Changeset 11422 for NEMO/branches/2019/fix_vvl_ticket1791/doc/latex/NEMO/subfiles/annex_iso.tex

Timestamp:

2019-08-08T15:40:47+02:00 (5 years ago)

Author:

jchanut

Message:

#1791, merge with trunk

Location:

NEMO/branches/2019/fix_vvl_ticket1791/doc

Files:

• . (modified) (1 prop)
• latex (modified) (1 prop)
• latex/NEMO (modified) (1 prop)
• latex/NEMO/subfiles/annex_iso.tex (modified) (17 diffs)

NEMO/branches/2019/fix_vvl_ticket1791/doc/latex

@@ -1 @@
-*.aux
-*.bbl
-*.blg
-*.dvi
-*.fdb*
-*.fls
-*.idx
-*.ilg
-*.ind
-*.log
-*.maf
-*.mtc*
-*.out
-*.pdf
-*.toc
-_minted-*
+figures

@@ -1 @@
-*.aux
-*.bbl
-*.blg
-*.dvi
-*.fdb*
-*.fls
-*.idx
-*.ilg
-*.ind
-*.log
-*.maf
-*.mtc*
-*.out
-*.pdf
-*.toc
-_minted-*
+figures

NEMO/branches/2019/fix_vvl_ticket1791/doc/latex/NEMO/subfiles/annex_iso.tex

@@ -4 +4 @@
 \newcommand{\rML}[1][i]{\ensuremath{_{\mathrm{ML}\,#1}}}
 \newcommand{\rMLt}[1][i]{\tilde{r}_{\mathrm{ML}\,#1}}
-\newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}}}
+%% Move to ../../global/new_cmds.tex to avoid error with \listoffigures
+%\newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}}
 \newcommand{\triadd}[5]{\ensuremath{{}_{#1}^{#2}{\mathbb{#3}}_{#4}^{\,#5}}}
 \newcommand{\triadt}[5]{\ensuremath{{}_{#1}^{#2}{\tilde{\mathbb{#3}}}_{#4}^{\,#5}}}
@@ -52 +53 @@
   the vertical skew flux is further reduced to ensure no vertical buoyancy flux,
   giving an almost pure horizontal diffusive tracer flux within the mixed layer.
-  This is similar to the tapering suggested by \citet{Gerdes1991}. See \autoref{subsec:Gerdes-taper}
+  This is similar to the tapering suggested by \citet{gerdes.koberle.ea_CD91}. See \autoref{subsec:Gerdes-taper}
 \item[\np{ln\_botmix\_triad}]
   See \autoref{sec:iso_bdry}. 
@@ -71 +72 @@
 \label{sec:iso}
 
-We have implemented into \NEMO a scheme inspired by \citet{Griffies_al_JPO98},
+We have implemented into \NEMO a scheme inspired by \citet{griffies.gnanadesikan.ea_JPO98},
 but formulated within the \NEMO framework, using scale factors rather than grid-sizes.
 
@@ -194 +195 @@
 \subsection{Expression of the skew-flux in terms of triad slopes}
 
-\citep{Griffies_al_JPO98} introduce a different discretization of the off-diagonal terms that
+\citep{griffies.gnanadesikan.ea_JPO98} introduce a different discretization of the off-diagonal terms that
 nicely solves the problem.
 % Instead of multiplying the mean slope calculated at the $u$-point by
@@ -201 +202 @@
 \begin{figure}[tb]
   \begin{center}
-    \includegraphics[width=1.05\textwidth]{Fig_GRIFF_triad_fluxes}
+    \includegraphics[width=\textwidth]{Fig_GRIFF_triad_fluxes}
     \caption{
       \protect\label{fig:ISO_triad}
@@ -265 +266 @@
 \begin{figure}[tb]
   \begin{center}
-    \includegraphics[width=0.80\textwidth]{Fig_GRIFF_qcells}
+    \includegraphics[width=\textwidth]{Fig_GRIFF_qcells}
     \caption{
       \protect\label{fig:qcells}
@@ -473 +474 @@
 
 To complete the discretization we now need only specify the triad volumes $_i^k\mathbb{V}_{i_p}^{k_p}$.
-\citet{Griffies_al_JPO98} identifies these $_i^k\mathbb{V}_{i_p}^{k_p}$ as the volumes of the quarter cells,
+\citet{griffies.gnanadesikan.ea_JPO98} identifies these $_i^k\mathbb{V}_{i_p}^{k_p}$ as the volumes of the quarter cells,
 defined in terms of the distances between $T$, $u$,$f$ and $w$-points.
 This is the natural discretization of \autoref{eq:cts-var}.
@@ -658 +659 @@
 \begin{figure}[h]
   \begin{center}
-    \includegraphics[width=0.60\textwidth]{Fig_GRIFF_bdry_triads}
+    \includegraphics[width=\textwidth]{Fig_GRIFF_bdry_triads}
     \caption{
       \protect\label{fig:bdry_triads}
@@ -685 +686 @@
 As discussed in \autoref{subsec:LDF_slp_iso},
 iso-neutral slopes relative to geopotentials must be bounded everywhere,
-both for consistency with the small-slope approximation and for numerical stability \citep{Cox1987, Griffies_Bk04}.
+both for consistency with the small-slope approximation and for numerical stability \citep{cox_OM87, griffies_bk04}.
 The bound chosen in \NEMO is applied to each component of the slope separately and
 has a value of $1/100$ in the ocean interior.
@@ -732 +733 @@
 \[
   % \label{eq:iso_tensor_ML}
-  D^{lT}=\nabla {\rm {\bf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad
+  D^{lT}=\nabla {\mathrm {\mathbf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad
   \mbox{with}\quad \;\;\Re =\left( {{
         \begin{array}{*{20}c}
@@ -829 +830 @@
     (\eg the green triad $i_p=1/2,k_p=-1/2$) are tapered to the appropriate basal triad.}
   % }
-  \includegraphics[width=0.60\textwidth]{Fig_GRIFF_MLB_triads}
+  \includegraphics[width=\textwidth]{Fig_GRIFF_MLB_triads}
 \end{figure}
 % >>>>>>>>>>>>>>>>>>>>>>>>>>>>
@@ -847 +848 @@
 \[
   % \label{eq:iso_tensor_ML2}
-  D^{lT}=\nabla {\rm {\bf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad
+  D^{lT}=\nabla {\mathrm {\mathbf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad
   \mbox{with}\quad \;\;\Re =\left( {{
         \begin{array}{*{20}c}
@@ -859 +860 @@
 \footnote{
   To ensure good behaviour where horizontal density gradients are weak,
-  we in fact follow \citet{Gerdes1991} and
+  we in fact follow \citet{gerdes.koberle.ea_CD91} and
   set $\rML^*=\mathrm{sgn}(\tilde{r}_i)\min(|\rMLt^2/\tilde{r}_i|,|\tilde{r}_i|)-\sigma_i$.
 }
@@ -865 +866 @@
 This approach is similar to multiplying the iso-neutral diffusion coefficient by
 $\tilde{r}_{\mathrm{max}}^{-2}\tilde{r}_i^{-2}$ for steep slopes,
-as suggested by \citet{Gerdes1991} (see also \citet{Griffies_Bk04}).
+as suggested by \citet{gerdes.koberle.ea_CD91} (see also \citet{griffies_bk04}).
 Again it is applied separately to each triad $_i^k\mathbb{R}_{i_p}^{k_p}$
 
@@ -925 +926 @@
 
 However, when \np{ln\_traldf\_triad} is set true,
-\NEMO instead implements eddy induced advection according to the so-called skew form \citep{Griffies_JPO98}.
+\NEMO instead implements eddy induced advection according to the so-called skew form \citep{griffies_JPO98}.
 It is based on a transformation of the advective fluxes using the non-divergent nature of the eddy induced velocity.
 For example in the (\textbf{i},\textbf{k}) plane,
@@ -1139 +1140 @@
 it is equivalent to a horizontal eiv (eddy-induced velocity) that is uniform within the mixed layer
 \autoref{eq:eiv_v}.
-This ensures that the eiv velocities do not restratify the mixed layer \citep{Treguier1997,Danabasoglu_al_2008}.
+This ensures that the eiv velocities do not restratify the mixed layer \citep{treguier.held.ea_JPO97,danabasoglu.ferrari.ea_JC08}.
 Equivantly, in terms of the skew-flux formulation we use here,
 the linear slope tapering within the mixed-layer gives a linearly varying vertical flux,
@@ -1153 +1154 @@
 $uw$ (integer +1/2 $i$, integer $j$, integer +1/2 $k$) and $vw$ (integer $i$, integer +1/2 $j$, integer +1/2 $k$)
 points (see Table \autoref{tab:cell}) respectively.
-We follow \citep{Griffies_Bk04} and calculate the streamfunction at a given $uw$-point from
+We follow \citep{griffies_bk04} and calculate the streamfunction at a given $uw$-point from
 the surrounding four triads according to:
 \[

@@ -1 @@
-*.aux
-*.bbl
-*.blg
-*.dvi
-*.fdb*
-*.fls
-*.idx
-*.ilg
-*.ind
-*.log
-*.maf
-*.mtc*
-*.out
-*.pdf
-*.toc
-_minted-*
+figures