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which further induce turbulence and promote mixing. Under moderate and strong winds,
however, a normal component of the wind stress dominates, which is supported by the
momentum flux from wind to waves (e.g. Kudryavtsev & Makin , 2002 ). The latter means
that, before this momentum is received by the upper ocean in the form of mean currents,
and thus enters the further cycle of air-sea interaction, it goes through a stage of surface
wave motion. This motion can directly affect or influence the upper-ocean mixing and
other processes, and thus skipping the wave phase of momentum transformation under-
mines the accuracy and perhaps the validity of approaches based on the assumption of
direct mixing of the upper ocean due to the wind. This should also be a sink of wave
energy, small by comparison with the breaking dissipation, but perhaps essential for the
swell decay.
The wave-Reynolds-number hypothesis thus attempts to link together three oceanic
features which are routinely treated as separate properties: the wind-waves, the near-
surface turbulence and the upper-ocean mixed layer. Mechanisms of MLD deepening are
believed to be affected by a number of ocean properties and processes: i.e. wind stress,
heating and cooling, advection, wave breaking, Langmuir circulation and internal waves,
with the surface wind forcing being the major factor in many circumstances (e.g. Martin ,
1985 ). In accordance with this hypothesis, the role of the wind stress, acting at the ocean
surface, may need to be reconsidered in terms of themixing throughout thewater column due
to wind-generated wave orbital motion. This mixing can be accounted for through the wave
energy spent on generation of turbulence, i.e. wave-turbulence dissipation ( Pleskachevsky
et al. , 2011 ).
The hypothesis of the wave Reynolds number, as mentioned above, refers to the mean
surface wave elevation
η
, propagating in time t and space x with amplitude a 0 :
η(
x
,
t
) =
a 0 cos
t
+
kx
).
(7.68)
This propagating elevation has two characteristic length scales: wave length
and wave
amplitude a . In deep water, the amplitude a decays exponentially away from the surface:
λ
a
(
z
) =
a 0 exp
(
kz
)
(7.69)
where z is the scalar vertical distance from the mean water level.
Wavelength
does not depend on depth z and defines the horizontal scale over which
the wave oscillations change phase. It also characterises the depth of penetration of the
wave oscillations (the distance from the surface where the oscillations can still be sensed
is approximately
λ
2). This scale, however, does not comprise the physical motion of
the water particles. The motion of physical particles involved in the wave oscillations is
depicted by the other scale, a , which is also the radius of wave orbits.
The wave Reynolds number (hereinafter WRN) is
λ/
a 2
au orb
ν
ω
ν
Re wave =
=
(7.70)
 
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