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branches/2017/dev_merge_2017/DOC/tex_sub/chap_model_basics.tex
r9389 r9393 5 5 % ================================================================ 6 6 7 \chapter{Model basics}7 \chapter{Model Basics} 8 8 \label{PE} 9 9 \minitoc … … 15 15 % Primitive Equations 16 16 % ================================================================ 17 \section{Primitive Equations}17 \section{Primitive equations} 18 18 \label{PE_PE} 19 19 … … 22 22 % ------------------------------------------------------------------------------------------------------------- 23 23 24 \subsection{Vector Invariant Formulation}24 \subsection{Vector invariant formulation} 25 25 \label{PE_Vector} 26 26 … … 100 100 % Boundary condition 101 101 % ------------------------------------------------------------------------------------------------------------- 102 \subsection{Boundary Conditions}102 \subsection{Boundary conditions} 103 103 \label{PE_boundary_condition} 104 104 … … 175 175 % The Horizontal Pressure Gradient 176 176 % ================================================================ 177 \section{ The Horizontal Pressure Gradient }177 \section{Horizontal pressure gradient } 178 178 \label{PE_hor_pg} 179 179 … … 181 181 % Pressure Formulation 182 182 % ------------------------------------------------------------------------------------------------------------- 183 \subsection{Pressure Formulation}183 \subsection{Pressure formulation} 184 184 \label{PE_p_formulation} 185 185 … … 212 212 % Free Surface Formulation 213 213 % ------------------------------------------------------------------------------------------------------------- 214 \subsection{Free Surface Formulation}214 \subsection{Free surface formulation} 215 215 \label{PE_free_surface} 216 216 … … 264 264 % Curvilinear z-coordinate System 265 265 % ================================================================ 266 \section{Curvilinear \textit{z-}coordinate System}266 \section{Curvilinear \textit{z-}coordinate system} 267 267 \label{PE_zco} 268 268 … … 271 271 % Tensorial Formalism 272 272 % ------------------------------------------------------------------------------------------------------------- 273 \subsection{Tensorial Formalism}273 \subsection{Tensorial formalism} 274 274 \label{PE_tensorial} 275 275 … … 366 366 % Continuous Model Equations 367 367 % ------------------------------------------------------------------------------------------------------------- 368 \subsection{Continuous Model Equations}368 \subsection{Continuous model equations} 369 369 \label{PE_zco_Eq} 370 370 … … 639 639 % Curvilinear generalised vertical coordinate System 640 640 % ================================================================ 641 \section{Curvilinear generalised vertical coordinate System}641 \section{Curvilinear generalised vertical coordinate system} 642 642 \label{PE_gco} 643 643 … … 691 691 % The s-coordinate Formulation 692 692 % ------------------------------------------------------------------------------------------------------------- 693 \subsection{ The \textit{s-}coordinate Formulation}693 \subsection{\textit{S-}coordinate formulation} 694 694 695 695 Starting from the set of equations established in \S\ref{PE_zco} for the special case $k=z$ … … 804 804 % Curvilinear z*-coordinate System 805 805 % ------------------------------------------------------------------------------------------------------------- 806 \subsection{Curvilinear \textit{z*}--coordinate System}806 \subsection{Curvilinear \textit{z*}--coordinate system} 807 807 \label{PE_zco_star} 808 808 … … 901 901 % Terrain following coordinate System 902 902 % ------------------------------------------------------------------------------------------------------------- 903 \subsection{Curvilinear Terrain-following \textit{s}--coordinate}903 \subsection{Curvilinear terrain-following \textit{s}--coordinate} 904 904 \label{PE_sco} 905 905 … … 999 999 % Subgrid Scale Physics 1000 1000 % ================================================================ 1001 \section{Subgrid Scale Physics}1001 \section{Subgrid scale physics} 1002 1002 \label{PE_zdf_ldf} 1003 1003 … … 1028 1028 % Vertical Subgrid Scale Physics 1029 1029 % ------------------------------------------------------------------------------------------------------------- 1030 \subsection{Vertical Subgrid Scale Physics}1030 \subsection{Vertical subgrid scale physics} 1031 1031 \label{PE_zdf} 1032 1032 … … 1063 1063 % Lateral Diffusive and Viscous Operators Formulation 1064 1064 % ------------------------------------------------------------------------------------------------------------- 1065 \subsection{Formulation of the Lateral Diffusive and Viscous Operators}1065 \subsection{Formulation of the lateral diffusive and viscous operators} 1066 1066 \label{PE_ldf} 1067 1067 … … 1122 1122 geopotential surfaces, and UBS advection schemes when flux form is chosen for the momentum advection. 1123 1123 1124 \subsubsection{Lateral Laplacian tracer diffusive operator}1124 \subsubsection{Lateral laplacian tracer diffusive operator} 1125 1125 1126 1126 The lateral Laplacian tracer diffusive operator is defined by (see Appendix~\ref{Apdx_B}):
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