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Commit cb65973f authored by Andrew Coward's avatar Andrew Coward
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This builds locally (updates to chap_DYN.tex). Also updated namelist submodule

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......@@ -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*}
\[
\begin{aligned}
% \label{eq:DYN_cor_metric}
f+\frac{1}{e_1 e_2 }\left( {v\frac{\partial e_2 }{\partial i} - u\frac{\partial e_1 }{\partial j}} \right)
\equiv f + \frac{1}{e_{1f} e_{2f} } \left( \overline v ^{i+1/2}\delta_{i+1/2} \left[ {e_{2u} } \right]
- \overline u ^{j+1/2}\delta_{j+1/2} \left[ {e_{1u} } \right] \right)
\end{aligned*}
\end{aligned}
\]
% 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:
\[
\begin{equation}
% \label{eq:DYN_adv}
\left\{
\begin{aligned}
\frac{1}{e_{1u}\,e_{2u}\,e_{3u}}
\left( \delta_{i+1/2} \left[ \overline{e_{2u}\,e_{3u}\;u }^{i} \ u_t \right]
+ & \delta_{j} \left[ \overline{e_{1u}\,e_{3u}\;v }^{i+1/2} \ u_f \right] \right. \\
\left. + & \delta_{k} \left[ \overline{e_{1w}\,e_{2w}\;w}^{i+1/2} \ u_{uw} \right] \right) \\[10pt]
\left( \delta_{i+1/2} \left[ \overline{e_{2u}\,e_{3u}\;u }^{i} \ u_t \right] \right.
+ & \delta_{j} \left[ \overline{e_{1u}\,e_{3u}\;v }^{i+1/2} \ u_f \right] \\
+ & \left. \delta_{k} \left[ \overline{e_{1w}\,e_{2w}\;w}^{i+1/2} \ u_{uw} \right] \right) \\[10pt]
\frac{1}{e_{1v}\,e_{2v}\,e_{3v}}
\left( \delta_{i} \left[ \overline{e_{2u}\,e_{3u }\;u }^{j+1/2} \ v_f \right]
+ & \delta_{j+1/2} \left[ \overline{e_{1u}\,e_{3u }\;v }^{i} \ v_t \right] \right. \\
\left. + & \delta_{k} \left[ \overline{e_{1w}\,e_{2w}\;w}^{j+1/2} \ v_{vw} \right] \right) \\
\left( \delta_{i} \left[ \overline{e_{2u}\,e_{3u }\;u }^{j+1/2} \ v_f \right] \right.
+ & \delta_{j+1/2} \left[ \overline{e_{1u}\,e_{3u }\;v }^{i} \ v_t \right] \\
+ & \left. \delta_{k} \left[ \overline{e_{1w}\,e_{2w}\;w}^{j+1/2} \ v_{vw} \right] \right) \\
\end{aligned}
\right.
\]
\end{equation}
Two advection schemes are available:
a $2^{nd}$ order centered finite difference scheme, CEN2,
......
Subproject commit 43a9e90e73133b4d705f0576a474c5c0b04c2204
Subproject commit 10fd1134aba6ea0c748fbd47cc95a9172ac6b838
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