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Changeset 11422 for NEMO/branches/2019/fix_vvl_ticket1791/doc/latex/NEMO/subfiles/chap_model_basics_zstar.tex – NEMO

Ignore:
Timestamp:
2019-08-08T15:40:47+02:00 (5 years ago)
Author:
jchanut
Message:

#1791, merge with trunk

Location:
NEMO/branches/2019/fix_vvl_ticket1791/doc
Files:
4 edited

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  • NEMO/branches/2019/fix_vvl_ticket1791/doc/latex

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        old new  
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  • NEMO/branches/2019/fix_vvl_ticket1791/doc/latex/NEMO

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  • NEMO/branches/2019/fix_vvl_ticket1791/doc/latex/NEMO/subfiles/chap_model_basics_zstar.tex

    r10544 r11422  
    1818 
    1919In 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.  
     20These coordinates systems is presented in a report \citep{levier.treguier.ea_rpt07} available on the \NEMO web site.  
    2121 
    2222\colorbox{yellow}{  end of to be updated} 
     
    7373% Surface Pressure Gradient and Sea Surface Height 
    7474% ================================================================ 
    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})} 
    7677\label{sec:DYN_hpg_spg} 
    7778%-----------------------------------------nam_dynspg---------------------------------------------------- 
     
    8990which imposes a very small time step when an explicit time stepping is used. 
    9091Two 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}), 
     92the filtered free surface, which is a modification of the continuous equations %(see \autoref{eq:PE_flt?}), 
    9293and the split-explicit free surface described below. 
    9394The extra term introduced in the filtered method is calculated implicitly, 
     
    9798% Explicit 
    9899%------------------------------------------------------------- 
    99 \subsubsection{Explicit (\protect\key{dynspg\_exp})} 
     100\subsubsection[Explicit (\texttt{\textbf{key\_dynspg\_exp}})] 
     101{Explicit (\protect\key{dynspg\_exp})} 
    100102\label{subsec:DYN_spg_exp} 
    101103 
     
    133135% Split-explicit time-stepping 
    134136%------------------------------------------------------------- 
    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})} 
    136139\label{subsec:DYN_spg_ts} 
    137140%--------------------------------------------namdom---------------------------------------------------- 
     
    139142\nlst{namdom}  
    140143%-------------------------------------------------------------------------------------------------------------- 
    141 The split-explicit free surface formulation used in OPA follows the one proposed by \citet{Griffies2004}. 
     144The split-explicit free surface formulation used in OPA follows the one proposed by \citet{Griffies2004?}. 
    142145The general idea is to solve the free surface equation with a small time step, 
    143146while the three dimensional prognostic variables are solved with a longer time step that 
     
    147150\begin{figure}[!t] 
    148151  \begin{center} 
    149     \includegraphics[width=0.90\textwidth]{Fig_DYN_dynspg_ts} 
     152    \includegraphics[width=\textwidth]{Fig_DYN_dynspg_ts} 
    150153    \caption{ 
    151154      \protect\label{fig:DYN_dynspg_ts} 
    152155      Schematic of the split-explicit time stepping scheme for the barotropic and baroclinic modes, 
    153       after \citet{Griffies2004}. 
     156      after \citet{Griffies2004?}. 
    154157      Time increases to the right. 
    155158      Baroclinic time steps are denoted by $t-\Delta t$, $t, t+\Delta t$, and $t+2\Delta t$. 
     
    171174 
    172175The 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} in 
     176which is weaker than the filtered free surface but still significant as shown by \citet{levier.treguier.ea_rpt07} in 
    174177the case of an analytical barotropic Kelvin wave.  
    175178 
     
    291294% Filtered formulation  
    292295%------------------------------------------------------------- 
    293 \subsubsection{Filtered formulation (\protect\key{dynspg\_flt})} 
     296\subsubsection[Filtered formulation (\texttt{\textbf{key\_dynspg\_flt}})] 
     297{Filtered formulation (\protect\key{dynspg\_flt})} 
    294298\label{subsec:DYN_spg_flt} 
    295299 
    296 The filtered formulation follows the \citet{Roullet2000} implementation. 
     300The filtered formulation follows the \citet{Roullet2000?} implementation. 
    297301The extra term introduced in the equations (see {\S}I.2.2) is solved implicitly. 
    298302The elliptic solvers available in the code are documented in \autoref{chap:MISC}. 
    299303The amplitude of the extra term is given by the namelist variable \np{rnu}. 
    300 The default value is 1, as recommended by \citet{Roullet2000} 
     304The default value is 1, as recommended by \citet{Roullet2000?} 
    301305 
    302306\colorbox{red}{\np{rnu}\forcode{ = 1} to be suppressed from namelist !} 
     
    305309% Non-linear free surface formulation  
    306310%------------------------------------------------------------- 
    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})} 
    308313\label{subsec:DYN_spg_vvl} 
    309314 
    310315In 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. 
     316This option is presented in a report \citep{levier.treguier.ea_rpt07} available on the NEMO web site. 
    312317The three time-stepping methods (explicit, split-explicit and filtered) are the same as in 
    313318\autoref{DYN_spg_linear} except that the ocean depth is now time-dependent. 
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