Changeset 11151 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_DYN.tex
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- 2019-06-20T14:59:58+02:00 (5 years ago)
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_DYN.tex
r11123 r11151 309 309 \begin{figure}[!ht] 310 310 \begin{center} 311 \includegraphics[width= 0.70\textwidth]{Fig_DYN_een_triad}311 \includegraphics[width=\textwidth]{Fig_DYN_een_triad} 312 312 \caption{ 313 313 \protect\label{fig:DYN_een_triad} … … 862 862 \begin{equation} 863 863 \label{eq:BT_dyn} 864 \frac{\partial {\ rm \overline{{\bf U}}_h} }{\partial t}=865 -f\;{\ rm {\bf k}}\times {\rm \overline{{\bf U}}_h}866 -g\nabla _h \eta -\frac{c_b^{\textbf U}}{H+\eta} \ rm {\overline{{\bf U}}_h} + \rm {\overline{\bf G}}864 \frac{\partial {\mathrm \overline{{\mathbf U}}_h} }{\partial t}= 865 -f\;{\mathrm {\mathbf k}}\times {\mathrm \overline{{\mathbf U}}_h} 866 -g\nabla _h \eta -\frac{c_b^{\textbf U}}{H+\eta} \mathrm {\overline{{\mathbf U}}_h} + \mathrm {\overline{\mathbf G}} 867 867 \end{equation} 868 868 \[ 869 869 % \label{eq:BT_ssh} 870 \frac{\partial \eta }{\partial t}=-\nabla \cdot \left[ {\left( {H+\eta } \right) \; {\ rm{\bf \overline{U}}}_h \,} \right]+P-E870 \frac{\partial \eta }{\partial t}=-\nabla \cdot \left[ {\left( {H+\eta } \right) \; {\mathrm{\mathbf \overline{U}}}_h \,} \right]+P-E 871 871 \] 872 872 % \end{subequations} 873 where $\ rm {\overline{\bf G}}$ is a forcing term held constant, containing coupling term between modes,873 where $\mathrm {\overline{\mathbf G}}$ is a forcing term held constant, containing coupling term between modes, 874 874 surface atmospheric forcing as well as slowly varying barotropic terms not explicitly computed to gain efficiency. 875 875 The third term on the right hand side of \autoref{eq:BT_dyn} represents the bottom stress … … 884 884 \begin{figure}[!t] 885 885 \begin{center} 886 \includegraphics[width= 0.7\textwidth]{Fig_DYN_dynspg_ts}886 \includegraphics[width=\textwidth]{Fig_DYN_dynspg_ts} 887 887 \caption{ 888 888 \protect\label{fig:DYN_dynspg_ts} … … 1092 1092 \[ 1093 1093 % \label{eq:spg_flt} 1094 \frac{\partial {\ rm {\bf U}}_h }{\partial t}= {\rm {\bf M}}1094 \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= {\mathrm {\mathbf M}} 1095 1095 - g \nabla \left( \tilde{\rho} \ \eta \right) 1096 1096 - g \ T_c \nabla \left( \widetilde{\rho} \ \partial_t \eta \right) … … 1098 1098 where $T_c$, is a parameter with dimensions of time which characterizes the force, 1099 1099 $\widetilde{\rho} = \rho / \rho_o$ is the dimensionless density, 1100 and $\ rm {\bf M}$ represents the collected contributions of the Coriolis, hydrostatic pressure gradient,1100 and $\mathrm {\mathbf M}$ represents the collected contributions of the Coriolis, hydrostatic pressure gradient, 1101 1101 non-linear and viscous terms in \autoref{eq:PE_dyn}. 1102 1102 } %end gmcomment … … 1152 1152 \left\{ 1153 1153 \begin{aligned} 1154 D_u^{l{\ rm {\bf U}}} =\frac{1}{e_{1u} }\delta_{i+1/2} \left[ {A_T^{lm}1154 D_u^{l{\mathrm {\mathbf U}}} =\frac{1}{e_{1u} }\delta_{i+1/2} \left[ {A_T^{lm} 1155 1155 \;\chi } \right]-\frac{1}{e_{2u} {\kern 1pt}e_{3u} }\delta_j \left[ 1156 1156 {A_f^{lm} \;e_{3f} \zeta } \right] \\ \\ 1157 D_v^{l{\ rm {\bf U}}} =\frac{1}{e_{2v} }\delta_{j+1/2} \left[ {A_T^{lm}1157 D_v^{l{\mathrm {\mathbf U}}} =\frac{1}{e_{2v} }\delta_{j+1/2} \left[ {A_T^{lm} 1158 1158 \;\chi } \right]+\frac{1}{e_{1v} {\kern 1pt}e_{3v} }\delta_i \left[ 1159 1159 {A_f^{lm} \;e_{3f} \zeta } \right] … … 1494 1494 \end{equation} 1495 1495 1496 Note a small tolerance ($\mathrm{rn\_wdmin2}$) has been introduced here {\it [Q: Why is1496 Note a small tolerance ($\mathrm{rn\_wdmin2}$) has been introduced here {\itshape [Q: Why is 1497 1497 this necessary/desirable?]}. Substituting from (\ref{dyn_wd_continuity_coef}) gives an 1498 1498 expression for the coefficient needed to multiply the outward flux at this cell in order … … 1541 1541 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1542 1542 \begin{figure}[!ht] \begin{center} 1543 \includegraphics[width= 0.8\textwidth]{Fig_WAD_dynhpg}1543 \includegraphics[width=\textwidth]{Fig_WAD_dynhpg} 1544 1544 \caption{ \label{Fig_WAD_dynhpg} 1545 1545 Illustrations of the three possible combinations of the logical variables controlling the
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