Changeset 9393 for branches/2017/dev_merge_2017/DOC/tex_sub/chap_LDF.tex
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branches/2017/dev_merge_2017/DOC/tex_sub/chap_LDF.tex
r9392 r9393 25 25 Note that this chapter describes the standard implementation of iso-neutral 26 26 tracer mixing, and Griffies's implementation, which is used if 27 \ forcode{traldf_grif= .true.}, is described in Appdx\ref{sec:triad}27 \np{traldf\_grif}\forcode{ = .true.}, is described in Appdx\ref{sec:triad} 28 28 29 29 %-----------------------------------nam_traldf - nam_dynldf-------------------------------------------- … … 36 36 % Direction of lateral Mixing 37 37 % ================================================================ 38 \section [Direction of Lateral Mixing (\textit{ldfslp})] 39 {Direction of Lateral Mixing (\protect\mdl{ldfslp})} 38 \section{Direction of lateral mixing (\protect\mdl{ldfslp})} 40 39 \label{LDF_slp} 41 40 … … 46 45 A direction for lateral mixing has to be defined when the desired operator does 47 46 not act along the model levels. This occurs when $(a)$ horizontal mixing is 48 required on tracer or momentum (\np{ln _traldf_hor} or \np{ln_dynldf_hor})47 required on tracer or momentum (\np{ln\_traldf\_hor} or \np{ln\_dynldf\_hor}) 49 48 in $s$- or mixed $s$-$z$- coordinates, and $(b)$ isoneutral mixing is required 50 49 whatever the vertical coordinate is. This direction of mixing is defined by its … … 57 56 %gm% add here afigure of the slope in i-direction 58 57 59 \subsection{ slopes for tracer geopotential mixing in the $s$-coordinate}58 \subsection{Slopes for tracer geopotential mixing in the $s$-coordinate} 60 59 61 60 In $s$-coordinates, geopotential mixing ($i.e.$ horizontal mixing) $r_1$ and … … 88 87 %gm% caution I'm not sure the simplification was a good idea! 89 88 90 These slopes are computed once in \rou{ldfslp\_init} when \forcode{ln_sco = .true.}rue, 91 and either \forcode{ln_traldf_hor = .true.}rue or \forcode{ln_dynldf_hor = .true.}rue. 92 93 \subsection{Slopes for tracer iso-neutral mixing}\label{LDF_slp_iso} 89 These slopes are computed once in \rou{ldfslp\_init} when \np{ln\_sco}\forcode{ = .true.}rue, 90 and either \np{ln\_traldf\_hor}\forcode{ = .true.}rue or \np{ln\_dynldf\_hor}\forcode{ = .true.}rue. 91 92 \subsection{Slopes for tracer iso-neutral mixing} 93 \label{LDF_slp_iso} 94 94 In iso-neutral mixing $r_1$ and $r_2$ are the slopes between the iso-neutral 95 95 and computational surfaces. Their formulation does not depend on the vertical … … 147 147 \item[$s$- or hybrid $s$-$z$- coordinate : ] in the current release of \NEMO, 148 148 iso-neutral mixing is only employed for $s$-coordinates if the 149 Griffies scheme is used (\ forcode{traldf_grif= .true.}; see Appdx \ref{sec:triad}).149 Griffies scheme is used (\np{traldf\_grif}\forcode{ = .true.}; see Appdx \ref{sec:triad}). 150 150 In other words, iso-neutral mixing will only be accurately represented with a 151 linear equation of state (\ forcode{nn_eos = 1} or 2). In the case of a "true" equation151 linear equation of state (\np{nn\_eos}\forcode{ = 1..2}). In the case of a "true" equation 152 152 of state, the evaluation of $i$ and $j$ derivatives in \eqref{Eq_ldfslp_iso} 153 153 will include a pressure dependent part, leading to the wrong evaluation of … … 212 212 ocean model are modified \citep{Weaver_Eby_JPO97, 213 213 Griffies_al_JPO98}. Griffies's scheme is now available in \NEMO if 214 \np{traldf _grif_iso} is set true; see Appdx \ref{sec:triad}. Here,214 \np{traldf\_grif\_iso} is set true; see Appdx \ref{sec:triad}. Here, 215 215 another strategy is presented \citep{Lazar_PhD97}: a local 216 216 filtering of the iso-neutral slopes (made on 9 grid-points) prevents … … 276 276 \colorbox{yellow}{add here a discussion about the flattening of the slopes, vs tapering the coefficient.} 277 277 278 \subsection{ slopes for momentum iso-neutral mixing}278 \subsection{Slopes for momentum iso-neutral mixing} 279 279 280 280 The iso-neutral diffusion operator on momentum is the same as the one used on … … 306 306 % Lateral Mixing Operator 307 307 % ================================================================ 308 \section [Lateral Mixing Operators (\textit{ldftra}, \textit{ldfdyn})] 309 {Lateral Mixing Operators (\protect\mdl{traldf}, \protect\mdl{traldf}) } 308 \section{Lateral mixing operators (\protect\mdl{traldf}, \protect\mdl{traldf}) } 310 309 \label{LDF_op} 311 310 … … 315 314 % Lateral Mixing Coefficients 316 315 % ================================================================ 317 \section [Lateral Mixing Coefficient (\textit{ldftra}, \textit{ldfdyn})] 318 {Lateral Mixing Coefficient (\protect\mdl{ldftra}, \protect\mdl{ldfdyn}) } 316 \section{Lateral mixing coefficient (\protect\mdl{ldftra}, \protect\mdl{ldfdyn}) } 319 317 \label{LDF_coef} 320 318 … … 344 342 as follows: 345 343 346 \subsubsection{Constant Mixing Coefficients (default option)}344 \subsubsection{Constant mixing coefficients (default option)} 347 345 When none of the \textbf{key\_dynldf\_...} and \textbf{key\_traldf\_...} keys are 348 346 defined, a constant value is used over the whole ocean for momentum and 349 tracers, which is specified through the \np{rn _ahm0} and \np{rn_aht0} namelist347 tracers, which is specified through the \np{rn\_ahm0} and \np{rn\_aht0} namelist 350 348 parameters. 351 349 352 \subsubsection{Vertically varying Mixing Coefficients (\protect\key{traldf\_c1d} and \key{dynldf\_c1d})}350 \subsubsection{Vertically varying mixing coefficients (\protect\key{traldf\_c1d} and \key{dynldf\_c1d})} 353 351 The 1D option is only available when using the $z$-coordinate with full step. 354 352 Indeed in all the other types of vertical coordinate, the depth is a 3D function … … 356 354 mixing coefficients will require 3D arrays. In the 1D option, a hyperbolic variation 357 355 of the lateral mixing coefficient is introduced in which the surface value is 358 \np{rn _aht0} (\np{rn_ahm0}), the bottom value is 1/4 of the surface value,356 \np{rn\_aht0} (\np{rn\_ahm0}), the bottom value is 1/4 of the surface value, 359 357 and the transition takes place around z=300~m with a width of 300~m 360 358 ($i.e.$ both the depth and the width of the inflection point are set to 300~m). 361 359 This profile is hard coded in file \hf{traldf\_c1d}, but can be easily modified by users. 362 360 363 \subsubsection{Horizontally Varying Mixing Coefficients (\protect\key{traldf\_c2d} and \protect\key{dynldf\_c2d})}361 \subsubsection{Horizontally varying mixing coefficients (\protect\key{traldf\_c2d} and \protect\key{dynldf\_c2d})} 364 362 By default the horizontal variation of the eddy coefficient depends on the local mesh 365 363 size and the type of operator used: … … 372 370 \end{equation} 373 371 where $e_{max}$ is the maximum of $e_1$ and $e_2$ taken over the whole masked 374 ocean domain, and $A_o^l$ is the \np{rn _ahm0} (momentum) or \np{rn_aht0} (tracer)372 ocean domain, and $A_o^l$ is the \np{rn\_ahm0} (momentum) or \np{rn\_aht0} (tracer) 375 373 namelist parameter. This variation is intended to reflect the lesser need for subgrid 376 374 scale eddy mixing where the grid size is smaller in the domain. It was introduced in … … 384 382 Other formulations can be introduced by the user for a given configuration. 385 383 For example, in the ORCA2 global ocean model (see Configurations), the laplacian 386 viscosity operator uses \np{rn _ahm0}~= 4.10$^4$ m$^2$/s poleward of 20$^{\circ}$387 north and south and decreases linearly to \np{rn _aht0}~= 2.10$^3$ m$^2$/s384 viscosity operator uses \np{rn\_ahm0}~= 4.10$^4$ m$^2$/s poleward of 20$^{\circ}$ 385 north and south and decreases linearly to \np{rn\_aht0}~= 2.10$^3$ m$^2$/s 388 386 at the equator \citep{Madec_al_JPO96, Delecluse_Madec_Bk00}. This modification 389 387 can be found in routine \rou{ldf\_dyn\_c2d\_orca} defined in \mdl{ldfdyn\_c2d}. … … 391 389 sub-domain options of ORCA2 and ORCA05 (see \&namcfg namelist). 392 390 393 \subsubsection{Space Varying Mixing Coefficients (\protect\key{traldf\_c3d} and \key{dynldf\_c3d})}391 \subsubsection{Space varying mixing coefficients (\protect\key{traldf\_c3d} and \key{dynldf\_c3d})} 394 392 395 393 The 3D space variation of the mixing coefficient is simply the combination of the … … 397 395 a grid size dependence of the magnitude of the coefficient. 398 396 399 \subsubsection{Space and Time Varying Mixing Coefficients}397 \subsubsection{Space and time varying mixing coefficients} 400 398 401 399 There is no default specification of space and time varying mixing coefficient. … … 423 421 (3) for isopycnal diffusion on momentum or tracers, an additional purely 424 422 horizontal background diffusion with uniform coefficient can be added by 425 setting a non zero value of \np{rn _ahmb0} or \np{rn_ahtb0}, a background horizontal423 setting a non zero value of \np{rn\_ahmb0} or \np{rn\_ahtb0}, a background horizontal 426 424 eddy viscosity or diffusivity coefficient (namelist parameters whose default 427 425 values are $0$). However, the technique used to compute the isopycnal … … 438 436 (6) it is possible to use both the laplacian and biharmonic operators concurrently. 439 437 440 (7) it is possible to run without explicit lateral diffusion on momentum (\np{ln _dynldf_lap}=441 \np{ln_dynldf_bilap} = false). This is recommended when using the UBS advection442 scheme on momentum (\np{ln _dynadv_ubs} = true, see \ref{DYN_adv_ubs})438 (7) it is possible to run without explicit lateral diffusion on momentum (\np{ln\_dynldf\_lap}\forcode{ = 439 }\np{ln\_dynldf\_bilap}\forcode{ = .false.}). This is recommended when using the UBS advection 440 scheme on momentum (\np{ln\_dynadv\_ubs}\forcode{ = .true.}, see \ref{DYN_adv_ubs}) 443 441 and can be useful for testing purposes. 444 442 … … 446 444 % Eddy Induced Mixing 447 445 % ================================================================ 448 \section [Eddy Induced Velocity (\textit{traadv\_eiv}, \textit{ldfeiv})] 449 {Eddy Induced Velocity (\protect\mdl{traadv\_eiv}, \protect\mdl{ldfeiv})} 446 \section{Eddy induced velocity (\protect\mdl{traadv\_eiv}, \protect\mdl{ldfeiv})} 450 447 \label{LDF_eiv} 451 448 … … 455 452 described in \S\ref{LDF_coef}. If none of the keys \key{traldf\_cNd}, 456 453 N=1,2,3 is set (the default), spatially constant iso-neutral $A_l$ and 457 GM diffusivity $A_e$ are directly set by \np{rn _aeih_0} and458 \np{rn _aeiv_0}. If 2D-varying coefficients are set with454 GM diffusivity $A_e$ are directly set by \np{rn\_aeih\_0} and 455 \np{rn\_aeiv\_0}. If 2D-varying coefficients are set with 459 456 \key{traldf\_c2d} then $A_l$ is reduced in proportion with horizontal 460 457 scale factor according to \eqref{Eq_title} \footnote{Except in global ORCA … … 467 464 case, $A_e$ at low latitudes $|\theta|<20^{\circ}$ is further 468 465 reduced by a factor $|f/f_{20}|$, where $f_{20}$ is the value of $f$ 469 at $20^{\circ}$~N} (\mdl{ldfeiv}) and \np{rn _aeiv_0} is ignored466 at $20^{\circ}$~N} (\mdl{ldfeiv}) and \np{rn\_aeiv\_0} is ignored 470 467 unless it is zero. 471 468 } … … 485 482 \end{equation} 486 483 where $A^{eiv}$ is the eddy induced velocity coefficient whose value is set 487 through \np{rn _aeiv}, a \textit{nam\_traldf} namelist parameter.484 through \np{rn\_aeiv}, a \textit{nam\_traldf} namelist parameter. 488 485 The three components of the eddy induced velocity are computed and add 489 486 to the eulerian velocity in \mdl{traadv\_eiv}. This has been preferred to a
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