Changeset 11558 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex
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- 2019-09-17T17:04:06+02:00 (5 years ago)
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex (modified) (21 diffs)
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex
r11543 r11558 1 1 \documentclass[../main/NEMO_manual]{subfiles} 2 3 %% Custom aliases 4 \newcommand{\cf}{\ensuremath{C\kern-0.14em f}} 2 5 3 6 \begin{document} … … 45 48 %--------------------------------------------namzdf-------------------------------------------------------- 46 49 47 \nlst{namzdf} 50 \begin{listing} 51 \nlst{namzdf} 52 \caption{\texttt{namzdf}} 53 \label{lst:namzdf} 54 \end{listing} 48 55 %-------------------------------------------------------------------------------------------------------------- 49 56 … … 80 87 %--------------------------------------------namric--------------------------------------------------------- 81 88 82 \nlst{namzdf_ric} 89 \begin{listing} 90 \nlst{namzdf_ric} 91 \caption{\texttt{namzdf\_ric}} 92 \label{lst:namzdf_ric} 93 \end{listing} 83 94 %-------------------------------------------------------------------------------------------------------------- 84 95 … … 137 148 %--------------------------------------------namzdf_tke-------------------------------------------------- 138 149 139 \nlst{namzdf_tke} 150 \begin{listing} 151 \nlst{namzdf_tke} 152 \caption{\texttt{namzdf\_tke}} 153 \label{lst:namzdf_tke} 154 \end{listing} 140 155 %-------------------------------------------------------------------------------------------------------------- 141 156 … … 238 253 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 239 254 \begin{figure}[!t] 240 \begin{center} 241 \includegraphics[width=\textwidth]{Fig_mixing_length} 242 \caption{ 243 \protect\label{fig:ZDF_mixing_length} 244 Illustration of the mixing length computation. 245 } 246 \end{center} 255 \centering 256 \includegraphics[width=\textwidth]{Fig_mixing_length} 257 \caption[Mixing length computation]{Illustration of the mixing length computation} 258 \label{fig:ZDF_mixing_length} 247 259 \end{figure} 248 260 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 421 433 %--------------------------------------------namzdf_gls--------------------------------------------------------- 422 434 423 \nlst{namzdf_gls} 435 \begin{listing} 436 \nlst{namzdf_gls} 437 \caption{\texttt{namzdf\_gls}} 438 \label{lst:namzdf_gls} 439 \end{listing} 424 440 %-------------------------------------------------------------------------------------------------------------- 425 441 … … 475 491 %--------------------------------------------------TABLE-------------------------------------------------- 476 492 \begin{table}[htbp] 477 \begin{center} 478 % \begin{tabular}{cp{70pt}cp{70pt}cp{70pt}cp{70pt}cp{70pt}cp{70pt}c} 479 \begin{tabular}{ccccc} 480 & $k-kl$ & $k-\epsilon$ & $k-\omega$ & generic \\ 481 % & \citep{mellor.yamada_RG82} & \citep{rodi_JGR87} & \citep{wilcox_AJ88} & \\ 482 \hline 483 \hline 484 \np{nn\_clo} & \textbf{0} & \textbf{1} & \textbf{2} & \textbf{3} \\ 485 \hline 486 $( p , n , m )$ & ( 0 , 1 , 1 ) & ( 3 , 1.5 , -1 ) & ( -1 , 0.5 , -1 ) & ( 2 , 1 , -0.67 ) \\ 487 $\sigma_k$ & 2.44 & 1. & 2. & 0.8 \\ 488 $\sigma_\psi$ & 2.44 & 1.3 & 2. & 1.07 \\ 489 $C_1$ & 0.9 & 1.44 & 0.555 & 1. \\ 490 $C_2$ & 0.5 & 1.92 & 0.833 & 1.22 \\ 491 $C_3$ & 1. & 1. & 1. & 1. \\ 492 $F_{wall}$ & Yes & -- & -- & -- \\ 493 \hline 494 \hline 495 \end{tabular} 496 \caption{ 497 \protect\label{tab:ZDF_GLS} 498 Set of predefined GLS parameters, or equivalently predefined turbulence models available with 499 \protect\np{ln\_zdfgls}\forcode{=.true.} and controlled by the \protect\np{nn\_clos} namelist variable in \protect\nam{zdf\_gls}. 500 } 501 \end{center} 493 \centering 494 % \begin{tabular}{cp{70pt}cp{70pt}cp{70pt}cp{70pt}cp{70pt}cp{70pt}c} 495 \begin{tabular}{ccccc} 496 & $k-kl$ & $k-\epsilon$ & $k-\omega$ & generic \\ 497 % & \citep{mellor.yamada_RG82} & \citep{rodi_JGR87} & \citep{wilcox_AJ88} & \\ 498 \hline 499 \hline 500 \np{nn\_clo} & \textbf{0} & \textbf{1} & \textbf{2} & \textbf{3} \\ 501 \hline 502 $( p , n , m )$ & ( 0 , 1 , 1 ) & ( 3 , 1.5 , -1 ) & ( -1 , 0.5 , -1 ) & ( 2 , 1 , -0.67 ) \\ 503 $\sigma_k$ & 2.44 & 1. & 2. & 0.8 \\ 504 $\sigma_\psi$ & 2.44 & 1.3 & 2. & 1.07 \\ 505 $C_1$ & 0.9 & 1.44 & 0.555 & 1. \\ 506 $C_2$ & 0.5 & 1.92 & 0.833 & 1.22 \\ 507 $C_3$ & 1. & 1. & 1. & 1. \\ 508 $F_{wall}$ & Yes & -- & -- & -- \\ 509 \hline 510 \hline 511 \end{tabular} 512 \caption[Set of predefined GLS parameters or equivalently predefined turbulence models available]{ 513 Set of predefined GLS parameters, or equivalently predefined turbulence models available with 514 \protect\np{ln\_zdfgls}\forcode{=.true.} and controlled by 515 the \protect\np{nn\_clos} namelist variable in \protect\nam{zdf\_gls}.} 516 \label{tab:ZDF_GLS} 502 517 \end{table} 503 518 %-------------------------------------------------------------------------------------------------------------- … … 542 557 %--------------------------------------------namzdf_osm--------------------------------------------------------- 543 558 544 \nlst{namzdf_osm} 559 \begin{listing} 560 \nlst{namzdf_osm} 561 \caption{\texttt{namzdf\_osm}} 562 \label{lst:namzdf_osm} 563 \end{listing} 545 564 %-------------------------------------------------------------------------------------------------------------- 546 565 … … 556 575 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 557 576 \begin{figure}[!t] 558 \begin{center} 559 \includegraphics[width=\textwidth]{Fig_ZDF_TKE_time_scheme} 560 \caption{ 561 \protect\label{fig:ZDF_TKE_time_scheme} 562 Illustration of the subgrid kinetic energy integration in GLS and TKE schemes and its links to the momentum and tracer time integration. 563 } 564 \end{center} 577 \centering 578 \includegraphics[width=\textwidth]{Fig_ZDF_TKE_time_scheme} 579 \caption[Subgrid kinetic energy integration in GLS and TKE schemes]{ 580 Illustration of the subgrid kinetic energy integration in GLS and TKE schemes and 581 its links to the momentum and tracer time integration.} 582 \label{fig:ZDF_TKE_time_scheme} 565 583 \end{figure} 566 584 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 676 694 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 677 695 \begin{figure}[!htb] 678 \begin{center} 679 \includegraphics[width=\textwidth]{Fig_npc} 680 \caption{ 681 \protect\label{fig:ZDF_npc} 682 Example of an unstable density profile treated by the non penetrative convective adjustment algorithm. 683 $1^{st}$ step: the initial profile is checked from the surface to the bottom. 684 It is found to be unstable between levels 3 and 4. 685 They are mixed. 686 The resulting $\rho$ is still larger than $\rho$(5): levels 3 to 5 are mixed. 687 The resulting $\rho$ is still larger than $\rho$(6): levels 3 to 6 are mixed. 688 The $1^{st}$ step ends since the density profile is then stable below the level 3. 689 $2^{nd}$ step: the new $\rho$ profile is checked following the same procedure as in $1^{st}$ step: 690 levels 2 to 5 are mixed. 691 The new density profile is checked. 692 It is found stable: end of algorithm. 693 } 694 \end{center} 696 \centering 697 \includegraphics[width=\textwidth]{Fig_npc} 698 \caption[Unstable density profile treated by the non penetrative convective adjustment algorithm]{ 699 Example of an unstable density profile treated by 700 the non penetrative convective adjustment algorithm. 701 $1^{st}$ step: the initial profile is checked from the surface to the bottom. 702 It is found to be unstable between levels 3 and 4. 703 They are mixed. 704 The resulting $\rho$ is still larger than $\rho$(5): levels 3 to 5 are mixed. 705 The resulting $\rho$ is still larger than $\rho$(6): levels 3 to 6 are mixed. 706 The $1^{st}$ step ends since the density profile is then stable below the level 3. 707 $2^{nd}$ step: the new $\rho$ profile is checked following the same procedure as in $1^{st}$ step: 708 levels 2 to 5 are mixed. 709 The new density profile is checked. 710 It is found stable: end of algorithm.} 711 \label{fig:ZDF_npc} 695 712 \end{figure} 696 713 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 838 855 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 839 856 \begin{figure}[!t] 840 \begin{center} 841 \includegraphics[width=\textwidth]{Fig_zdfddm} 842 \caption{ 843 \protect\label{fig:ZDF_ddm} 844 From \citet{merryfield.holloway.ea_JPO99} : 845 (a) Diapycnal diffusivities $A_f^{vT}$ and $A_f^{vS}$ for temperature and salt in regions of salt fingering. 846 Heavy curves denote $A^{\ast v} = 10^{-3}~m^2.s^{-1}$ and thin curves $A^{\ast v} = 10^{-4}~m^2.s^{-1}$; 847 (b) diapycnal diffusivities $A_d^{vT}$ and $A_d^{vS}$ for temperature and salt in regions of 848 diffusive convection. 849 Heavy curves denote the Federov parameterisation and thin curves the Kelley parameterisation. 850 The latter is not implemented in \NEMO. 851 } 852 \end{center} 857 \centering 858 \includegraphics[width=\textwidth]{Fig_zdfddm} 859 \caption[Diapycnal diffusivities for temperature and salt in regions of salt fingering and 860 diffusive convection]{ 861 From \citet{merryfield.holloway.ea_JPO99}: 862 (a) Diapycnal diffusivities $A_f^{vT}$ and $A_f^{vS}$ for temperature and salt in 863 regions of salt fingering. 864 Heavy curves denote $A^{\ast v} = 10^{-3}~m^2.s^{-1}$ and 865 thin curves $A^{\ast v} = 10^{-4}~m^2.s^{-1}$; 866 (b) diapycnal diffusivities $A_d^{vT}$ and $A_d^{vS}$ for temperature and salt in 867 regions of diffusive convection. 868 Heavy curves denote the Federov parameterisation and thin curves the Kelley parameterisation. 869 The latter is not implemented in \NEMO.} 870 \label{fig:ZDF_ddm} 853 871 \end{figure} 854 872 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 893 911 %--------------------------------------------namdrg-------------------------------------------------------- 894 912 % 895 \nlst{namdrg} 896 \nlst{namdrg_top} 897 \nlst{namdrg_bot} 913 \begin{listing} 914 \nlst{namdrg} 915 \caption{\texttt{namdrg}} 916 \label{lst:namdrg} 917 \end{listing} 918 \begin{listing} 919 \nlst{namdrg_top} 920 \caption{\texttt{namdrg\_top}} 921 \label{lst:namdrg_top} 922 \end{listing} 923 \begin{listing} 924 \nlst{namdrg_bot} 925 \caption{\texttt{namdrg\_bot}} 926 \label{lst:namdrg_bot} 927 \end{listing} 898 928 899 929 %-------------------------------------------------------------------------------------------------------------- … … 1175 1205 %--------------------------------------------namzdf_iwm------------------------------------------ 1176 1206 % 1177 \nlst{namzdf_iwm} 1207 \begin{listing} 1208 \nlst{namzdf_iwm} 1209 \caption{\texttt{namzdf\_iwm}} 1210 \label{lst:namzdf_iwm} 1211 \end{listing} 1178 1212 %-------------------------------------------------------------------------------------------------------------- 1179 1213 … … 1287 1321 1288 1322 \begin{table}[htbp] 1289 \begin{center} 1290 % \begin{tabular}{cp{70pt}cp{70pt}cp{70pt}cp{70pt}} 1291 \begin{tabular}{r|ccc} 1292 \hline 1293 spatial discretization & 2nd order centered & 3rd order upwind & 4th order compact \\ 1294 advective CFL criterion & 0.904 & 0.472 & 0.522 \\ 1295 \hline 1296 \end{tabular} 1297 \caption{ 1298 \protect\label{tab:ZDF_zad_Aimp_CFLcrit} 1299 The advective CFL criteria for a range of spatial discretizations for the Leap-Frog with Robert Asselin filter time-stepping 1300 ($\nu=0.1$) as given in \citep{lemarie.debreu.ea_OM15}. 1301 } 1302 \end{center} 1323 \centering 1324 % \begin{tabular}{cp{70pt}cp{70pt}cp{70pt}cp{70pt}} 1325 \begin{tabular}{r|ccc} 1326 \hline 1327 spatial discretization & 2$^nd$ order centered & 3$^rd$ order upwind & 4$^th$ order compact \\ 1328 advective CFL criterion & 0.904 & 0.472 & 0.522 \\ 1329 \hline 1330 \end{tabular} 1331 \caption[Advective CFL criteria for the leapfrog with Robert Asselin filter time-stepping]{ 1332 The advective CFL criteria for a range of spatial discretizations for 1333 the leapfrog with Robert Asselin filter time-stepping 1334 ($\nu=0.1$) as given in \citep{lemarie.debreu.ea_OM15}.} 1335 \label{tab:ZDF_zad_Aimp_CFLcrit} 1303 1336 \end{table} 1304 1337 … … 1331 1364 Cu_{cut} &= 2Cu_{max} - Cu_{min} \nonumber \\ 1332 1365 Fcu &= 4Cu_{max}*(Cu_{max}-Cu_{min}) \nonumber \\ 1333 C\kern-0.14emf &=1366 \cf &= 1334 1367 \begin{cases} 1335 1368 0.0 &\text{if $Cu \leq Cu_{min}$} \\ … … 1340 1373 1341 1374 \begin{figure}[!t] 1342 \begin{center} 1343 \includegraphics[width=\textwidth]{Fig_ZDF_zad_Aimp_coeff} 1344 \caption{ 1345 \protect\label{fig:ZDF_zad_Aimp_coeff} 1346 The value of the partitioning coefficient ($C\kern-0.14em f$) used to partition vertical velocities into parts to 1347 be treated implicitly and explicitly for a range of typical Courant numbers (\forcode{ln_zad_Aimp=.true.}) 1348 } 1349 \end{center} 1375 \centering 1376 \includegraphics[width=\textwidth]{Fig_ZDF_zad_Aimp_coeff} 1377 \caption[Partitioning coefficient used to partition vertical velocities into parts]{ 1378 The value of the partitioning coefficient (\cf) used to partition vertical velocities into 1379 parts to be treated implicitly and explicitly for a range of typical Courant numbers 1380 (\forcode{ln_zad_Aimp=.true.}).} 1381 \label{fig:ZDF_zad_Aimp_coeff} 1350 1382 \end{figure} 1351 1383 … … 1356 1388 \begin{align} 1357 1389 \label{eq:ZDF_Eqn_zad_Aimp_partition2} 1358 w_{i_{ijk}} &= C\kern-0.14emf_{ijk} w_{n_{ijk}} \nonumber \\1359 w_{n_{ijk}} &= (1- C\kern-0.14emf_{ijk}) w_{n_{ijk}}1390 w_{i_{ijk}} &= \cf_{ijk} w_{n_{ijk}} \nonumber \\ 1391 w_{n_{ijk}} &= (1-\cf_{ijk}) w_{n_{ijk}} 1360 1392 \end{align} 1361 1393 … … 1363 1395 the three cases from \autoref{eq:ZDF_Eqn_zad_Aimp_partition} can be considered as: 1364 1396 fully-explicit; mixed explicit/implicit and mostly-implicit. With the settings shown the 1365 coefficient ( $C\kern-0.14em f$) varies as shown in \autoref{fig:ZDF_zad_Aimp_coeff}. Note with these values1397 coefficient (\cf) varies as shown in \autoref{fig:ZDF_zad_Aimp_coeff}. Note with these values 1366 1398 the $Cu_{cut}$ boundary between the mixed implicit-explicit treatment and 'mostly 1367 1399 implicit' is 0.45 which is just below the stability limited given in … … 1381 1413 1382 1414 \begin{figure}[!t] 1383 \begin{center} 1384 \includegraphics[width=\textwidth]{Fig_ZDF_zad_Aimp_overflow_frames} 1385 \caption{ 1386 \protect\label{fig:ZDF_zad_Aimp_overflow_frames} 1387 A time-series of temperature vertical cross-sections for the OVERFLOW test case. These results are for the default 1388 settings with \forcode{nn_rdt=10.0} and without adaptive implicit vertical advection (\forcode{ln_zad_Aimp=.false.}). 1389 } 1390 \end{center} 1415 \centering 1416 \includegraphics[width=\textwidth]{Fig_ZDF_zad_Aimp_overflow_frames} 1417 \caption[OVERFLOW: time-series of temperature vertical cross-sections]{ 1418 A time-series of temperature vertical cross-sections for the OVERFLOW test case. 1419 These results are for the default settings with \forcode{nn_rdt=10.0} and 1420 without adaptive implicit vertical advection (\forcode{ln_zad_Aimp=.false.}).} 1421 \label{fig:ZDF_zad_Aimp_overflow_frames} 1391 1422 \end{figure} 1392 1423 1393 1424 \subsection{Adaptive-implicit vertical advection in the OVERFLOW test-case} 1425 1394 1426 The \href{https://forge.ipsl.jussieu.fr/nemo/chrome/site/doc/NEMO/guide/html/test\_cases.html\#overflow}{OVERFLOW test case} 1395 1427 provides a simple illustration of the adaptive-implicit advection in action. The example here differs from the basic test case … … 1428 1460 implicit and explicit components of the vertical velocity are available via XIOS as 1429 1461 \texttt{wimp} and \texttt{wexp} respectively. Likewise, the partitioning coefficient 1430 ( $C\kern-0.14em f$) is also available as \texttt{wi\_cff}. For a quick oversight of1462 (\cf) is also available as \texttt{wi\_cff}. For a quick oversight of 1431 1463 the schemes activity the global maximum values of the absolute implicit component 1432 1464 of the vertical velocity and the partitioning coefficient are written to the netCDF … … 1460 1492 1461 1493 \begin{figure}[!t] 1462 \ begin{center}1463 1464 \caption{1465 \protect\label{fig:ZDF_zad_Aimp_overflow_all_rdt}1466 Sample temperature vertical cross-sections from mid- and end-run using different values for \forcode{nn_rdt}1467 and with or without adaptive implicit vertical advection. Without the adaptive implicit vertical advection only1468 the run with the shortest timestep is able to run to completion. Note also that the colour-scale has been1469 chosen to confirm that temperatures remain within the original range of 10$^o$ to 20$^o$.1470 }1471 \ end{center}1494 \centering 1495 \includegraphics[width=\textwidth]{Fig_ZDF_zad_Aimp_overflow_all_rdt} 1496 \caption[OVERFLOW: sample temperature vertical cross-sections from mid- and end-run]{ 1497 Sample temperature vertical cross-sections from mid- and end-run using 1498 different values for \forcode{nn_rdt} and with or without adaptive implicit vertical advection. 1499 Without the adaptive implicit vertical advection 1500 only the run with the shortest timestep is able to run to completion. 1501 Note also that the colour-scale has been chosen to confirm that 1502 temperatures remain within the original range of 10$^o$ to 20$^o$.} 1503 \label{fig:ZDF_zad_Aimp_overflow_all_rdt} 1472 1504 \end{figure} 1473 1505 1474 1506 \begin{figure}[!t] 1475 \begin{center} 1476 \includegraphics[width=\textwidth]{Fig_ZDF_zad_Aimp_maxCf} 1477 \caption{ 1478 \protect\label{fig:ZDF_zad_Aimp_maxCf} 1479 The maximum partitioning coefficient during a series of test runs with increasing model timestep length. 1480 At the larger timesteps, the vertical velocity is treated mostly implicitly at some location throughout 1481 the run. 1482 } 1483 \end{center} 1507 \centering 1508 \includegraphics[width=\textwidth]{Fig_ZDF_zad_Aimp_maxCf} 1509 \caption[OVERFLOW: maximum partitioning coefficient during a series of test runs]{ 1510 The maximum partitioning coefficient during a series of test runs with 1511 increasing model timestep length. 1512 At the larger timesteps, 1513 the vertical velocity is treated mostly implicitly at some location throughout the run.} 1514 \label{fig:ZDF_zad_Aimp_maxCf} 1484 1515 \end{figure} 1485 1516 1486 1517 \begin{figure}[!t] 1487 \begin{center} 1488 \includegraphics[width=\textwidth]{Fig_ZDF_zad_Aimp_maxCf_loc} 1489 \caption{ 1490 \protect\label{fig:ZDF_zad_Aimp_maxCf_loc} 1491 The maximum partitioning coefficient for the \forcode{nn_rdt=10.0s} case overlaid with information on the gridcell i- and k- 1492 locations of the maximum value. 1493 } 1494 \end{center} 1518 \centering 1519 \includegraphics[width=\textwidth]{Fig_ZDF_zad_Aimp_maxCf_loc} 1520 \caption[OVERFLOW: maximum partitioning coefficient for the case overlaid]{ 1521 The maximum partitioning coefficient for the \forcode{nn_rdt=10.0} case overlaid with 1522 information on the gridcell i- and k-locations of the maximum value.} 1523 \label{fig:ZDF_zad_Aimp_maxCf_loc} 1495 1524 \end{figure} 1496 1525
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