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- 2019-09-25T22:00:42+02:00 (5 years ago)
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_model_basics.tex
r11597 r11598 6 6 \label{chap:MB} 7 7 8 \thispagestyle{plain} 9 8 10 \chaptertoc 9 11 10 %% ================================================================================================= 12 \paragraph{Changes record} ~\\ 13 14 {\footnotesize 15 \begin{tabularx}{\textwidth}{l||X|X} 16 Release & Author(s) & Modifications \\ 17 \hline 18 {\em 4.0} & {\em ...} & {\em ...} \\ 19 {\em 3.6} & {\em ...} & {\em ...} \\ 20 {\em 3.4} & {\em ...} & {\em ...} \\ 21 {\em <=3.4} & {\em ...} & {\em ...} 22 \end{tabularx} 23 } 24 25 \clearpage 26 11 27 %% ================================================================================================= 12 28 \section{Primitive equations} 13 29 \label{sec:MB_PE} 14 30 15 %% =================================================================================================16 31 %% ================================================================================================= 17 32 \subsection{Vector invariant formulation} … … 92 107 Their nature and formulation are discussed in \autoref{sec:MB_zdf_ldf} and \autoref{subsec:MB_boundary_condition}. 93 108 94 %% =================================================================================================95 109 %% ================================================================================================= 96 110 \subsection{Boundary conditions} … … 166 180 167 181 %% ================================================================================================= 168 %% =================================================================================================169 182 \section{Horizontal pressure gradient} 170 183 \label{sec:MB_hor_pg} 171 184 172 %% =================================================================================================173 185 %% ================================================================================================= 174 186 \subsection{Pressure formulation} … … 204 216 205 217 %% ================================================================================================= 206 %% =================================================================================================207 218 \subsection{Free surface formulation} 208 219 \label{subsec:MB_free_surface} … … 255 266 256 267 %% ================================================================================================= 257 %% =================================================================================================258 268 \section{Curvilinear \textit{z-}coordinate system} 259 269 \label{sec:MB_zco} 260 270 261 %% =================================================================================================262 271 %% ================================================================================================= 263 272 \subsection{Tensorial formalism} … … 301 310 \end{equation} 302 311 303 % >>>>>>>>>>>>>>>>>>>>>>>>>>>>304 312 \begin{figure}[!tb] 305 313 \centering … … 344 352 where $q$ is a scalar quantity and $\vect A = (a_1,a_2,a_3)$ a vector in the $(i,j,k)$ coordinates system. 345 353 346 %% =================================================================================================347 354 %% ================================================================================================= 348 355 \subsection{Continuous model equations} … … 530 537 531 538 %% ================================================================================================= 532 %% =================================================================================================533 539 \section{Curvilinear generalised vertical coordinate system} 534 540 \label{sec:MB_gco} … … 611 617 %} 612 618 613 %% =================================================================================================614 619 %% ================================================================================================= 615 620 \subsection{\textit{S}-coordinate formulation} … … 701 706 702 707 %% ================================================================================================= 703 %% =================================================================================================704 708 \subsection{Curvilinear \zstar-coordinate system} 705 709 \label{subsec:MB_zco_star} … … 788 792 789 793 %% ================================================================================================= 790 %% =================================================================================================791 794 \subsection{Curvilinear terrain-following \textit{s}--coordinate} 792 795 \label{subsec:MB_sco} 793 796 794 %% =================================================================================================795 797 %% ================================================================================================= 796 798 \subsubsection{Introduction} … … 875 877 876 878 %% ================================================================================================= 877 %% =================================================================================================878 879 \subsection{\texorpdfstring{Curvilinear \ztilde-coordinate}{}} 879 880 \label{subsec:MB_zco_tilde} … … 884 885 Its use is therefore not recommended. 885 886 886 %% =================================================================================================887 887 %% ================================================================================================= 888 888 \section{Subgrid scale physics} … … 909 909 The formulation of these terms and their underlying physics are briefly discussed in the next two subsections. 910 910 911 %% =================================================================================================912 911 %% ================================================================================================= 913 912 \subsection{Vertical subgrid scale physics} … … 943 942 944 943 %% ================================================================================================= 945 %% =================================================================================================946 944 \subsection{Formulation of the lateral diffusive and viscous operators} 947 945 \label{subsec:MB_ldf} … … 998 996 999 997 %% ================================================================================================= 1000 %% =================================================================================================1001 998 \subsubsection{Lateral laplacian tracer diffusive operator} 1002 999 … … 1040 1037 while in $s$-coordinates $\pd[]{k}$ is replaced by $\pd[]{s}$. 1041 1038 1042 %% =================================================================================================1043 1039 %% ================================================================================================= 1044 1040 \subsubsection{Eddy induced velocity} … … 1079 1075 1080 1076 %% ================================================================================================= 1081 %% =================================================================================================1082 1077 \subsubsection{Lateral bilaplacian tracer diffusive operator} 1083 1078 … … 1091 1086 the harmonic eddy diffusion coefficient set to the square root of the biharmonic one. 1092 1087 1093 %% =================================================================================================1094 1088 %% ================================================================================================= 1095 1089 \subsubsection{Lateral Laplacian momentum diffusive operator} … … 1126 1120 1127 1121 %% ================================================================================================= 1128 %% =================================================================================================1129 1122 \subsubsection{Lateral bilaplacian momentum diffusive operator} 1130 1123
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