Changeset 11693 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_LDF.tex
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 20191014T14:53:52+02:00 (13 months ago)
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_LDF.tex
r11690 r11693 68 68 \label{sec:LDF_slp} 69 69 70 \ gmcomment{70 \cmtgm{ 71 71 we should emphasize here that the implementation is a rather old one. 72 72 Better work can be achieved by using \citet{griffies.gnanadesikan.ea_JPO98, griffies_bk04} isoneutral scheme. … … 84 84 $r_{1f}$, $r_{1vw}$, $r_{2t}$, $r_{2vw}$ for $v$. 85 85 86 %gm% add here afigure of the slope in idirection 86 \cmtgm{Add here afigure of the slope in idirection} 87 87 88 88 %% ================================================================================================= … … 94 94 the diffusive fluxes in the three directions are set to zero and $T$ is assumed to be horizontally uniform, 95 95 \ie\ a linear function of $z_T$, the depth of a $T$point. 96 %gm { Steven : My version is obviously wrong since I'm left with an arbitrary constant which is the local vertical temperature gradient} 96 \cmtgm{Steven : My version is obviously wrong since 97 I'm left with an arbitrary constant which is the local vertical temperature gradient} 97 98 98 99 \begin{equation} … … 112 113 \end{equation} 113 114 114 %gm% caution I'm not sure the simplification was a good idea! 115 \cmtgm{Caution I'm not sure the simplification was a good idea!} 115 116 116 117 These slopes are computed once in \rou{ldf\_slp\_init} when \np[=.true.]{ln_sco}{ln\_sco}, … … 144 145 \end{equation} 145 146 146 %gm% rewrite this as the explanation is not very clear !!! 147 \cmtgm{rewrite this as the explanation is not very clear !!!} 147 148 %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 Tpoints leads to a flattening of slopes as the depth increases. This is due to the strong increase of the $in situ$ density with depth. 148 149 … … 173 174 will include a pressure dependent part, leading to the wrong evaluation of the neutral slopes. 174 175 175 %gm%176 176 Note: The solution for $s$coordinate passes trough the use of different (and better) expression for 177 177 the constraint on isoneutral fluxes. … … 182 182 \alpha \ \textbf{F}(T) = \beta \ \textbf{F}(S) 183 183 \] 184 % gm{where vector F is ....}184 \cmtgm{where vector F is ....} 185 185 186 186 This constraint leads to the following definition for the slopes: … … 229 229 This allows an isoneutral diffusion scheme without additional background horizontal mixing. 230 230 This technique can be viewed as a diffusion operator that acts along largescale 231 (2~$\Delta$x) \ gmcomment{2deltax doesnt seem very large scale} isoneutral surfaces.231 (2~$\Delta$x) \cmtgm{2deltax doesnt seem very large scale} isoneutral surfaces. 232 232 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. 233 233 … … 478 478 479 479 %%gm from Triad appendix : to be incorporated.... 480 \ gmcomment{480 \cmtgm{ 481 481 Values of isoneutral diffusivity and GM coefficient are set as described in \autoref{sec:LDF_coef}. 482 482 If none of the keys \key{traldf\_cNd}, N=1,2,3 is set (the default), spatially constant isoneutral $A_l$ and … … 544 544 \colorbox{yellow}{TBC} 545 545 546 \ onlyinsubfile{\input{../../global/epilogue}}546 \subinc{\input{../../global/epilogue}} 547 547 548 548 \end{document}
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