Geoscience Reference
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the surface winds to the water
...
Hence, the turbulence of the upper ocean is nourished by the energy
supplied in the waves. Consequently, the turbulence characteristics should depend on the state of the
ocean surface.”
In a retrospective, starting from historical works by
Dobroklonskiy
(
1947
) and
Bowden
(
1950
) who first attempted to take into account the wave influence on the ocean turbulence
theoretically, credit has to be given to
Kitaigorodskii & Mitropolskiy
(
1968
),
Longuet-
Higgins
(
1969a
),
Korotaev
et al.
(
1971
),
Yefimov & Khristoforov
(
1971
),
Benilov
(
1973
),
Benilov & Lozovatskiy
(
1977
),
Kitaigorodskii & Lumley
(
1983
),
Benilov
et al.
(
1993
),
Craig & Banner
(
1994
) and
Craig
(
1996
), among many others.
Benilov & Ly
(
2002
), in
terms of the momentum
τ
0
(9.20)
, describe the wave-breaking stress as
τ
w
=
τ
w
+
τ
c
(9.27)
where
τ
c
is the
momentum
(9.21)
flux produced by the wave breaking (it finally goes to the mean current
as discussed in
Section 9.2.1
).
Benilov & Ly
(
2002
) suggested a three-layer model of the mixed-layer turbulence, the
upper part being controlled by this wave breaking. They used a
k
τ
w
is spent on the wave growth and is carried away by the waves, and
model for the evolution
of turbulent kinetic energy (TKE), with the energy budget having an extra term for the
turbulent diffusion of wave kinetic energy.
In the upper layer, the potential wave field possesses the best part of the kinetic energy,
and production of the turbulence by breaking significantly exceeds the mean-shear effect.
The turbulent diffusion of the wave kinetic energy dominates over the diffusion of TKE at
these depths of the order of wave height.
Below this layer, as the wave kinetic energy rapidly drops, diffusion of turbulent kinetic
energy exceeds the wave effect in the energy budget, and direct wave impact rapidly dimin-
ishes. Indirectly, however, the wave-breaking turbulence affects the dynamics of the entire
Ekman layer below it.
Thus, immediately below the wave-breaking diffusive layer there is a transitional turbu-
lent diffusive layer. Here, the turbulent diffusion still exceeds the mean shear contribution
to the TKE budget, that is the main source of turbulence here is the TKE flux from the
breaking-controlled layer above.
And it is only below that we can see the logarithmic mean-velocity profile, which is
an analogy to the wall-law turbulence. In this turbulent sublayer, the mean-shear produc-
tion of TKE dominates. As in the case of the atmospheric boundary layer discussed in
Section 9.2.1
, however, this logarithmic layer 'knows' about the surface waves and their
breaking. The roughness scale of this profile, the water-side friction velocity
u
∗
w
,the
volumetric dissipation rate
−
dis
of the constant-flux layer, and the vertical extent of this
logarithmic layer - they all are defined by the wave breaking and the dynamics of the
wave-breaking and transitional sublayers above.
Thus, the mixing scheme of
Benilov & Ly
(
2002
) provides a full and convincing picture
of the turbulence profile in the water column with the free wind-forced surface. This profile
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