Role of wave breaking in the air–sea interaction - Breaking and Dissipation of Ocean Surface Waves - page 381

Layers I and II depict the free atmosphere, which 'does not know about the ocean sur-
face', and the outer (planetary) boundary layer, respectively. At the boundary height h e
between the two layers, interactions start to occur through the entrainments due to turbu-
lent vertical velocities. In the case of the full development ( Pierson & Moskowitz , 1964 ),
this height can be estimated ( Benilov et al. , 1978 ). At such height, total kinetic energy
should be equal to the energy of the fully-developed sea which leads to

10 u 2
g

h e ≈ (9.26)

where u is the wind-velocity scale. Thus, the height of the boundary layer can reach several
hundred metres.
Chalikov & Belevich ( 1993 ) argue that the velocities and entrainments at h e maybedue
to variations of the stress field over the ocean caused by the non-uniform and non-stationary
wavy surface, and therefore 'it is quite possible that wind-waves affect the weather and
climate'.
Below the interface, the mixed layer VII is located above the thermocline VIII which
starts at depth h m . This mixed layer obtains momentum and energy through the transition

zone VI whose depth

−

h t is linked to the wavy surface from below. The total amount of
the momentum and energy are described by expressions (9.20) and (9.22) . Because of
the turbulent vertical velocities at the thermocline border, mixing through the thermocline
due to the waves is possible (e.g. Martin , 1985 ). As mentioned above, direct impact of
the breaking waves at this border is hardly feasible unless depth

−

− h m is small (that is

comparable to wave height).
Thus, the surface waves play an important role in the dynamic regime of both the atmo-
spheric boundary layer and the upper ocean. In the ocean-circulation models, it is quite
typical to disregard the waves (although some trends in this regard are noticeable lately,
see also Section 9.2.2 ). In reality, however, the waves support a major part of the momen-
tum flux from the atmosphere to the ocean, and they do not release it immediately upon
receiving. It is redistributed across the spectrum by means of nonlinear interactions S nl
in (2.61) , and can go both back to the atmosphere and to the current through the wave
breaking and non-breaking dissipation. The transition-delay depends on the temporal and
spatial scales of the wave-energy dissipation, and at this scale the waves are an indepen-
dent player rather than a mere momentum-transfer means. Additionally, both breaking and
non-breaking waves are a source of turbulence in the mixed ocean layer.
As the role of the waves in the lower-atmosphere and upper-ocean dynamics gains
recognition, multiple implementations of this role are being discussed which correspond to
different physical mechanisms. Some of them are depicted in a recent scheme reproduced
from Ardhuin et al. ( 2005 )( Figure 9.9 ). This scheme also shows the body of the ocean
below thermocline all the way to the bottom boundary layers.
At the top, we see the momentum fluxes already described above in the Figure 9.8
scheme of Chalikov & Belevich ( 1993 ), i.e. total stress

a , momentum flux to waves

τ