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branches/2017/dev_merge_2017/DOC/TexFiles/Chapters/Chap_DYN.tex
r7646 r9363 70 70 %-------------------------------------------------------------------------------------------------------------- 71 71 \subsection [Horizontal divergence and relative vorticity (\textit{divcur})] 72 {Horizontal divergence and relative vorticity (\ mdl{divcur})}72 {Horizontal divergence and relative vorticity (\protect\mdl{divcur})} 73 73 \label{DYN_divcur} 74 74 … … 103 103 %-------------------------------------------------------------------------------------------------------------- 104 104 \subsection [Sea surface height evolution and vertical velocity (\textit{sshwzv})] 105 {Horizontal divergence and relative vorticity (\ mdl{sshwzv})}105 {Horizontal divergence and relative vorticity (\protect\mdl{sshwzv})} 106 106 \label{DYN_sshwzv} 107 107 … … 179 179 % ------------------------------------------------------------------------------------------------------------- 180 180 \subsection [Vorticity term (\textit{dynvor}) ] 181 {Vorticity term (\ mdl{dynvor})}181 {Vorticity term (\protect\mdl{dynvor})} 182 182 \label{DYN_vor} 183 183 %------------------------------------------nam_dynvor---------------------------------------------------- … … 200 200 % enstrophy conserving scheme 201 201 %------------------------------------------------------------- 202 \subsubsection{Enstrophy conserving scheme (\ np{ln\_dynvor\_ens}=true)}202 \subsubsection{Enstrophy conserving scheme (\protect\np{ln\_dynvor\_ens}=true)} 203 203 \label{DYN_vor_ens} 204 204 … … 221 221 % energy conserving scheme 222 222 %------------------------------------------------------------- 223 \subsubsection{Energy conserving scheme (\ np{ln\_dynvor\_ene}=true)}223 \subsubsection{Energy conserving scheme (\protect\np{ln\_dynvor\_ene}=true)} 224 224 \label{DYN_vor_ene} 225 225 … … 238 238 % mix energy/enstrophy conserving scheme 239 239 %------------------------------------------------------------- 240 \subsubsection{Mixed energy/enstrophy conserving scheme (\ np{ln\_dynvor\_mix}=true) }240 \subsubsection{Mixed energy/enstrophy conserving scheme (\protect\np{ln\_dynvor\_mix}=true) } 241 241 \label{DYN_vor_mix} 242 242 … … 261 261 % energy and enstrophy conserving scheme 262 262 %------------------------------------------------------------- 263 \subsubsection{Energy and enstrophy conserving scheme (\ np{ln\_dynvor\_een}=true) }263 \subsubsection{Energy and enstrophy conserving scheme (\protect\np{ln\_dynvor\_een}=true) } 264 264 \label{DYN_vor_een} 265 265 … … 297 297 \begin{figure}[!ht] \begin{center} 298 298 \includegraphics[width=0.70\textwidth]{Fig_DYN_een_triad} 299 \caption{ \ label{Fig_DYN_een_triad}299 \caption{ \protect\label{Fig_DYN_een_triad} 300 300 Triads used in the energy and enstrophy conserving scheme (een) for 301 301 $u$-component (upper panel) and $v$-component (lower panel).} … … 347 347 %-------------------------------------------------------------------------------------------------------------- 348 348 \subsection [Kinetic Energy Gradient term (\textit{dynkeg})] 349 {Kinetic Energy Gradient term (\ mdl{dynkeg})}349 {Kinetic Energy Gradient term (\protect\mdl{dynkeg})} 350 350 \label{DYN_keg} 351 351 … … 364 364 %-------------------------------------------------------------------------------------------------------------- 365 365 \subsection [Vertical advection term (\textit{dynzad}) ] 366 {Vertical advection term (\ mdl{dynzad}) }366 {Vertical advection term (\protect\mdl{dynzad}) } 367 367 \label{DYN_zad} 368 368 … … 406 406 %-------------------------------------------------------------------------------------------------------------- 407 407 \subsection [Coriolis plus curvature metric terms (\textit{dynvor}) ] 408 {Coriolis plus curvature metric terms (\ mdl{dynvor}) }408 {Coriolis plus curvature metric terms (\protect\mdl{dynvor}) } 409 409 \label{DYN_cor_flux} 410 410 … … 428 428 %-------------------------------------------------------------------------------------------------------------- 429 429 \subsection [Flux form Advection term (\textit{dynadv}) ] 430 {Flux form Advection term (\ mdl{dynadv}) }430 {Flux form Advection term (\protect\mdl{dynadv}) } 431 431 \label{DYN_adv_flux} 432 432 … … 460 460 % 2nd order centred scheme 461 461 %------------------------------------------------------------- 462 \subsubsection{$2^{nd}$ order centred scheme (cen2) (\ np{ln\_dynadv\_cen2}=true)}462 \subsubsection{$2^{nd}$ order centred scheme (cen2) (\protect\np{ln\_dynadv\_cen2}=true)} 463 463 \label{DYN_adv_cen2} 464 464 … … 481 481 % UBS scheme 482 482 %------------------------------------------------------------- 483 \subsubsection{Upstream Biased Scheme (UBS) (\ np{ln\_dynadv\_ubs}=true)}483 \subsubsection{Upstream Biased Scheme (UBS) (\protect\np{ln\_dynadv\_ubs}=true)} 484 484 \label{DYN_adv_ubs} 485 485 … … 533 533 % ================================================================ 534 534 \section [Hydrostatic pressure gradient (\textit{dynhpg})] 535 {Hydrostatic pressure gradient (\ mdl{dynhpg})}535 {Hydrostatic pressure gradient (\protect\mdl{dynhpg})} 536 536 \label{DYN_hpg} 537 537 %------------------------------------------nam_dynhpg--------------------------------------------------- … … 554 554 % z-coordinate with full step 555 555 %-------------------------------------------------------------------------------------------------------------- 556 \subsection [$z$-coordinate with full step (\ np{ln\_dynhpg\_zco}) ]557 {$z$-coordinate with full step (\ np{ln\_dynhpg\_zco}=true)}556 \subsection [$z$-coordinate with full step (\protect\np{ln\_dynhpg\_zco}) ] 557 {$z$-coordinate with full step (\protect\np{ln\_dynhpg\_zco}=true)} 558 558 \label{DYN_hpg_zco} 559 559 … … 595 595 % z-coordinate with partial step 596 596 %-------------------------------------------------------------------------------------------------------------- 597 \subsection [$z$-coordinate with partial step (\ np{ln\_dynhpg\_zps})]598 {$z$-coordinate with partial step (\ np{ln\_dynhpg\_zps}=true)}597 \subsection [$z$-coordinate with partial step (\protect\np{ln\_dynhpg\_zps})] 598 {$z$-coordinate with partial step (\protect\np{ln\_dynhpg\_zps}=true)} 599 599 \label{DYN_hpg_zps} 600 600 … … 673 673 % Time-scheme 674 674 %-------------------------------------------------------------------------------------------------------------- 675 \subsection [Time-scheme (\ np{ln\_dynhpg\_imp}) ]676 {Time-scheme (\ np{ln\_dynhpg\_imp}= true/false)}675 \subsection [Time-scheme (\protect\np{ln\_dynhpg\_imp}) ] 676 {Time-scheme (\protect\np{ln\_dynhpg\_imp}= true/false)} 677 677 \label{DYN_hpg_imp} 678 678 … … 733 733 % ================================================================ 734 734 \section [Surface pressure gradient (\textit{dynspg}) ] 735 {Surface pressure gradient (\ mdl{dynspg})}735 {Surface pressure gradient (\protect\mdl{dynspg})} 736 736 \label{DYN_spg} 737 737 %-----------------------------------------nam_dynspg---------------------------------------------------- … … 772 772 % Explicit free surface formulation 773 773 %-------------------------------------------------------------------------------------------------------------- 774 \subsection{Explicit free surface (\ key{dynspg\_exp})}774 \subsection{Explicit free surface (\protect\key{dynspg\_exp})} 775 775 \label{DYN_spg_exp} 776 776 … … 793 793 % Split-explict free surface formulation 794 794 %-------------------------------------------------------------------------------------------------------------- 795 \subsection{Split-Explicit free surface (\ key{dynspg\_ts})}795 \subsection{Split-Explicit free surface (\protect\key{dynspg\_ts})} 796 796 \label{DYN_spg_ts} 797 797 %------------------------------------------namsplit----------------------------------------------------------- … … 830 830 \begin{figure}[!t] \begin{center} 831 831 \includegraphics[width=0.7\textwidth]{Fig_DYN_dynspg_ts} 832 \caption{ \ label{Fig_DYN_dynspg_ts}832 \caption{ \protect\label{Fig_DYN_dynspg_ts} 833 833 Schematic of the split-explicit time stepping scheme for the external 834 834 and internal modes. Time increases to the right. In this particular exemple, … … 839 839 The former are used to obtain time filtered quantities at $t+\rdt$ while the latter are used to obtain time averaged 840 840 transports to advect tracers. 841 a) Forward time integration: \ np{ln\_bt\_fw}=true,\np{ln\_bt\_av}=true.842 b) Centred time integration: \ np{ln\_bt\_fw}=false,\np{ln\_bt\_av}=true.843 c) Forward time integration with no time filtering (POM-like scheme): \ np{ln\_bt\_fw}=true,\np{ln\_bt\_av}=false. }841 a) Forward time integration: \protect\np{ln\_bt\_fw}=true, \protect\np{ln\_bt\_av}=true. 842 b) Centred time integration: \protect\np{ln\_bt\_fw}=false, \protect\np{ln\_bt\_av}=true. 843 c) Forward time integration with no time filtering (POM-like scheme): \protect\np{ln\_bt\_fw}=true, \protect\np{ln\_bt\_av}=false. } 844 844 \end{center} \end{figure} 845 845 %> > > > > > > > > > > > > > > > > > > > > > > > > > > > … … 975 975 % Filtered free surface formulation 976 976 %-------------------------------------------------------------------------------------------------------------- 977 \subsection{Filtered free surface (\ key{dynspg\_flt})}977 \subsection{Filtered free surface (\protect\key{dynspg\_flt})} 978 978 \label{DYN_spg_fltp} 979 979 … … 1002 1002 % ================================================================ 1003 1003 \section [Lateral diffusion term (\textit{dynldf})] 1004 {Lateral diffusion term (\ mdl{dynldf})}1004 {Lateral diffusion term (\protect\mdl{dynldf})} 1005 1005 \label{DYN_ldf} 1006 1006 %------------------------------------------nam_dynldf---------------------------------------------------- … … 1036 1036 1037 1037 % ================================================================ 1038 \subsection [Iso-level laplacian operator (\ np{ln\_dynldf\_lap}) ]1039 {Iso-level laplacian operator (\ np{ln\_dynldf\_lap}=true)}1038 \subsection [Iso-level laplacian operator (\protect\np{ln\_dynldf\_lap}) ] 1039 {Iso-level laplacian operator (\protect\np{ln\_dynldf\_lap}=true)} 1040 1040 \label{DYN_ldf_lap} 1041 1041 … … 1060 1060 % Rotated laplacian operator 1061 1061 %-------------------------------------------------------------------------------------------------------------- 1062 \subsection [Rotated laplacian operator (\ np{ln\_dynldf\_iso}) ]1063 {Rotated laplacian operator (\ np{ln\_dynldf\_iso}=true)}1062 \subsection [Rotated laplacian operator (\protect\np{ln\_dynldf\_iso}) ] 1063 {Rotated laplacian operator (\protect\np{ln\_dynldf\_iso}=true)} 1064 1064 \label{DYN_ldf_iso} 1065 1065 … … 1129 1129 % Iso-level bilaplacian operator 1130 1130 %-------------------------------------------------------------------------------------------------------------- 1131 \subsection [Iso-level bilaplacian operator (\ np{ln\_dynldf\_bilap})]1132 {Iso-level bilaplacian operator (\ np{ln\_dynldf\_bilap}=true)}1131 \subsection [Iso-level bilaplacian operator (\protect\np{ln\_dynldf\_bilap})] 1132 {Iso-level bilaplacian operator (\protect\np{ln\_dynldf\_bilap}=true)} 1133 1133 \label{DYN_ldf_bilap} 1134 1134 … … 1145 1145 % Vertical diffusion term 1146 1146 % ================================================================ 1147 \section [Vertical diffusion term (\ mdl{dynzdf})]1148 {Vertical diffusion term (\ mdl{dynzdf})}1147 \section [Vertical diffusion term (\protect\mdl{dynzdf})] 1148 {Vertical diffusion term (\protect\mdl{dynzdf})} 1149 1149 \label{DYN_zdf} 1150 1150 %----------------------------------------------namzdf------------------------------------------------------ … … 1223 1223 % ================================================================ 1224 1224 \section [Time evolution term (\textit{dynnxt})] 1225 {Time evolution term (\ mdl{dynnxt})}1225 {Time evolution term (\protect\mdl{dynnxt})} 1226 1226 \label{DYN_nxt} 1227 1227
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