Changeset 11582 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex
- Timestamp:
- 2019-09-20T11:44:31+02:00 (5 years ago)
- File:
-
- 1 edited
-
NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex (modified) (24 diffs)
Legend:
- Unmodified
- Added
- Removed
-
NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex
r11578 r11582 3 3 %% Custom aliases 4 4 \newcommand{\cf}{\ensuremath{C\kern-0.14em f}} 5 6 \onlyinsubfile{\makeindex} 5 7 6 8 \begin{document} … … 42 44 are computed and added to the general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively. 43 45 %These trends can be computed using either a forward time stepping scheme 44 %(namelist parameter \np {ln_zdfexp}{ln\_zdfexp}\forcode{=.true.}) or a backward time stepping scheme45 %(\np {ln_zdfexp}{ln\_zdfexp}\forcode{=.false.}) depending on the magnitude of the mixing coefficients,46 %(namelist parameter \np[=.true.]{ln_zdfexp}{ln\_zdfexp}) or a backward time stepping scheme 47 %(\np[=.false.]{ln_zdfexp}{ln\_zdfexp}) depending on the magnitude of the mixing coefficients, 46 48 %and thus of the formulation used (see \autoref{chap:TD}). 47 49 … … 92 94 %-------------------------------------------------------------------------------------------------------------- 93 95 94 When \np {ln_zdfric}{ln\_zdfric}\forcode{=.true.}, a local Richardson number dependent formulation for the vertical momentum and96 When \np[=.true.]{ln_zdfric}{ln\_zdfric}, a local Richardson number dependent formulation for the vertical momentum and 95 97 tracer eddy coefficients is set through the \nam{zdf_ric}{zdf\_ric} namelist variables. 96 98 The vertical mixing coefficients are diagnosed from the large scale variables computed by the model. … … 118 120 119 121 A simple mixing-layer model to transfer and dissipate the atmospheric forcings 120 (wind-stress and buoyancy fluxes) can be activated setting the \np {ln_mldw}{ln\_mldw}\forcode{=.true.} in the namelist.122 (wind-stress and buoyancy fluxes) can be activated setting the \np[=.true.]{ln_mldw}{ln\_mldw} in the namelist. 121 123 122 124 In this case, the local depth of turbulent wind-mixing or "Ekman depth" $h_{e}(x,y,t)$ is evaluated and … … 225 227 which is valid in a stable stratified region with constant values of the Brunt-Vais\"{a}l\"{a} frequency. 226 228 The resulting length scale is bounded by the distance to the surface or to the bottom 227 (\np {nn_mxl}{nn\_mxl}\forcode{=0}) or by the local vertical scale factor (\np{nn_mxl}{nn\_mxl}\forcode{=1}).229 (\np[=0]{nn_mxl}{nn\_mxl}) or by the local vertical scale factor (\np[=1]{nn_mxl}{nn\_mxl}). 228 230 \citet{blanke.delecluse_JPO93} notice that this simplification has two major drawbacks: 229 231 it makes no sense for locally unstable stratification and the computation no longer uses all 230 232 the information contained in the vertical density profile. 231 To overcome these drawbacks, \citet{madec.delecluse.ea_NPM98} introduces the \np {nn_mxl}{nn\_mxl}\forcode{=2, 3} cases,233 To overcome these drawbacks, \citet{madec.delecluse.ea_NPM98} introduces the \np[=2, 3]{nn_mxl}{nn\_mxl} cases, 232 234 which add an extra assumption concerning the vertical gradient of the computed length scale. 233 235 So, the length scales are first evaluated as in \autoref{eq:ZDF_tke_mxl0_1} and then bounded such that: … … 267 269 where $l^{(k)}$ is computed using \autoref{eq:ZDF_tke_mxl0_1}, \ie\ $l^{(k)} = \sqrt {2 {\bar e}^{(k)} / {N^2}^{(k)} }$. 268 270 269 In the \np {nn_mxl}{nn\_mxl}\forcode{=2} case, the dissipation and mixing length scales take the same value:270 $ l_k= l_\epsilon = \min \left(\ l_{up} \;,\; l_{dwn}\ \right)$, while in the \np {nn_mxl}{nn\_mxl}\forcode{=3} case,271 In the \np[=2]{nn_mxl}{nn\_mxl} case, the dissipation and mixing length scales take the same value: 272 $ l_k= l_\epsilon = \min \left(\ l_{up} \;,\; l_{dwn}\ \right)$, while in the \np[=3]{nn_mxl}{nn\_mxl} case, 271 273 the dissipation and mixing turbulent length scales are give as in \citet{gaspar.gregoris.ea_JGR90}: 272 274 \[ … … 312 314 $\alpha_{CB} = 100$ the Craig and Banner's value. 313 315 As the surface boundary condition on TKE is prescribed through $\bar{e}_o = e_{bb} |\tau| / \rho_o$, 314 with $e_{bb}$ the \np{rn_ebb}{rn\_ebb} namelist parameter, setting \np {rn_ebb}{rn\_ebb}\forcode{ = 67.83} corresponds316 with $e_{bb}$ the \np{rn_ebb}{rn\_ebb} namelist parameter, setting \np[=67.83]{rn_ebb}{rn\_ebb} corresponds 315 317 to $\alpha_{CB} = 100$. 316 Further setting \np {ln_mxl0}{ln\_mxl0}\forcode{ =.true.}, applies \autoref{eq:ZDF_Lsbc} as the surface boundary condition on the length scale,318 Further setting \np[=.true.]{ln_mxl0}{ln\_mxl0}, applies \autoref{eq:ZDF_Lsbc} as the surface boundary condition on the length scale, 317 319 with $\beta$ hard coded to the Stacey's value. 318 320 Note that a minimal threshold of \np{rn_emin0}{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) is applied on the … … 385 387 (\ie\ near-inertial oscillations and ocean swells and waves). 386 388 387 When using this parameterization (\ie\ when \np {nn_etau}{nn\_etau}\forcode{=1}),389 When using this parameterization (\ie\ when \np[=1]{nn_etau}{nn\_etau}), 388 390 the TKE input to the ocean ($S$) imposed by the winds in the form of near-inertial oscillations, 389 391 swell and waves is parameterized by \autoref{eq:ZDF_Esbc} the standard TKE surface boundary condition, … … 398 400 (no penetration if $f_i=1$, \ie\ if the ocean is entirely covered by sea-ice). 399 401 The value of $f_r$, usually a few percents, is specified through \np{rn_efr}{rn\_efr} namelist parameter. 400 The vertical mixing length scale, $h_\tau$, can be set as a 10~m uniform value (\np {nn_etau}{nn\_etau}\forcode{=0}) or402 The vertical mixing length scale, $h_\tau$, can be set as a 10~m uniform value (\np[=0]{nn_etau}{nn\_etau}) or 401 403 a latitude dependent value (varying from 0.5~m at the Equator to a maximum value of 30~m at high latitudes 402 (\np {nn_etau}{nn\_etau}\forcode{=1}).403 404 Note that two other option exist, \np {nn_etau}{nn\_etau}\forcode{=2, 3}.404 (\np[=1]{nn_etau}{nn\_etau}). 405 406 Note that two other option exist, \np[=2, 3]{nn_etau}{nn\_etau}. 405 407 They correspond to applying \autoref{eq:ZDF_Ehtau} only at the base of the mixed layer, 406 408 or to using the high frequency part of the stress to evaluate the fraction of TKE that penetrates the ocean. … … 508 510 \caption[Set of predefined GLS parameters or equivalently predefined turbulence models available]{ 509 511 Set of predefined GLS parameters, or equivalently predefined turbulence models available with 510 \protect\np {ln_zdfgls}{ln\_zdfgls}\forcode{=.true.} and controlled by512 \protect\np[=.true.]{ln_zdfgls}{ln\_zdfgls} and controlled by 511 513 the \protect\np{nn_clos}{nn\_clos} namelist variable in \protect\nam{zdf_gls}{zdf\_gls}.} 512 514 \label{tab:ZDF_GLS} … … 519 521 $C_{\mu}$ and $C_{\mu'}$ are calculated from stability function proposed by \citet{galperin.kantha.ea_JAS88}, 520 522 or by \citet{kantha.clayson_JGR94} or one of the two functions suggested by \citet{canuto.howard.ea_JPO01} 521 (\np {nn_stab_func}{nn\_stab\_func}\forcode{=0, 3}, resp.).523 (\np[=0, 3]{nn_stab_func}{nn\_stab\_func}, resp.). 522 524 The value of $C_{0\mu}$ depends on the choice of the stability function. 523 525 … … 525 527 Neumann condition through \np{nn_bc_surf}{nn\_bc\_surf} and \np{nn_bc_bot}{nn\_bc\_bot}, resp. 526 528 As for TKE closure, the wave effect on the mixing is considered when 527 \np {rn_crban}{rn\_crban}\forcode{ > 0.} \citep{craig.banner_JPO94, mellor.blumberg_JPO04}.529 \np[ > 0.]{rn_crban}{rn\_crban} \citep{craig.banner_JPO94, mellor.blumberg_JPO04}. 528 530 The \np{rn_crban}{rn\_crban} namelist parameter is $\alpha_{CB}$ in \autoref{eq:ZDF_Esbc} and 529 531 \np{rn_charn}{rn\_charn} provides the value of $\beta$ in \autoref{eq:ZDF_Lsbc}. … … 536 538 the entrainment depth predicted in stably stratified situations, 537 539 and that its value has to be chosen in accordance with the algebraic model for the turbulent fluxes. 538 The clipping is only activated if \np {ln_length_lim}{ln\_length\_lim}\forcode{=.true.},540 The clipping is only activated if \np[=.true.]{ln_length_lim}{ln\_length\_lim}, 539 541 and the $c_{lim}$ is set to the \np{rn_clim_galp}{rn\_clim\_galp} value. 540 542 … … 707 709 708 710 Options are defined through the \nam{zdf}{zdf} namelist variables. 709 The non-penetrative convective adjustment is used when \np {ln_zdfnpc}{ln\_zdfnpc}\forcode{=.true.}.711 The non-penetrative convective adjustment is used when \np[=.true.]{ln_zdfnpc}{ln\_zdfnpc}. 710 712 It is applied at each \np{nn_npc}{nn\_npc} time step and mixes downwards instantaneously the statically unstable portion of 711 713 the water column, but only until the density structure becomes neutrally stable … … 751 753 752 754 Options are defined through the \nam{zdf}{zdf} namelist variables. 753 The enhanced vertical diffusion parameterisation is used when \np {ln_zdfevd}{ln\_zdfevd}\forcode{=.true.}.755 The enhanced vertical diffusion parameterisation is used when \np[=.true.]{ln_zdfevd}{ln\_zdfevd}. 754 756 In this case, the vertical eddy mixing coefficients are assigned very large values 755 757 in regions where the stratification is unstable 756 758 (\ie\ when $N^2$ the Brunt-Vais\"{a}l\"{a} frequency is negative) \citep{lazar_phd97, lazar.madec.ea_JPO99}. 757 This is done either on tracers only (\np {nn_evdm}{nn\_evdm}\forcode{=0}) or758 on both momentum and tracers (\np {nn_evdm}{nn\_evdm}\forcode{=1}).759 760 In practice, where $N^2\leq 10^{-12}$, $A_T^{vT}$ and $A_T^{vS}$, and if \np {nn_evdm}{nn\_evdm}\forcode{=1},759 This is done either on tracers only (\np[=0]{nn_evdm}{nn\_evdm}) or 760 on both momentum and tracers (\np[=1]{nn_evdm}{nn\_evdm}). 761 762 In practice, where $N^2\leq 10^{-12}$, $A_T^{vT}$ and $A_T^{vS}$, and if \np[=1]{nn_evdm}{nn\_evdm}, 761 763 the four neighbouring $A_u^{vm} \;\mbox{and}\;A_v^{vm}$ values also, are set equal to 762 764 the namelist parameter \np{rn_avevd}{rn\_avevd}. … … 795 797 The OSMOSIS turbulent closure scheme already includes enhanced vertical diffusion in the case of convection, 796 798 %as governed by the variables $bvsqcon$ and $difcon$ found in \mdl{zdfkpp}, 797 therefore \np {ln_zdfevd}{ln\_zdfevd}\forcode{=.false.} should be used with the OSMOSIS scheme.799 therefore \np[=.false.]{ln_zdfevd}{ln\_zdfevd} should be used with the OSMOSIS scheme. 798 800 % gm% + one word on non local flux with KPP scheme trakpp.F90 module... 799 801 … … 1002 1004 c_b^T = - r 1003 1005 \] 1004 When \np {ln_lin}{ln\_lin} \forcode{= .true.}, the value of $r$ used is \np{rn_Uc0}{rn\_Uc0}*\np{rn_Cd0}{rn\_Cd0}.1005 Setting \np {ln_OFF}{ln\_OFF} \forcode{= .true.} (and \forcode{ln_lin=.true.}) is equivalent to setting $r=0$ and leads to a free-slip boundary condition.1006 When \np[=.true.]{ln_lin}{ln\_lin}, the value of $r$ used is \np{rn_Uc0}{rn\_Uc0}*\np{rn_Cd0}{rn\_Cd0}. 1007 Setting \np[=.true.]{ln_OFF}{ln\_OFF} (and \forcode{ln_lin=.true.}) is equivalent to setting $r=0$ and leads to a free-slip boundary condition. 1006 1008 1007 1009 These values are assigned in \mdl{zdfdrg}. 1008 1010 Note that there is support for local enhancement of these values via an externally defined 2D mask array 1009 (\np {ln_boost}{ln\_boost}\forcode{=.true.}) given in the \ifile{bfr\_coef} input NetCDF file.1011 (\np[=.true.]{ln_boost}{ln\_boost}) given in the \ifile{bfr\_coef} input NetCDF file. 1010 1012 The mask values should vary from 0 to 1. 1011 1013 Locations with a non-zero mask value will have the friction coefficient increased by … … 1043 1045 $C_D$= \np{rn_Cd0}{rn\_Cd0}, and $e_b$ =\np{rn_bfeb2}{rn\_bfeb2}. 1044 1046 Note that for applications which consider tides explicitly, a low or even zero value of \np{rn_bfeb2}{rn\_bfeb2} is recommended. A local enhancement of $C_D$ is again possible via an externally defined 2D mask array 1045 (\np {ln_boost}{ln\_boost}\forcode{=.true.}).1047 (\np[=.true.]{ln_boost}{ln\_boost}). 1046 1048 This works in the same way as for the linear friction case with non-zero masked locations increased by 1047 1049 $mask\_value$ * \np{rn_boost}{rn\_boost} * \np{rn_Cd0}{rn\_Cd0}. … … 1055 1057 In the non-linear friction case, the drag coefficient, $C_D$, can be optionally enhanced using 1056 1058 a "law of the wall" scaling. This assumes that the model vertical resolution can capture the logarithmic layer which typically occur for layers thinner than 1 m or so. 1057 If \np {ln_loglayer}{ln\_loglayer} \forcode{= .true.}, $C_D$ is no longer constant but is related to the distance to the wall (or equivalently to the half of the top/bottom layer thickness):1059 If \np[=.true.]{ln_loglayer}{ln\_loglayer}, $C_D$ is no longer constant but is related to the distance to the wall (or equivalently to the half of the top/bottom layer thickness): 1058 1060 \[ 1059 1061 C_D = \left ( {\kappa \over {\mathrm log}\left ( 0.5 \; e_{3b} / rn\_{z0} \right ) } \right )^2 … … 1070 1072 1071 1073 \noindent The log-layer enhancement can also be applied to the top boundary friction if 1072 under ice-shelf cavities are activated (\np {ln_isfcav}{ln\_isfcav}\forcode{=.true.}).1074 under ice-shelf cavities are activated (\np[=.true.]{ln_isfcav}{ln\_isfcav}). 1073 1075 %In this case, the relevant namelist parameters are \np{rn_tfrz0}{rn\_tfrz0}, \np{rn_tfri2}{rn\_tfri2} and \np{rn_tfri2_max}{rn\_tfri2\_max}. 1074 1076 … … 1076 1078 % Explicit bottom Friction 1077 1079 % ------------------------------------------------------------------------------------------------------------- 1078 \subsection[Explicit top/bottom friction (\forcode{ln_drgimp=.false.})]{Explicit top/bottom friction (\protect\np {ln_drgimp}{ln\_drgimp}\forcode{=.false.})}1080 \subsection[Explicit top/bottom friction (\forcode{ln_drgimp=.false.})]{Explicit top/bottom friction (\protect\np[=.false.]{ln_drgimp}{ln\_drgimp})} 1079 1081 \label{subsec:ZDF_drg_stability} 1080 1082 1081 Setting \np {ln_drgimp}{ln\_drgimp} \forcode{= .false.} means that bottom friction is treated explicitly in time, which has the advantage of simplifying the interaction with the split-explicit free surface (see \autoref{subsec:ZDF_drg_ts}). The latter does indeed require the knowledge of bottom stresses in the course of the barotropic sub-iteration, which becomes less straightforward in the implicit case. In the explicit case, top/bottom stresses can be computed using \textit{before} velocities and inserted in the overall momentum tendency budget. This reads:1083 Setting \np[=.false.]{ln_drgimp}{ln\_drgimp} means that bottom friction is treated explicitly in time, which has the advantage of simplifying the interaction with the split-explicit free surface (see \autoref{subsec:ZDF_drg_ts}). The latter does indeed require the knowledge of bottom stresses in the course of the barotropic sub-iteration, which becomes less straightforward in the implicit case. In the explicit case, top/bottom stresses can be computed using \textit{before} velocities and inserted in the overall momentum tendency budget. This reads: 1082 1084 1083 1085 At the top (below an ice shelf cavity): … … 1137 1139 % Implicit Bottom Friction 1138 1140 % ------------------------------------------------------------------------------------------------------------- 1139 \subsection[Implicit top/bottom friction (\forcode{ln_drgimp=.true.})]{Implicit top/bottom friction (\protect\np {ln_drgimp}{ln\_drgimp}\forcode{=.true.})}1141 \subsection[Implicit top/bottom friction (\forcode{ln_drgimp=.true.})]{Implicit top/bottom friction (\protect\np[=.true.]{ln_drgimp}{ln\_drgimp})} 1140 1142 \label{subsec:ZDF_drg_imp} 1141 1143 … … 1170 1172 \label{subsec:ZDF_drg_ts} 1171 1173 1172 With split-explicit free surface, the sub-stepping of barotropic equations needs the knowledge of top/bottom stresses. An obvious way to satisfy this is to take them as constant over the course of the barotropic integration and equal to the value used to update the baroclinic momentum trend. Provided \np {ln_drgimp}{ln\_drgimp}\forcode{= .false.} and a centred or \textit{leap-frog} like integration of barotropic equations is used (\ie\ \forcode{ln_bt_fw=.false.}, cf \autoref{subsec:DYN_spg_ts}), this does ensure that barotropic and baroclinic dynamics feel the same stresses during one leapfrog time step. However, if \np{ln_drgimp}{ln\_drgimp}\forcode{= .true.}, stresses depend on the \textit{after} value of the velocities which themselves depend on the barotropic iteration result. This cyclic dependency makes difficult obtaining consistent stresses in 2d and 3d dynamics. Part of this mismatch is then removed when setting the final barotropic component of 3d velocities to the time splitting estimate. This last step can be seen as a necessary evil but should be minimized since it interferes with the adjustment to the boundary conditions.1174 With split-explicit free surface, the sub-stepping of barotropic equations needs the knowledge of top/bottom stresses. An obvious way to satisfy this is to take them as constant over the course of the barotropic integration and equal to the value used to update the baroclinic momentum trend. Provided \np[=.false.]{ln_drgimp}{ln\_drgimp} and a centred or \textit{leap-frog} like integration of barotropic equations is used (\ie\ \forcode{ln_bt_fw=.false.}, cf \autoref{subsec:DYN_spg_ts}), this does ensure that barotropic and baroclinic dynamics feel the same stresses during one leapfrog time step. However, if \np[=.true.]{ln_drgimp}{ln\_drgimp}, stresses depend on the \textit{after} value of the velocities which themselves depend on the barotropic iteration result. This cyclic dependency makes difficult obtaining consistent stresses in 2d and 3d dynamics. Part of this mismatch is then removed when setting the final barotropic component of 3d velocities to the time splitting estimate. This last step can be seen as a necessary evil but should be minimized since it interferes with the adjustment to the boundary conditions. 1173 1175 1174 1176 The strategy to handle top/bottom stresses with split-explicit free surface in \NEMO\ is as follows: … … 1508 1510 % ================================================================ 1509 1511 1510 \ biblio1511 1512 \ pindex1512 \onlyinsubfile{\bibliography{../main/bibliography}} 1513 1514 \onlyinsubfile{\printindex} 1513 1515 1514 1516 \end{document}
Note: See TracChangeset
for help on using the changeset viewer.
