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

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:

• . (modified) (1 prop)
• latex (modified) (1 prop)
• latex/NEMO (modified) (1 prop)
• latex/NEMO/subfiles/chap_conservation.tex (modified) (10 diffs)

NEMO/branches/2019/fix_vvl_ticket1791/doc/latex

@@ -1 @@
-*.aux
-*.bbl
-*.blg
-*.dvi
-*.fdb*
-*.fls
-*.idx
-*.ilg
-*.ind
-*.log
-*.maf
-*.mtc*
-*.out
-*.pdf
-*.toc
-_minted-*
+figures

@@ -1 @@
-*.aux
-*.bbl
-*.blg
-*.dvi
-*.fdb*
-*.fls
-*.idx
-*.ilg
-*.ind
-*.log
-*.maf
-*.mtc*
-*.out
-*.pdf
-*.toc
-_minted-*
+figures

NEMO/branches/2019/fix_vvl_ticket1791/doc/latex/NEMO/subfiles/chap_conservation.tex

@@ -21 +21 @@
 horizontal kinetic energy and/or potential enstrophy of horizontally non-divergent flow,
 and variance of temperature and salinity will be conserved in the absence of dissipative effects and forcing.
-\citet{Arakawa1966} has first pointed out the advantage of this approach.
+\citet{arakawa_JCP66} has first pointed out the advantage of this approach.
 He showed that if integral constraints on energy are maintained,
 the computation will be free of the troublesome "non linear" instability originally pointed out by
-\citet{Phillips1959}.
+\citet{phillips_TAMS59}.
 A consistent formulation of the energetic properties is also extremely important in carrying out
 long-term numerical simulations for an oceanographic model.
-Such a formulation avoids systematic errors that accumulate with time \citep{Bryan1997}.
+Such a formulation avoids systematic errors that accumulate with time \citep{bryan_JCP97}.
 
 The general philosophy of OPA which has led to the discrete formulation presented in {\S}II.2 and II.3 is to
@@ -39 +39 @@
 Note that in some very specific cases as passive tracer studies, the positivity of the advective scheme is required.
 In that case, and in that case only, the advective scheme used for passive tracer is a flux correction scheme
-\citep{Marti1992, Levy1996, Levy1998}.
+\citep{Marti1992?, Levy1996?, Levy1998?}.
 
 % -------------------------------------------------------------------------------------------------------------
@@ -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}

@@ -1 @@
-*.aux
-*.bbl
-*.blg
-*.dvi
-*.fdb*
-*.fls
-*.idx
-*.ilg
-*.ind
-*.log
-*.maf
-*.mtc*
-*.out
-*.pdf
-*.toc
-_minted-*
+figures