Changeset 11263 for NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_LDF.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/chap_LDF.tex
r10442 r11263 38 38 % Direction of lateral Mixing 39 39 % ================================================================ 40 \section{Direction of lateral mixing (\protect\mdl{ldfslp})} 40 \section[Direction of lateral mixing (\textit{ldfslp.F90})] 41 {Direction of lateral mixing (\protect\mdl{ldfslp})} 41 42 \label{sec:LDF_slp} 42 43 … … 44 45 \gmcomment{ 45 46 we should emphasize here that the implementation is a rather old one. 46 Better work can be achieved by using \citet{ Griffies_al_JPO98, Griffies_Bk04} iso-neutral scheme.47 Better work can be achieved by using \citet{griffies.gnanadesikan.ea_JPO98, griffies_bk04} iso-neutral scheme. 47 48 } 48 49 … … 119 120 %In practice, \autoref{eq:ldfslp_iso} is of little help in evaluating the neutral surface slopes. Indeed, for an unsimplified equation of state, the density has a strong dependancy on pressure (here approximated as the depth), therefore applying \autoref{eq:ldfslp_iso} using the $in situ$ density, $\rho$, computed at T-points leads to a flattening of slopes as the depth increases. This is due to the strong increase of the $in situ$ density with depth. 120 121 121 %By definition, neutral surfaces are tangent to the local $in situ$ density \citep{ McDougall1987}, therefore in \autoref{eq:ldfslp_iso}, all the derivatives have to be evaluated at the same local pressure (which in decibars is approximated by the depth in meters).122 %By definition, neutral surfaces are tangent to the local $in situ$ density \citep{mcdougall_JPO87}, therefore in \autoref{eq:ldfslp_iso}, all the derivatives have to be evaluated at the same local pressure (which in decibars is approximated by the depth in meters). 122 123 123 124 %In the $z$-coordinate, the derivative of the \autoref{eq:ldfslp_iso} numerator is evaluated at the same depth \nocite{as what?} ($T$-level, which is the same as the $u$- and $v$-levels), so the $in situ$ density can be used for its evaluation. … … 135 136 thus the $in situ$ density can be used. 136 137 This is not the case for the vertical derivatives: $\delta_{k+1/2}[\rho]$ is replaced by $-\rho N^2/g$, 137 where $N^2$ is the local Brunt-Vais\"{a}l\"{a} frequency evaluated following \citet{ McDougall1987}138 where $N^2$ is the local Brunt-Vais\"{a}l\"{a} frequency evaluated following \citet{mcdougall_JPO87} 138 139 (see \autoref{subsec:TRA_bn2}). 139 140 … … 154 155 Note: The solution for $s$-coordinate passes trough the use of different (and better) expression for 155 156 the constraint on iso-neutral fluxes. 156 Following \citet{ Griffies_Bk04}, instead of specifying directly that there is a zero neutral diffusive flux of157 Following \citet{griffies_bk04}, instead of specifying directly that there is a zero neutral diffusive flux of 157 158 locally referenced potential density, we stay in the $T$-$S$ plane and consider the balance between 158 159 the neutral direction diffusive fluxes of potential temperature and salinity: … … 201 202 a minimum background horizontal diffusion for numerical stability reasons. 202 203 To overcome this problem, several techniques have been proposed in which the numerical schemes of 203 the ocean model are modified \citep{ Weaver_Eby_JPO97, Griffies_al_JPO98}.204 the ocean model are modified \citep{weaver.eby_JPO97, griffies.gnanadesikan.ea_JPO98}. 204 205 Griffies's scheme is now available in \NEMO if \np{traldf\_grif\_iso} is set true; see Appdx \autoref{apdx:triad}. 205 Here, another strategy is presented \citep{ Lazar_PhD97}:206 Here, another strategy is presented \citep{lazar_phd97}: 206 207 a local filtering of the iso-neutral slopes (made on 9 grid-points) prevents the development of 207 208 grid point noise generated by the iso-neutral diffusion operator (\autoref{fig:LDF_ZDF1}). … … 212 213 213 214 Nevertheless, this iso-neutral operator does not ensure that variance cannot increase, 214 contrary to the \citet{ Griffies_al_JPO98} operator which has that property.215 contrary to the \citet{griffies.gnanadesikan.ea_JPO98} operator which has that property. 215 216 216 217 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 217 218 \begin{figure}[!ht] 218 219 \begin{center} 219 \includegraphics[width= 0.70\textwidth]{Fig_LDF_ZDF1}220 \includegraphics[width=\textwidth]{Fig_LDF_ZDF1} 220 221 \caption { 221 222 \protect\label{fig:LDF_ZDF1} … … 235 236 236 237 237 % In addition and also for numerical stability reasons \citep{ Cox1987, Griffies_Bk04},238 % In addition and also for numerical stability reasons \citep{cox_OM87, griffies_bk04}, 238 239 % the slopes are bounded by $1/100$ everywhere. This limit is decreasing linearly 239 240 % to zero fom $70$ meters depth and the surface (the fact that the eddies "feel" the 240 241 % surface motivates this flattening of isopycnals near the surface). 241 242 242 For numerical stability reasons \citep{ Cox1987, Griffies_Bk04}, the slopes must also be bounded by243 For numerical stability reasons \citep{cox_OM87, griffies_bk04}, the slopes must also be bounded by 243 244 $1/100$ everywhere. 244 245 This constraint is applied in a piecewise linear fashion, increasing from zero at the surface to … … 249 250 \begin{figure}[!ht] 250 251 \begin{center} 251 \includegraphics[width= 0.70\textwidth]{Fig_eiv_slp}252 \includegraphics[width=\textwidth]{Fig_eiv_slp} 252 253 \caption{ 253 254 \protect\label{fig:eiv_slp} … … 301 302 % Lateral Mixing Operator 302 303 % ================================================================ 303 \section{Lateral mixing operators (\protect\mdl{traldf}, \protect\mdl{traldf}) } 304 \section[Lateral mixing operators (\textit{traldf.F90})] 305 {Lateral mixing operators (\protect\mdl{traldf}, \protect\mdl{traldf})} 304 306 \label{sec:LDF_op} 305 307 … … 309 311 % Lateral Mixing Coefficients 310 312 % ================================================================ 311 \section{Lateral mixing coefficient (\protect\mdl{ldftra}, \protect\mdl{ldfdyn}) } 313 \section[Lateral mixing coefficient (\textit{ldftra.F90}, \textit{ldfdyn.F90})] 314 {Lateral mixing coefficient (\protect\mdl{ldftra}, \protect\mdl{ldfdyn})} 312 315 \label{sec:LDF_coef} 313 316 … … 339 342 which is specified through the \np{rn\_ahm0} and \np{rn\_aht0} namelist parameters. 340 343 341 \subsubsection{Vertically varying mixing coefficients (\protect\key{traldf\_c1d} and \key{dynldf\_c1d})} 344 \subsubsection[Vertically varying mixing coefficients (\texttt{\textbf{key\_traldf\_c1d}} and \texttt{\textbf{key\_dynldf\_c1d}})] 345 {Vertically varying mixing coefficients (\protect\key{traldf\_c1d} and \key{dynldf\_c1d})} 342 346 The 1D option is only available when using the $z$-coordinate with full step. 343 347 Indeed in all the other types of vertical coordinate, … … 350 354 This profile is hard coded in file \textit{traldf\_c1d.h90}, but can be easily modified by users. 351 355 352 \subsubsection{Horizontally varying mixing coefficients (\protect\key{traldf\_c2d} and \protect\key{dynldf\_c2d})} 356 \subsubsection[Horizontally varying mixing coefficients (\texttt{\textbf{key\_traldf\_c2d}} and \texttt{\textbf{key\_dynldf\_c2d}})] 357 {Horizontally varying mixing coefficients (\protect\key{traldf\_c2d} and \protect\key{dynldf\_c2d})} 353 358 By default the horizontal variation of the eddy coefficient depends on the local mesh size and 354 359 the type of operator used: … … 366 371 This variation is intended to reflect the lesser need for subgrid scale eddy mixing where 367 372 the grid size is smaller in the domain. 368 It was introduced in the context of the DYNAMO modelling project \citep{ Willebrand_al_PO01}.373 It was introduced in the context of the DYNAMO modelling project \citep{willebrand.barnier.ea_PO01}. 369 374 Note that such a grid scale dependance of mixing coefficients significantly increase the range of stability of 370 375 model configurations presenting large changes in grid pacing such as global ocean models. … … 376 381 For example, in the ORCA2 global ocean model (see Configurations), 377 382 the laplacian viscosity operator uses \np{rn\_ahm0}~= 4.10$^4$ m$^2$/s poleward of 20$^{\circ}$ north and south and 378 decreases linearly to \np{rn\_aht0}~= 2.10$^3$ m$^2$/s at the equator \citep{ Madec_al_JPO96, Delecluse_Madec_Bk00}.383 decreases linearly to \np{rn\_aht0}~= 2.10$^3$ m$^2$/s at the equator \citep{madec.delecluse.ea_JPO96, delecluse.madec_icol99}. 379 384 This modification can be found in routine \rou{ldf\_dyn\_c2d\_orca} defined in \mdl{ldfdyn\_c2d}. 380 385 Similar modified horizontal variations can be found with the Antarctic or Arctic sub-domain options of 381 386 ORCA2 and ORCA05 (see \&namcfg namelist). 382 387 383 \subsubsection{Space varying mixing coefficients (\protect\key{traldf\_c3d} and \key{dynldf\_c3d})} 388 \subsubsection[Space varying mixing coefficients (\texttt{\textbf{key\_traldf\_c3d}} and \texttt{\textbf{key\_dynldf\_c3d}})] 389 {Space varying mixing coefficients (\protect\key{traldf\_c3d} and \key{dynldf\_c3d})} 384 390 385 391 The 3D space variation of the mixing coefficient is simply the combination of the 1D and 2D cases, … … 430 436 % Eddy Induced Mixing 431 437 % ================================================================ 432 \section{Eddy induced velocity (\protect\mdl{traadv\_eiv}, \protect\mdl{ldfeiv})} 438 \section[Eddy induced velocity (\textit{traadv\_eiv.F90}, \textit{ldfeiv.F90})] 439 {Eddy induced velocity (\protect\mdl{traadv\_eiv}, \protect\mdl{ldfeiv})} 433 440 \label{sec:LDF_eiv} 434 441 … … 475 482 since it allows us to take advantage of all the advection schemes offered for the tracers 476 483 (see \autoref{sec:TRA_adv}) and not just the $2^{nd}$ order advection scheme as in 477 previous releases of OPA \citep{ Madec1998}.484 previous releases of OPA \citep{madec.delecluse.ea_NPM98}. 478 485 This is particularly useful for passive tracers where \emph{positivity} of the advection scheme is of 479 486 paramount importance.
Note: See TracChangeset
for help on using the changeset viewer.