Geoscience Reference
In-Depth Information
3.
The salinity conservation equation:
∂
∂
S
t
+
∂
(
S u
x
)
∂
∂
∂
S
x
j
=
D
"
+
S
S
ss
∂
∂
x
j
j
j
4.
The temperature conservation equation:
∂
∂
T
t
+
∂
(
T u
x
)
∂
∂
∂
T
x
j
=
D
"
+
S
T
ss
∂
∂
x
j
j
j
where
,
S
, and
T
are the local density, salinity, and temperature of the fluid,
respectively;
c
s
is the speed of sound in sea water;
u
i
is the velocity in the
x
i
direction
(
i
,
j
= 1, 2, 3);
ρ
Ω
ij
is the Coriolis tensor;
P
is the pressure of the fluid;
g
i
is the
gravitational vector;
v
t
is the turbulent eddy viscosity;
is the Kronecker's delta;
k
is the turbulent kinetic energy;
S
and
T
are the salinity and temperature;
D
S
and
D
T
are the associated dispersion coefficients; and
t
denotes time. The
S
ss
terms refer to
the respective source-sink terms and thus differ from equation to equation. Water
density
δ
is calculated from salinity, temperature, and pressure using the UNESCO
equation of state.
21
ρ
9.2.A.2
Wind Stress
The wind friction at the air-sea interface originates from the vertical shear term
assuming a balance between the wind shear and the water shear at the surface. In a
right-handed Cartesian coordinate system (
x, y, z
), with corresponding current com-
ponents
u
,
v
,
w
, the balance along the
x
-axis can be expressed as
ρ
ρ
∂
∂
u
z
τ
ρ
xz
==
air
C
WW
ν
t
w
x
where
ρ
air
is the density of air,
W
is the wind speed with a component
W
x
along the
x
-axis, and
C
w
is the wind drag coefficient. The same formulation applies to the
y
-axis.
The wind friction is thus a boundary condition to the vertical shear term. The wind
drag coefficient can be calculated as:
2
C
w
=
C
w
0
for
W
<
W
0
C
w
=
C
w
0
+ (
C
w
1
−
C
w
0
)
⋅
(
W
−
W
0
)/(
W
1
−
W
0
)
for
W
0
≤
W
≤
W
1
C
w
=
C
w
1
for
W
>
W
1
where
C
w
0
= 0.0013 for
W
0
= 0 m/s and
C
w
1
= 0.0026 for
W
1
= 24 m/s.
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