# Changeset 3267 for branches/2011/dev_NEMO_MERGE_2011/DOC/TexFiles/Chapters/Chap_LDF.tex

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

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