Changeset 11123 for NEMO/trunk/doc/latex/NEMO/subfiles/annex_iso.tex
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- 2019-06-17T14:22:27+02:00 (5 years ago)
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- NEMO/trunk/doc/latex/NEMO/subfiles
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NEMO/trunk/doc/latex/NEMO/subfiles/annex_iso.tex
r10442 r11123 52 52 the vertical skew flux is further reduced to ensure no vertical buoyancy flux, 53 53 giving an almost pure horizontal diffusive tracer flux within the mixed layer. 54 This is similar to the tapering suggested by \citet{ Gerdes1991}. See \autoref{subsec:Gerdes-taper}54 This is similar to the tapering suggested by \citet{gerdes.koberle.ea_CD91}. See \autoref{subsec:Gerdes-taper} 55 55 \item[\np{ln\_botmix\_triad}] 56 56 See \autoref{sec:iso_bdry}. … … 71 71 \label{sec:iso} 72 72 73 We have implemented into \NEMO a scheme inspired by \citet{ Griffies_al_JPO98},73 We have implemented into \NEMO a scheme inspired by \citet{griffies.gnanadesikan.ea_JPO98}, 74 74 but formulated within the \NEMO framework, using scale factors rather than grid-sizes. 75 75 … … 194 194 \subsection{Expression of the skew-flux in terms of triad slopes} 195 195 196 \citep{ Griffies_al_JPO98} introduce a different discretization of the off-diagonal terms that196 \citep{griffies.gnanadesikan.ea_JPO98} introduce a different discretization of the off-diagonal terms that 197 197 nicely solves the problem. 198 198 % Instead of multiplying the mean slope calculated at the $u$-point by … … 473 473 474 474 To complete the discretization we now need only specify the triad volumes $_i^k\mathbb{V}_{i_p}^{k_p}$. 475 \citet{ Griffies_al_JPO98} identifies these $_i^k\mathbb{V}_{i_p}^{k_p}$ as the volumes of the quarter cells,475 \citet{griffies.gnanadesikan.ea_JPO98} identifies these $_i^k\mathbb{V}_{i_p}^{k_p}$ as the volumes of the quarter cells, 476 476 defined in terms of the distances between $T$, $u$,$f$ and $w$-points. 477 477 This is the natural discretization of \autoref{eq:cts-var}. … … 685 685 As discussed in \autoref{subsec:LDF_slp_iso}, 686 686 iso-neutral slopes relative to geopotentials must be bounded everywhere, 687 both for consistency with the small-slope approximation and for numerical stability \citep{ Cox1987, Griffies_Bk04}.687 both for consistency with the small-slope approximation and for numerical stability \citep{cox_OM87, griffies_bk04}. 688 688 The bound chosen in \NEMO is applied to each component of the slope separately and 689 689 has a value of $1/100$ in the ocean interior. … … 859 859 \footnote{ 860 860 To ensure good behaviour where horizontal density gradients are weak, 861 we in fact follow \citet{ Gerdes1991} and861 we in fact follow \citet{gerdes.koberle.ea_CD91} and 862 862 set $\rML^*=\mathrm{sgn}(\tilde{r}_i)\min(|\rMLt^2/\tilde{r}_i|,|\tilde{r}_i|)-\sigma_i$. 863 863 } … … 865 865 This approach is similar to multiplying the iso-neutral diffusion coefficient by 866 866 $\tilde{r}_{\mathrm{max}}^{-2}\tilde{r}_i^{-2}$ for steep slopes, 867 as suggested by \citet{ Gerdes1991} (see also \citet{Griffies_Bk04}).867 as suggested by \citet{gerdes.koberle.ea_CD91} (see also \citet{griffies_bk04}). 868 868 Again it is applied separately to each triad $_i^k\mathbb{R}_{i_p}^{k_p}$ 869 869 … … 925 925 926 926 However, when \np{ln\_traldf\_triad} is set true, 927 \NEMO instead implements eddy induced advection according to the so-called skew form \citep{ Griffies_JPO98}.927 \NEMO instead implements eddy induced advection according to the so-called skew form \citep{griffies_JPO98}. 928 928 It is based on a transformation of the advective fluxes using the non-divergent nature of the eddy induced velocity. 929 929 For example in the (\textbf{i},\textbf{k}) plane, … … 1139 1139 it is equivalent to a horizontal eiv (eddy-induced velocity) that is uniform within the mixed layer 1140 1140 \autoref{eq:eiv_v}. 1141 This ensures that the eiv velocities do not restratify the mixed layer \citep{ Treguier1997,Danabasoglu_al_2008}.1141 This ensures that the eiv velocities do not restratify the mixed layer \citep{treguier.held.ea_JPO97,danabasoglu.ferrari.ea_JC08}. 1142 1142 Equivantly, in terms of the skew-flux formulation we use here, 1143 1143 the linear slope tapering within the mixed-layer gives a linearly varying vertical flux, … … 1153 1153 $uw$ (integer +1/2 $i$, integer $j$, integer +1/2 $k$) and $vw$ (integer $i$, integer +1/2 $j$, integer +1/2 $k$) 1154 1154 points (see Table \autoref{tab:cell}) respectively. 1155 We follow \citep{ Griffies_Bk04} and calculate the streamfunction at a given $uw$-point from1155 We follow \citep{griffies_bk04} and calculate the streamfunction at a given $uw$-point from 1156 1156 the surrounding four triads according to: 1157 1157 \[
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