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NEMO Workspace
Documentation
Reference manuals
Commits
cb65973f
Commit
cb65973f
authored
4 months ago
by
Andrew Coward
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This builds locally (updates to chap_DYN.tex). Also updated namelist submodule
parent
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latex/NEMO/subfiles/chap_DYN.tex
+13
-11
13 additions, 11 deletions
latex/NEMO/subfiles/chap_DYN.tex
namelists
+1
-1
1 addition, 1 deletion
namelists
with
14 additions
and
12 deletions
latex/NEMO/subfiles/chap_DYN.tex
+
13
−
11
View file @
cb65973f
...
...
@@ -161,7 +161,7 @@ This option can be useful when the value of the timestep is limited by vertical
\end{listing}
The vector invariant form of the momentum equation is most commonly used in
coarse-resolution applications of the
\NEMO\
ocean model. For higher resolutions it
coarse-resolution
(1
$^
\textrm
{
o
}$
)
applications of the
\NEMO\
ocean model. For higher resolutions it
requires the activation of Hollingsworth correction (
\np
[=1]
{
nn
_
dynkeg
}{
nn
\_
dynkeg
}
)
following Arakawa (2001) The flux form option (see next section) has been present since
version
$
2
$
. By structuring the equations in vector invariant form, the dynamics are
...
...
@@ -412,12 +412,14 @@ no slip or partial slip boundary conditions are applied following \autoref{chap:
In flux form, the vorticity term reduces to a Coriolis term in which the Coriolis parameter has been modified to account for the "metric" term.
This altered Coriolis parameter is thus discretised at
$
f
$
-points.
It is given by:
\begin{aligned*}
\[
\begin
{
aligned
}
% \label{eq:DYN_cor_metric}
f
+
\frac
{
1
}{
e
_
1
e
_
2
}
\left
(
{
v
\frac
{
\partial
e
_
2
}{
\partial
i
}
-
u
\frac
{
\partial
e
_
1
}{
\partial
j
}}
\right
)
\equiv
f
+
\frac
{
1
}{
e
_{
1
f
}
e
_{
2
f
}
}
\left
(
\overline
v
^{
i
+
1
/
2
}
\delta
_{
i
+
1
/
2
}
\left
[
{
e
_{
2
u
}
}
\right
]
-
\overline
u
^{
j
+
1
/
2
}
\delta
_{
j
+
1
/
2
}
\left
[
{
e
_{
1
u
}
}
\right
]
\right
)
\end{aligned*}
\end
{
aligned
}
\]
% energy conserving scheme at T-point
%% =================================================================================================
...
...
@@ -457,21 +459,21 @@ it is is centred in time (\textit{now} velocity) at stage 2 and 3.
\label
{
subsec:DYN
_
adv
_
flux
}
The discrete expression of the advection term is given by:
\
[
\
begin{equation}
% \label{eq:DYN_adv}
\left\{
\begin{aligned}
\frac
{
1
}{
e
_{
1u
}
\,
e
_{
2u
}
\,
e
_{
3u
}}
\left
(
\delta
_{
i
+
1
/
2
}
\left
[
\overline
{
e
_{
2
u
}
\,
e
_{
3
u
}
\;
u
}^{
i
}
\
u
_
t
\right
]
+
&
\delta
_{
j
}
\left
[
\overline
{
e
_{
1
u
}
\,
e
_{
3
u
}
\;
v
}^{
i
+
1
/
2
}
\
u
_
f
\right
]
\right
.
\\
\left
.
+
&
\delta
_{
k
}
\left
[
\overline
{
e
_{
1
w
}
\,
e
_{
2
w
}
\;
w
}^{
i
+
1
/
2
}
\
u
_{
uw
}
\right
]
\right
)
\\
[
10
pt
]
\left
(
\delta
_{
i+1/2
}
\left
[ \overline{e_{2u}\,e_{3u}\;u }^{i} \ u_t \right]
\right
.
+
&
\delta
_{
j
}
\left
[ \overline{e_{1u}\,e_{3u}\;v }^{i+1/2} \ u_f \right]
\\
+
&
\left
.
\delta
_{
k
}
\left
[ \overline{e_{1w}\,e_{2w}\;w}^{i+1/2} \ u_{uw} \right]
\right
)
\\
[10pt]
\frac
{
1
}{
e
_{
1v
}
\,
e
_{
2v
}
\,
e
_{
3v
}}
\left
(
\delta
_{
i
}
\left
[
\overline
{
e
_{
2
u
}
\,
e
_{
3
u
}
\;
u
}^{
j
+
1
/
2
}
\
v
_
f
\right
]
+
&
\delta
_{
j
+
1
/
2
}
\left
[
\overline
{
e
_{
1
u
}
\,
e
_{
3
u
}
\;
v
}^{
i
}
\
v
_
t
\right
]
\right
.
\\
\left
.
+
&
\delta
_{
k
}
\left
[
\overline
{
e
_{
1
w
}
\,
e
_{
2
w
}
\;
w
}^{
j
+
1
/
2
}
\
v
_{
vw
}
\right
]
\right
)
\\
\left
(
\delta
_{
i
}
\left
[ \overline{e_{2u}\,e_{3u }\;u }^{j+1/2} \ v_f \right]
\right
.
+
&
\delta
_{
j+1/2
}
\left
[ \overline{e_{1u}\,e_{3u }\;v }^{i} \ v_t \right]
\\
+
&
\left
.
\delta
_{
k
}
\left
[ \overline{e_{1w}\,e_{2w}\;w}^{j+1/2} \ v_{vw} \right]
\right
)
\\
\end{aligned}
\right
.
\
]
\
end{equation}
Two advection schemes are available:
a
$
2
^{
nd
}$
order centered finite difference scheme, CEN2,
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