air–sea interaction - Breaking and Dissipation of Ocean Surface Waves - page 402

scatter, and these passive-acoustic observations reveal interesting dependences for the bub-
ble size of breaking occurring in a variety of environmental conditions, with wind speeds
from 10m

/ sto20m / s and across the spectral band ranging from 0 . 8 f p below the spectral

peak f p up to double peak frequency 2 f p .
Now, moving to the process of injection of the bubbles by the breaking waves, this
process can be approximately subdivided into two essentially different phases: the bubble-
submersion stage and the bubble-rise stage (e.g. Bortkovskii , 1998 ). Because of these two
dynamic phases, the structure of active and passive whitecaps is also different as described
above. Dynamically, in the course of active breaking, the structure is more or less perma-
nent, but it rapidly changes following the breaker passage - towards the quasi-stationary
residual bubble foams with the mean bubble size several time larger. At strong wind speeds,
this transition occurs in the space of 0

5s.
Bortkovskii ( 1998 ) assumes that descending water motion is formed beneath the break-
ing crest which transports the bubbles created at the surface downward, and that the veloc-
ity of this motion gradually decreases with depth. Entrainment of the bubbles at the surface
followed by their vertical submersion can happen in a number of ways. For spilling break-
ers, for example, Koga & Toba ( 1981 ) demonstrated in laboratory experiments that at the
front edge of the bulge sliding down the front face of a breaking wave, diffusive penetration
of the bubbles into the water happens, having significant vertical velocity components. For
plunging breakers, the entrainment is direct due to the impact of the plunging jet. The ver-
tical velocity of the core of the plunging water volume u pl decreases exponentially away
from the surface, and at the wind speed U 10 =

. 5-2 .

s in field observations, for example,
Bortkovskii ( 1998 ) measured the following dependence:

15m /

u pl = 70 exp ( − 0 . 011 z ) (9.49)

where this velocity is expressed in cm/s. Accordingly, close to the surface, measured bubble
velocities are of the order of 60-100 cm /

s( Bezzabotnov et al. , 1986 ). It is interesting to
note that these values are actually close to estimates of the vertical component of the orbital
velocity at wave crests with the limiting inclination (2.56) , corresponding to the breaking
onset, which should be of the order of 35-60 cm

s( Longuet-Higgins & Turner , 1974 ).
Estimates show that the bubbles reach their lowest position in several seconds
( Bortkovskii , 1998 ). Production of the bubbles of all sizes stops simultaneously, upon the
passage of the whitecap, and the entrainment rate of bubbles of all sizes by the down-
ward water motion is the same, at least in the plunging jet. The buoyancy of the bubbles
of different sizes, however, is different and therefore their rates of surfacing are not the
same. As a result, depth distribution of the bubble sizes is not uniform: smaller bubbles
penetrate deeper. Again, temperature plays a role here. The lifetime of the bubbles in cold
water is longer (3.18) , and therefore the mass loss is slower, buoyancy is higher and depth
penetration is smaller ( Hwang et al. , 1991 ; Bortkovskii , 1998 ).
Transfer of gases from the atmosphere to the ocean due to bubbles is a well-known
phenomenon (e.g. Thorpe , 1982 , 1992 ; Merlivat & Memery , 1983 ; Melville , 1996 ; Woolf ,
1997 ; Donelan , 1998 ; Bortkovskii , 2003 ; McNeil & D'Asaro , 2007 , among many others),

/