Changeset 11512 for NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_A.tex

Timestamp:

2019-09-09T12:05:20+02:00 (5 years ago)

Author:

smasson

Message:

dev_r10984_HPC-13 : merge with trunk@11511, see #2285

File:

• NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_A.tex (modified) (6 diffs)

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_A.tex

@@ -9 +9 @@
 \label{apdx:A}
 
-\minitoc
+\chaptertoc
 
 \vfill
@@ -31 +31 @@
 
 In order to establish the set of Primitive Equation in curvilinear $s$-coordinates
-(\ie an orthogonal curvilinear coordinate in the horizontal and
+(\ie\ an orthogonal curvilinear coordinate in the horizontal and
 an Arbitrary Lagrangian Eulerian (ALE) coordinate in the vertical),
 we start from the set of equations established in \autoref{subsec:PE_zco_Eq} for
@@ -329 +329 @@
 \]
 This leads to the $s-$coordinate formulation of the total $z-$coordinate time derivative,
-\ie the total $s-$coordinate time derivative :
+\ie\ the total $s-$coordinate time derivative :
 \begin{align}
   \label{apdx:A_sco_Dt_vect}
@@ -368 +368 @@
 %
 Introducing the vertical scale factor inside the horizontal derivative of the first two terms 
-(\ie the horizontal divergence), it becomes :
+(\ie\ the horizontal divergence), it becomes :
 \begin{align*}
   {
@@ -411 +411 @@
 \end{align*}
 which leads to the $s-$coordinate flux formulation of the total $s-$coordinate time derivative, 
-\ie the total $s-$coordinate time derivative in flux form:
+\ie\ the total $s-$coordinate time derivative in flux form:
 \begin{flalign}
   \label{apdx:A_sco_Dt_flux}
@@ -569 +569 @@
 in particular the pressure gradient.
 By contrast, $\omega$ is not $w$, the third component of the velocity, but the dia-surface velocity component,
-\ie the volume flux across the moving $s$-surfaces per unit horizontal area. 
+\ie\ the volume flux across the moving $s$-surfaces per unit horizontal area.