Changeset 11263 for NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_iso.tex
- Timestamp:
- 2019-07-12T12:47:53+02:00 (5 years ago)
- Location:
- NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc
- Files:
-
- 4 edited
Legend:
- Unmodified
- Added
- Removed
-
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc
- Property svn:ignore deleted
-
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex
- Property svn:ignore
-
old new 1 *.aux 2 *.bbl 3 *.blg 4 *.dvi 5 *.fdb* 6 *.fls 7 *.idx 8 *.ilg 9 *.ind 10 *.log 11 *.maf 12 *.mtc* 13 *.out 14 *.pdf 15 *.toc 16 _minted-* 1 figures
-
- Property svn:ignore
-
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO
- Property svn:ignore deleted
-
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_iso.tex
r10442 r11263 4 4 \newcommand{\rML}[1][i]{\ensuremath{_{\mathrm{ML}\,#1}}} 5 5 \newcommand{\rMLt}[1][i]{\tilde{r}_{\mathrm{ML}\,#1}} 6 \newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}}} 6 %% Move to ../../global/new_cmds.tex to avoid error with \listoffigures 7 %\newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}} 7 8 \newcommand{\triadd}[5]{\ensuremath{{}_{#1}^{#2}{\mathbb{#3}}_{#4}^{\,#5}}} 8 9 \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, 53 54 giving an almost pure horizontal diffusive tracer flux within the mixed layer. 54 This is similar to the tapering suggested by \citet{ Gerdes1991}. See \autoref{subsec:Gerdes-taper}55 This is similar to the tapering suggested by \citet{gerdes.koberle.ea_CD91}. See \autoref{subsec:Gerdes-taper} 55 56 \item[\np{ln\_botmix\_triad}] 56 57 See \autoref{sec:iso_bdry}. … … 71 72 \label{sec:iso} 72 73 73 We have implemented into \NEMO a scheme inspired by \citet{ Griffies_al_JPO98},74 We have implemented into \NEMO a scheme inspired by \citet{griffies.gnanadesikan.ea_JPO98}, 74 75 but formulated within the \NEMO framework, using scale factors rather than grid-sizes. 75 76 … … 194 195 \subsection{Expression of the skew-flux in terms of triad slopes} 195 196 196 \citep{ Griffies_al_JPO98} introduce a different discretization of the off-diagonal terms that197 \citep{griffies.gnanadesikan.ea_JPO98} introduce a different discretization of the off-diagonal terms that 197 198 nicely solves the problem. 198 199 % Instead of multiplying the mean slope calculated at the $u$-point by … … 201 202 \begin{figure}[tb] 202 203 \begin{center} 203 \includegraphics[width= 1.05\textwidth]{Fig_GRIFF_triad_fluxes}204 \includegraphics[width=\textwidth]{Fig_GRIFF_triad_fluxes} 204 205 \caption{ 205 206 \protect\label{fig:ISO_triad} … … 265 266 \begin{figure}[tb] 266 267 \begin{center} 267 \includegraphics[width= 0.80\textwidth]{Fig_GRIFF_qcells}268 \includegraphics[width=\textwidth]{Fig_GRIFF_qcells} 268 269 \caption{ 269 270 \protect\label{fig:qcells} … … 473 474 474 475 To complete the discretization we now need only specify the triad volumes $_i^k\mathbb{V}_{i_p}^{k_p}$. 475 \citet{ Griffies_al_JPO98} identifies these $_i^k\mathbb{V}_{i_p}^{k_p}$ as the volumes of the quarter cells,476 \citet{griffies.gnanadesikan.ea_JPO98} identifies these $_i^k\mathbb{V}_{i_p}^{k_p}$ as the volumes of the quarter cells, 476 477 defined in terms of the distances between $T$, $u$,$f$ and $w$-points. 477 478 This is the natural discretization of \autoref{eq:cts-var}. … … 658 659 \begin{figure}[h] 659 660 \begin{center} 660 \includegraphics[width= 0.60\textwidth]{Fig_GRIFF_bdry_triads}661 \includegraphics[width=\textwidth]{Fig_GRIFF_bdry_triads} 661 662 \caption{ 662 663 \protect\label{fig:bdry_triads} … … 685 686 As discussed in \autoref{subsec:LDF_slp_iso}, 686 687 iso-neutral slopes relative to geopotentials must be bounded everywhere, 687 both for consistency with the small-slope approximation and for numerical stability \citep{ Cox1987, Griffies_Bk04}.688 both for consistency with the small-slope approximation and for numerical stability \citep{cox_OM87, griffies_bk04}. 688 689 The bound chosen in \NEMO is applied to each component of the slope separately and 689 690 has a value of $1/100$ in the ocean interior. … … 732 733 \[ 733 734 % \label{eq:iso_tensor_ML} 734 D^{lT}=\nabla {\ rm {\bf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad735 D^{lT}=\nabla {\mathrm {\mathbf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad 735 736 \mbox{with}\quad \;\;\Re =\left( {{ 736 737 \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.} 830 831 % } 831 \includegraphics[width= 0.60\textwidth]{Fig_GRIFF_MLB_triads}832 \includegraphics[width=\textwidth]{Fig_GRIFF_MLB_triads} 832 833 \end{figure} 833 834 % >>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 847 848 \[ 848 849 % \label{eq:iso_tensor_ML2} 849 D^{lT}=\nabla {\ rm {\bf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad850 D^{lT}=\nabla {\mathrm {\mathbf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad 850 851 \mbox{with}\quad \;\;\Re =\left( {{ 851 852 \begin{array}{*{20}c} … … 859 860 \footnote{ 860 861 To ensure good behaviour where horizontal density gradients are weak, 861 we in fact follow \citet{ Gerdes1991} and862 we in fact follow \citet{gerdes.koberle.ea_CD91} and 862 863 set $\rML^*=\mathrm{sgn}(\tilde{r}_i)\min(|\rMLt^2/\tilde{r}_i|,|\tilde{r}_i|)-\sigma_i$. 863 864 } … … 865 866 This approach is similar to multiplying the iso-neutral diffusion coefficient by 866 867 $\tilde{r}_{\mathrm{max}}^{-2}\tilde{r}_i^{-2}$ for steep slopes, 867 as suggested by \citet{ Gerdes1991} (see also \citet{Griffies_Bk04}).868 as suggested by \citet{gerdes.koberle.ea_CD91} (see also \citet{griffies_bk04}). 868 869 Again it is applied separately to each triad $_i^k\mathbb{R}_{i_p}^{k_p}$ 869 870 … … 925 926 926 927 However, when \np{ln\_traldf\_triad} is set true, 927 \NEMO instead implements eddy induced advection according to the so-called skew form \citep{ Griffies_JPO98}.928 \NEMO instead implements eddy induced advection according to the so-called skew form \citep{griffies_JPO98}. 928 929 It is based on a transformation of the advective fluxes using the non-divergent nature of the eddy induced velocity. 929 930 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 1140 1141 \autoref{eq:eiv_v}. 1141 This ensures that the eiv velocities do not restratify the mixed layer \citep{ Treguier1997,Danabasoglu_al_2008}.1142 This ensures that the eiv velocities do not restratify the mixed layer \citep{treguier.held.ea_JPO97,danabasoglu.ferrari.ea_JC08}. 1142 1143 Equivantly, in terms of the skew-flux formulation we use here, 1143 1144 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 $k$) 1154 1155 points (see Table \autoref{tab:cell}) respectively. 1155 We follow \citep{ Griffies_Bk04} and calculate the streamfunction at a given $uw$-point from1156 We follow \citep{griffies_bk04} and calculate the streamfunction at a given $uw$-point from 1156 1157 the surrounding four triads according to: 1157 1158 \[
Note: See TracChangeset
for help on using the changeset viewer.