Changeset 11597 for NEMO/trunk/doc/latex/NEMO/subfiles/apdx_triads.tex

Timestamp:

2019-09-25T20:20:19+02:00 (5 years ago)

Author:

nicolasmartin

Message:

Continuation of coding rules application
Recovery of some sections deleted by the previous commit

File:

• NEMO/trunk/doc/latex/NEMO/subfiles/apdx_triads.tex (modified) (22 diffs)

NEMO/trunk/doc/latex/NEMO/subfiles/apdx_triads.tex

@@ -17 +17 @@
 \chaptertoc
 
+%% =================================================================================================
 \section[Choice of \forcode{namtra\_ldf} namelist parameters]{Choice of \protect\nam{tra_ldf}{tra\_ldf} namelist parameters}
-%-----------------------------------------nam_traldf------------------------------------------------------
-
-%---------------------------------------------------------------------------------------------------------
+
 
 Two scheme are available to perform the iso-neutral diffusion.
@@ -63 +62 @@
 \end{description}
 
+%% =================================================================================================
 \section{Triad formulation of iso-neutral diffusion}
 \label{sec:TRIADS_iso}
@@ -69 +69 @@
 but formulated within the \NEMO\ framework, using scale factors rather than grid-sizes.
 
+%% =================================================================================================
 \subsection{Iso-neutral diffusion operator}
 
@@ -156 +157 @@
 is evaluated at $w$-points but involves horizontal gradients defined at $u$-points.
 
+%% =================================================================================================
 \subsection{Standard discretization}
 
@@ -187 +189 @@
 (\ie\ they enter the computation of density), but it does not work for a passive tracer.
 
+%% =================================================================================================
 \subsection{Expression of the skew-flux in terms of triad slopes}
 
@@ -282 +285 @@
 and in \autoref{eq:TRIADS_i31} $a'_{1}={\:}_i^k{\mathbb{A}_w}_{1/2}^{1/2}$.
 
+%% =================================================================================================
 \subsection{Full triad fluxes}
 
@@ -365 +369 @@
 \end{flalign}
 
+%% =================================================================================================
 \subsection{Ensuring the scheme does not increase tracer variance}
 \label{subsec:TRIADS_variance}
@@ -462 +467 @@
 \]
 
+%% =================================================================================================
 \subsection{Triad volumes in Griffes's scheme and in \NEMO}
 
@@ -490 +496 @@
 we can replace $\overline{A}_{\,i+1/2}^k$ by $A_{i+1/2}^k$ in the above.
 
+%% =================================================================================================
 \subsection{Summary of the scheme}
 
@@ -625 +632 @@
 \end{description}
 
+%% =================================================================================================
 \subsection{Treatment of the triads at the boundaries}
 \label{sec:TRIADS_iso_bdry}
@@ -673 +681 @@
 % >>>>>>>>>>>>>>>>>>>>>>>>>>>>
 
+%% =================================================================================================
 \subsection{ Limiting of the slopes within the interior}
 \label{sec:TRIADS_limit}
@@ -701 +710 @@
 and so acts to reduce gravitational potential energy.
 
+%% =================================================================================================
 \subsection{Tapering within the surface mixed layer}
 \label{sec:TRIADS_taper}
@@ -707 +717 @@
 When the Griffies triads are used, we offer two options for this.
 
+%% =================================================================================================
 \subsubsection{Linear slope tapering within the surface mixed layer}
 \label{sec:TRIADS_lintaper}
@@ -822 +833 @@
 % >>>>>>>>>>>>>>>>>>>>>>>>>>>>
 
+%% =================================================================================================
 \subsubsection{Additional truncation of skew iso-neutral flux components}
 \label{subsec:TRIADS_Gerdes-taper}
@@ -864 +876 @@
 % This may give strange looking results,
 % particularly where the mixed-layer depth varies strongly laterally.
+%% =================================================================================================
 \section{Eddy induced advection formulated as a skew flux}
 \label{sec:TRIADS_skew-flux}
 
+%% =================================================================================================
 \subsection{Continuous skew flux formulation}
 \label{sec:TRIADS_continuous-skew-flux}
@@ -975 +989 @@
 Since it has the same divergence as the advective form it also preserves the tracer variance.
 
+%% =================================================================================================
 \subsection{Discrete skew flux formulation}
 
@@ -1017 +1032 @@
 It also ensures the following two key properties.
 
+%% =================================================================================================
 \subsubsection{No change in tracer variance}
 
@@ -1039 +1055 @@
 Hence the two fluxes associated with each triad make no net contribution to the variance budget.
 
+%% =================================================================================================
 \subsubsection{Reduction in gravitational PE}
 
@@ -1093 +1110 @@
 \beta_i^k\delta_{k+ k_p}[S^i]<0$, this PE change is negative.
 
+%% =================================================================================================
 \subsection{Treatment of the triads at the boundaries}
 \label{sec:TRIADS_skew_bdry}
@@ -1104 +1122 @@
 The namelist parameter \np{ln_botmix_triad}{ln\_botmix\_triad} has no effect on the eddy-induced skew-fluxes.
 
+%% =================================================================================================
 \subsection{Limiting of the slopes within the interior}
 \label{sec:TRIADS_limitskew}
@@ -1111 +1130 @@
 Each individual triad \rtriadt{R} is so limited.
 
+%% =================================================================================================
 \subsection{Tapering within the surface mixed layer}
 \label{sec:TRIADS_taperskew}
@@ -1131 +1151 @@
 (the horizontal flux convergence is relatively insignificant within the mixed-layer).
 
+%% =================================================================================================
 \subsection{Streamfunction diagnostics}
 \label{sec:TRIADS_sfdiag}