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In-Depth Information
y
ı
y
T
n
1
v
H
v
z
v
A
C
ı
y
y
v
!
K
H
.
z
w
/
n
C
1
ı
z
T
n
C
1
/
C
xyı
z
C
xyQ
r
ı
z
(15.17)
xy
2t
ı
2t
.
x
y
z
u
z
u
u
a
S
v
z
v
v
a
S
z
S/
D
ı
x
.y
/
ı
y
.x
/
ı
z
.xy
w
S
/
y
ı
x
S
n
1
u
z
u
u
H
A
C
xy
z
QS
sor
C
ı
x
x
u
y
ı
y
S
n
1
v
z
v
v
H
A
C
ı
y
y
v
!
K
H
/
n
C
1
ı
z
S
n
C
1
C
xyı
z
(15.18)
.
z
w
In (
15.14
,
15.15
,
15.16
,
15.17
and
15.18
),
F
u
and
F
v
are the horizontal mixing terms,
atm
and
tp
are the atmospheric surface pressure and tidal potential respectively,
is the surface elevation term that can be distributed among any of the three
time levels,
and
D
˛
1
n
C
1
C
˛
2
n
C
˛
3
n
1
, according to the temporal weighting
terms
A
H
are the horizontal
mixing coefficients for the velocity and scalar fields (temperature and salinity)
respectively, likewise
˛
1
,
˛
2
,or
˛
3
, which are specified by the user.
A
M
and
K
M
and
K
M
for the vertical mixing, Q is a volume flux
source term (with
T
sor
,
S
sor
,
u
sor
,and
v
sor
as the term source values),
Q
r
is the
solar radiation,
z
denote the grid-cell dimensions defined at the center of the grid cells, and the
superscripts
u
,
v
and
w
indicate the grid-cell dimensions computed at those velocity
locations on the staggered Arakawa C-grid.
is a function describing the solar extinction,
x
,
y
and
p
i
are
the reference density of seawater and the internal pressure, respectively, and the
horizontal advection velocity terms are given by
u
a
f
is the Coriolis term,
0
and
and
v
a
.Theterm
C
curv
is used
to correct the horizontal advection of momentum for the horizontal curvature of the
grid. It is calculated as
C
curv
D
v
y
ı
2x
.y/
2xy
u
x
ı
2y
.x/
2xy
(15.19)
The horizontal mixing terms for the momentum equations are given by
!
y
x
u
M
u
z
u
A
F
u
ı
x
u
n
1
D
ı
x
2
x
u
x
!
x
x
x
v
z
v
v
M
v
z
v
v
M
A
A
ı
y
u
n
1
C
ı
x
v
n
1
C
ı
y
(15.20)
y
v
x
v
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