Changeset 11422 for NEMO/branches/2019/fix_vvl_ticket1791/doc/latex/NEMO/subfiles/chap_model_basics_zstar.tex
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- 2019-08-08T15:40:47+02:00 (5 years ago)
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old new 1 *.aux 2 *.bbl 3 *.blg 4 *.dvi 5 *.fdb* 6 *.fls 7 *.idx 8 *.ilg 9 *.ind 10 *.log 11 *.maf 12 *.mtc* 13 *.out 14 *.pdf 15 *.toc 16 _minted-* 1 figures
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NEMO/branches/2019/fix_vvl_ticket1791/doc/latex/NEMO/subfiles/chap_model_basics_zstar.tex
r10544 r11422 18 18 19 19 In that case, the free surface equation is nonlinear, and the variations of volume are fully taken into account. 20 These coordinates systems is presented in a report \citep{ Levier2007} available on the \NEMO web site.20 These coordinates systems is presented in a report \citep{levier.treguier.ea_rpt07} available on the \NEMO web site. 21 21 22 22 \colorbox{yellow}{ end of to be updated} … … 73 73 % Surface Pressure Gradient and Sea Surface Height 74 74 % ================================================================ 75 \section{Surface pressure gradient and sea surface heigth (\protect\mdl{dynspg})} 75 \section[Surface pressure gradient and sea surface heigth (\textit{dynspg.F90})] 76 {Surface pressure gradient and sea surface heigth (\protect\mdl{dynspg})} 76 77 \label{sec:DYN_hpg_spg} 77 78 %-----------------------------------------nam_dynspg---------------------------------------------------- … … 89 90 which imposes a very small time step when an explicit time stepping is used. 90 91 Two methods are proposed to allow a longer time step for the three-dimensional equations: 91 the filtered free surface, which is a modification of the continuous equations %(see \autoref{eq:PE_flt }),92 the filtered free surface, which is a modification of the continuous equations %(see \autoref{eq:PE_flt?}), 92 93 and the split-explicit free surface described below. 93 94 The extra term introduced in the filtered method is calculated implicitly, … … 97 98 % Explicit 98 99 %------------------------------------------------------------- 99 \subsubsection{Explicit (\protect\key{dynspg\_exp})} 100 \subsubsection[Explicit (\texttt{\textbf{key\_dynspg\_exp}})] 101 {Explicit (\protect\key{dynspg\_exp})} 100 102 \label{subsec:DYN_spg_exp} 101 103 … … 133 135 % Split-explicit time-stepping 134 136 %------------------------------------------------------------- 135 \subsubsection{Split-explicit time-stepping (\protect\key{dynspg\_ts})} 137 \subsubsection[Split-explicit time-stepping (\texttt{\textbf{key\_dynspg\_ts}})] 138 {Split-explicit time-stepping (\protect\key{dynspg\_ts})} 136 139 \label{subsec:DYN_spg_ts} 137 140 %--------------------------------------------namdom---------------------------------------------------- … … 139 142 \nlst{namdom} 140 143 %-------------------------------------------------------------------------------------------------------------- 141 The split-explicit free surface formulation used in OPA follows the one proposed by \citet{Griffies2004 }.144 The split-explicit free surface formulation used in OPA follows the one proposed by \citet{Griffies2004?}. 142 145 The general idea is to solve the free surface equation with a small time step, 143 146 while the three dimensional prognostic variables are solved with a longer time step that … … 147 150 \begin{figure}[!t] 148 151 \begin{center} 149 \includegraphics[width= 0.90\textwidth]{Fig_DYN_dynspg_ts}152 \includegraphics[width=\textwidth]{Fig_DYN_dynspg_ts} 150 153 \caption{ 151 154 \protect\label{fig:DYN_dynspg_ts} 152 155 Schematic of the split-explicit time stepping scheme for the barotropic and baroclinic modes, 153 after \citet{Griffies2004 }.156 after \citet{Griffies2004?}. 154 157 Time increases to the right. 155 158 Baroclinic time steps are denoted by $t-\Delta t$, $t, t+\Delta t$, and $t+2\Delta t$. … … 171 174 172 175 The split-explicit formulation has a damping effect on external gravity waves, 173 which is weaker than the filtered free surface but still significant as shown by \citet{ Levier2007} in176 which is weaker than the filtered free surface but still significant as shown by \citet{levier.treguier.ea_rpt07} in 174 177 the case of an analytical barotropic Kelvin wave. 175 178 … … 291 294 % Filtered formulation 292 295 %------------------------------------------------------------- 293 \subsubsection{Filtered formulation (\protect\key{dynspg\_flt})} 296 \subsubsection[Filtered formulation (\texttt{\textbf{key\_dynspg\_flt}})] 297 {Filtered formulation (\protect\key{dynspg\_flt})} 294 298 \label{subsec:DYN_spg_flt} 295 299 296 The filtered formulation follows the \citet{Roullet2000 } implementation.300 The filtered formulation follows the \citet{Roullet2000?} implementation. 297 301 The extra term introduced in the equations (see {\S}I.2.2) is solved implicitly. 298 302 The elliptic solvers available in the code are documented in \autoref{chap:MISC}. 299 303 The amplitude of the extra term is given by the namelist variable \np{rnu}. 300 The default value is 1, as recommended by \citet{Roullet2000 }304 The default value is 1, as recommended by \citet{Roullet2000?} 301 305 302 306 \colorbox{red}{\np{rnu}\forcode{ = 1} to be suppressed from namelist !} … … 305 309 % Non-linear free surface formulation 306 310 %------------------------------------------------------------- 307 \subsection{Non-linear free surface formulation (\protect\key{vvl})} 311 \subsection[Non-linear free surface formulation (\texttt{\textbf{key\_vvl}})] 312 {Non-linear free surface formulation (\protect\key{vvl})} 308 313 \label{subsec:DYN_spg_vvl} 309 314 310 315 In the non-linear free surface formulation, the variations of volume are fully taken into account. 311 This option is presented in a report \citep{ Levier2007} available on the NEMO web site.316 This option is presented in a report \citep{levier.treguier.ea_rpt07} available on the NEMO web site. 312 317 The three time-stepping methods (explicit, split-explicit and filtered) are the same as in 313 318 \autoref{DYN_spg_linear} except that the ocean depth is now time-dependent.
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