Changeset 11151 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_conservation.tex

Timestamp:

2019-06-20T14:59:58+02:00 (5 years ago)

Author:

nicolasmartin

Message:

New version of NEMO_manual.tex
New class scrreport for the document (KOMA-script version of default report)
Foreword is now placed before ToC.
All figures are configured with 1.0\textwidth as default.
For compatibilty, \frontmatter, \mainmatter and \backmatter cmds have been removed and old fonts in LaTeX subfiles have been replaced

• \bf -> \mathbf or \bfseries
• \it -> \itshape
• \rm -> \mathrm or \rmfamily
• \tt -> \ttfamily

File:

• NEMO/trunk/doc/latex/NEMO/subfiles/chap_conservation.tex (modified) (8 diffs)

NEMO/trunk/doc/latex/NEMO/subfiles/chap_conservation.tex

@@ -65 +65 @@
   % \label{eq:vor_vorticity}
   \int_D {{\textbf {k}}\cdot \frac{1}{e_3 }\nabla \times \left( {\varsigma
-        \;{\rm {\bf k}}\times {\textbf {U}}_h } \right)\;dv} =0
+        \;{\mathrm {\mathbf k}}\times {\textbf {U}}_h } \right)\;dv} =0
 \]
 
@@ -189 +189 @@
 \[
   % \label{eq:dynldf_dyn}
-  \int\limits_D {\frac{1}{e_3 }{\rm {\bf k}}\cdot \nabla \times \left[ {\nabla
+  \int\limits_D {\frac{1}{e_3 }{\mathrm {\mathbf k}}\cdot \nabla \times \left[ {\nabla
         _h \left( {A^{lm}\;\chi } \right)-\nabla _h \times \left( {A^{lm}\;\zeta
-            \;{\rm {\bf k}}} \right)} \right]\;dv} =0
+            \;{\mathrm {\mathbf k}}} \right)} \right]\;dv} =0
 \]
 
@@ -197 +197 @@
   % \label{eq:dynldf_div}
   \int\limits_D {\nabla _h \cdot \left[ {\nabla _h \left( {A^{lm}\;\chi }
-        \right)-\nabla _h \times \left( {A^{lm}\;\zeta \;{\rm {\bf k}}} \right)}
+        \right)-\nabla _h \times \left( {A^{lm}\;\zeta \;{\mathrm {\mathbf k}}} \right)}
     \right]\;dv} =0
 \]
@@ -203 +203 @@
 \[
   % \label{eq:dynldf_curl}
-  \int_D {{\rm {\bf U}}_h \cdot \left[ {\nabla _h \left( {A^{lm}\;\chi }
-        \right)-\nabla _h \times \left( {A^{lm}\;\zeta \;{\rm {\bf k}}} \right)}
+  \int_D {{\mathrm {\mathbf U}}_h \cdot \left[ {\nabla _h \left( {A^{lm}\;\chi }
+        \right)-\nabla _h \times \left( {A^{lm}\;\zeta \;{\mathrm {\mathbf k}}} \right)}
     \right]\;dv} \leqslant 0
 \]
@@ -210 +210 @@
 \[
   % \label{eq:dynldf_curl2}
-  \mbox{if}\quad A^{lm}=cste\quad \quad \int_D {\zeta \;{\rm {\bf k}}\cdot
+  \mbox{if}\quad A^{lm}=cste\quad \quad \int_D {\zeta \;{\mathrm {\mathbf k}}\cdot
     \nabla \times \left[ {\nabla _h \left( {A^{lm}\;\chi } \right)-\nabla _h
-        \times \left( {A^{lm}\;\zeta \;{\rm {\bf k}}} \right)} \right]\;dv}
+        \times \left( {A^{lm}\;\zeta \;{\mathrm {\mathbf k}}} \right)} \right]\;dv}
   \leqslant 0
 \]
@@ -220 +220 @@
   \mbox{if}\quad A^{lm}=cste\quad \quad \int_D {\chi \;\nabla _h \cdot \left[
       {\nabla _h \left( {A^{lm}\;\chi } \right)-\nabla _h \times \left(
-          {A^{lm}\;\zeta \;{\rm {\bf k}}} \right)} \right]\;dv} \leqslant 0
+          {A^{lm}\;\zeta \;{\mathrm {\mathbf k}}} \right)} \right]\;dv} \leqslant 0
 \]
 
@@ -260 +260 @@
   % \label{eq:dynzdf_vor}
   \begin{aligned}
-    & \int_D {\frac{1}{e_3 }{\rm {\bf k}}\cdot \nabla \times \left( {\frac{1}{e_3
-          }\frac{\partial }{\partial k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\rm
-                  {\bf U}}_h }{\partial k}} \right)} \right)\;dv} =0 \\
-    & \int_D {\zeta \,{\rm {\bf k}}\cdot \nabla \times \left( {\frac{1}{e_3
-          }\frac{\partial }{\partial k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\rm
-                  {\bf U}}_h }{\partial k}} \right)} \right)\;dv} \leq 0 \\
+    & \int_D {\frac{1}{e_3 }{\mathrm {\mathbf k}}\cdot \nabla \times \left( {\frac{1}{e_3
+          }\frac{\partial }{\partial k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\mathrm
+                  {\mathbf U}}_h }{\partial k}} \right)} \right)\;dv} =0 \\
+    & \int_D {\zeta \,{\mathrm {\mathbf k}}\cdot \nabla \times \left( {\frac{1}{e_3
+          }\frac{\partial }{\partial k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\mathrm
+                  {\mathbf U}}_h }{\partial k}} \right)} \right)\;dv} \leq 0 \\
   \end{aligned}
 \]
@@ -273 +273 @@
   \begin{aligned}
     &\int_D {\nabla \cdot \left( {\frac{1}{e_3 }\frac{\partial }{\partial
-            k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\rm {\bf U}}_h }{\partial k}}
+            k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\mathrm {\mathbf U}}_h }{\partial k}}
           \right)} \right)\;dv} =0 \\
     & \int_D {\chi \;\nabla \cdot \left( {\frac{1}{e_3 }\frac{\partial }{\partial
-            k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\rm {\bf U}}_h }{\partial k}}
+            k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\mathrm {\mathbf U}}_h }{\partial k}}
           \right)} \right)\;dv} \leq 0 \\
   \end{aligned}