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2012-01-18T11:28:11+01:00 (9 years ago)
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agn
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dev_NEMO_MERGE_2011:(DOC) Finish griffies description, remove need for pstricks

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  • branches/2011/dev_NEMO_MERGE_2011/DOC/TexFiles/Chapters/Chap_LDF.tex

    r3221 r3267  
    2121and for tracers only, eddy induced advection on tracers). These three aspects  
    2222of the lateral diffusion are set through namelist parameters and CPP keys  
    23 (see the \textit{nam\_traldf} and \textit{nam\_dynldf} below). 
     23(see the \textit{nam\_traldf} and \textit{nam\_dynldf} below). Note 
     24that this chapter describes the default implementation of iso-neutral 
     25tracer mixing, and Griffies's implementation, which is used if 
     26\np{traldf\_grif}=true, is described in Appdx\ref{sec:triad} 
    2427 
    2528%-----------------------------------nam_traldf - nam_dynldf-------------------------------------------- 
     
    128131$\ $\newline    % force a new ligne 
    129132 
    130 A space variation in the eddy coefficient appeals several remarks: 
     133The following points are relevant when the eddy coefficient varies spatially: 
    131134 
    132135(1) the momentum diffusion operator acting along model level surfaces is  
    133136written in terms of curl and divergent components of the horizontal current  
    134 (see \S\ref{PE_ldf}). Although the eddy coefficient can be set to different values  
    135 in these two terms, this option is not available.  
     137(see \S\ref{PE_ldf}). Although the eddy coefficient could be set to different values  
     138in these two terms, this option is not currently available.  
    136139 
    137140(2) with an horizontally varying viscosity, the quadratic integral constraints  
     
    275278 
    276279\item[$s$- or hybrid $s$-$z$- coordinate : ] in the current release of \NEMO,  
    277 there is no specific treatment for iso-neutral mixing in the $s$-coordinate.  
     280iso-neutral mixing is only employed for $s$-coordinates if the 
     281Griffies scheme is used (\np{traldf\_grif}=true; see Appdx \ref{sec:triad}).  
    278282In other words, iso-neutral mixing will only be accurately represented with a  
    279283linear equation of state (\np{nn\_eos}=1 or 2). In the case of a "true" equation  
     
    332336\end{description} 
    333337 
    334 This implementation is a rather old one. It is similar to the one proposed  
    335 by Cox [1987], except for the background horizontal diffusion. Indeed,  
    336 the Cox implementation of isopycnal diffusion in GFDL-type models requires  
    337 a minimum background horizontal diffusion for numerical stability reasons.  
    338 To overcome this problem, several techniques have been proposed in which  
    339 the numerical schemes of the ocean model are modified \citep{Weaver_Eby_JPO97,  
    340 Griffies_al_JPO98}. Here, another strategy has been chosen \citep{Lazar_PhD97}:  
    341 a local filtering of the iso-neutral slopes (made on 9 grid-points) prevents  
    342 the development of grid point noise generated by the iso-neutral diffusion  
    343 operator (Fig.~\ref{Fig_LDF_ZDF1}). This allows an iso-neutral diffusion scheme  
    344 without additional background horizontal mixing. This technique can be viewed  
    345 as a diffusion operator that acts along large-scale (2~$\Delta$x)  
    346 \gmcomment{2deltax doesnt seem very large scale}  
    347 iso-neutral surfaces. The diapycnal diffusion required for numerical stability is  
    348 thus minimized and its net effect on the flow is quite small when compared to  
    349 the effect of an horizontal background mixing.  
     338This implementation is a rather old one. It is similar to the one 
     339proposed by Cox [1987], except for the background horizontal 
     340diffusion. Indeed, the Cox implementation of isopycnal diffusion in 
     341GFDL-type models requires a minimum background horizontal diffusion 
     342for numerical stability reasons.  To overcome this problem, several 
     343techniques have been proposed in which the numerical schemes of the 
     344ocean model are modified \citep{Weaver_Eby_JPO97, 
     345  Griffies_al_JPO98}. Griffies's scheme is now available in \NEMO if 
     346\np{traldf\_grif\_iso} is set true; see Appdx \ref{sec:triad}. Here, 
     347another strategy is presented \citep{Lazar_PhD97}: a local 
     348filtering of the iso-neutral slopes (made on 9 grid-points) prevents 
     349the development of grid point noise generated by the iso-neutral 
     350diffusion operator (Fig.~\ref{Fig_LDF_ZDF1}). This allows an 
     351iso-neutral diffusion scheme without additional background horizontal 
     352mixing. This technique can be viewed as a diffusion operator that acts 
     353along large-scale (2~$\Delta$x) \gmcomment{2deltax doesnt seem very 
     354  large scale} iso-neutral surfaces. The diapycnal diffusion required 
     355for numerical stability is thus minimized and its net effect on the 
     356flow is quite small when compared to the effect of an horizontal 
     357background mixing. 
    350358 
    351359Nevertheless, this iso-neutral operator does not ensure that variance cannot increase,  
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