# Changeset 11693 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_LDF.tex

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Timestamp:
2019-10-14T14:53:52+02:00 (13 months ago)
Message:

Macros renaming

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 r11690 \label{sec:LDF_slp} \gmcomment{ \cmtgm{ we should emphasize here that the implementation is a rather old one. Better work can be achieved by using \citet{griffies.gnanadesikan.ea_JPO98, griffies_bk04} iso-neutral scheme. $r_{1f}$, $r_{1vw}$, $r_{2t}$, $r_{2vw}$ for $v$. %gm% add here afigure of the slope in i-direction \cmtgm{Add here afigure of the slope in i-direction} %% ================================================================================================= the diffusive fluxes in the three directions are set to zero and $T$ is assumed to be horizontally uniform, \ie\ a linear function of $z_T$, the depth of a $T$-point. %gm { Steven : My version is obviously wrong since I'm left with an arbitrary constant which is the local vertical temperature gradient} \cmtgm{Steven : My version is obviously wrong since I'm left with an arbitrary constant which is the local vertical temperature gradient} %gm%  caution I'm not sure the simplification was a good idea! \cmtgm{Caution I'm not sure the simplification was a good idea!} These slopes are computed once in \rou{ldf\_slp\_init} when \np[=.true.]{ln_sco}{ln\_sco}, %gm% rewrite this as the explanation is not very clear !!! \cmtgm{rewrite this as the explanation is not very clear !!!} %In practice, \autoref{eq:LDF_slp_iso} is of little help in evaluating the neutral surface slopes. Indeed, for an unsimplified equation of state, the density has a strong dependancy on pressure (here approximated as the depth), therefore applying \autoref{eq:LDF_slp_iso} using the $in situ$ density, $\rho$, computed at T-points leads to a flattening of slopes as the depth increases. This is due to the strong increase of the $in situ$ density with depth. will include a pressure dependent part, leading to the wrong evaluation of the neutral slopes. %gm% Note: The solution for $s$-coordinate passes trough the use of different (and better) expression for the constraint on iso-neutral fluxes. \alpha \ \textbf{F}(T) = \beta \ \textbf{F}(S) \] % gm{  where vector F is ....} \cmtgm{where vector F is ....} This constraint leads to the following definition for the slopes: 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. (2~$\Delta$x) \cmtgm{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. %%gm  from Triad appendix  : to be incorporated.... \gmcomment{ \cmtgm{ Values of iso-neutral diffusivity and GM coefficient are set as described in \autoref{sec:LDF_coef}. If none of the keys \key{traldf\_cNd}, N=1,2,3 is set (the default), spatially constant iso-neutral $A_l$ and \colorbox{yellow}{TBC} \onlyinsubfile{\input{../../global/epilogue}} \subinc{\input{../../global/epilogue}} \end{document}