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surface, the total wind stress
τ
can be represented by three components: turbulent stress
τ
turb
, wave-induced stress
τ
wave
and viscous or tangential stress
τ
ν
(e.g.
Kudryavtsev
et al.
,
2001
):
τ
=
τ
turb
+
τ
wave
+
τ
ν
.
(7.36)
The atmospheric turbulent momentum flux decreases to zero at the surface itself where the
turbulence vanishes. Therefore, directly at the surface the total wind stress is a combina-
tion of stress
τ
wave
induced by the ocean waves and the viscous stress
τ
ν
which generates
surface currents.
Among the different contributions to the total stress
(7.36)
, the wave-induced stress is
directly related to the momentum exchange between the wind and the waves, and it is this
part which is used by
Tsagareli
et al.
(
2010
) as the constraint for the wind-input source
term. It is estimated at the air-sea interface as:
τ
wave
=
τ
−
τ
ν
.
(7.37)
On the other hand, the wave-induced stress is determined by the wind momentum
input as:
f
max
τ
wave
=
M
(
f
)
df
,
(7.38)
f
min
where
M
is the momentum-input function, and the integration limits signify mini-
mal and maximal frequency
f
which still contribute to this input. The momentum-input
function
M
(
f
)
(
f
)
can be obtained from the wind energy-input source term
S
in
(
f
)
in
(2.61)
:
)
=
ρ
w
g
S
in
(
f
)
M
(
f
df
.
(7.39)
c
(
f
)
Therefore,
τ
wave
=
ρ
w
g
f
max
S
in
(
f
)
df
.
(7.40)
c
(
f
)
f
min
This constraint is apparent from the physical point of view. In the practical sense, sat-
isfying this criterion determines the credibility of a parameterised form for the wind-input
source term
S
in
, and sets the main physical framework for investigation of the behaviour
of this parameterisation and its validation, before it is employed in a model together with
other sources.
Wave-induced stress is dependent on the upper limit of the integral in
(7.40)
. Contribu-
tion of short-wave scales to the total stress is significant, and therefore the higher the upper
limit of the integral, the more precise is the estimate of the wave-induced stress. Thus, the
upper limit of
f
max
10 Hz was selected by
Tsagareli
et al.
(
2010
) which signifies the
shortest waves in the capillary range still involved in air-sea coupling.
Computation of the wave-induced stress using
(7.37)
required knowledge of the viscous
stress. Here, the viscous-stress contribution to the total stress was estimated according to
=
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