Changeset 7351 for branches/2016/dev_INGV_UKMO_2016/DOC/TexFiles/Chapters/Chap_STP.tex

Timestamp:

2016-11-28T17:04:10+01:00 (7 years ago)

Author:

emanuelaclementi

Message:

ticket #1805 step 3: /2016/dev_INGV_UKMO_2016 aligned to the trunk at revision 7161

File:

• branches/2016/dev_INGV_UKMO_2016/DOC/TexFiles/Chapters/Chap_STP.tex (modified) (7 diffs)

branches/2016/dev_INGV_UKMO_2016/DOC/TexFiles/Chapters/Chap_STP.tex

@@ +1 @@
+\documentclass[NEMO_book]{subfiles}
+\begin{document}
 
 % ================================================================
-% Chapter 2 � Time Domain (step.F90)
+% Chapter 2 ——— Time Domain (step.F90)
 % ================================================================
 \chapter{Time Domain (STP) }
@@ -21 +23 @@
 
 Having defined the continuous equations in Chap.~\ref{PE}, we need now to choose 
-a time discretization. In the present chapter, we provide a general description of the \NEMO 
+a time discretization, a key feature of an ocean model as it exerts a strong influence  
+on the structure of the computer code ($i.e.$ on its flowchart). 
+In the present chapter, we provide a general description of the \NEMO 
 time stepping strategy and the consequences for the order in which the equations are
 solved.
@@ -158 +162 @@
 \end{equation} 
 
+%%gm
+%%gm   UPDATE the next paragraphs with time varying thickness ...
+%%gm
+
 This scheme is rather time consuming since it requires a matrix inversion, 
 but it becomes attractive since a value of 3 or more is needed for N in
@@ -188 +196 @@
 
 % -------------------------------------------------------------------------------------------------------------
-%        Hydrostatic Pressure gradient
-% -------------------------------------------------------------------------------------------------------------
-\section{Hydrostatic Pressure Gradient --- semi-implicit scheme}
-\label{STP_hpg_imp}
+%        Surface Pressure gradient
+% -------------------------------------------------------------------------------------------------------------
+\section{Surface Pressure Gradient}
+\label{STP_spg_ts}
+
+===>>>>  TO BE written....  :-)
 
 %\gmcomment{ 
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 \begin{figure}[!t]     \begin{center}
-\includegraphics[width=0.7\textwidth]{./TexFiles/Figures/Fig_TimeStepping_flowchart.pdf}
+\includegraphics[width=0.7\textwidth]{Fig_TimeStepping_flowchart}
 \caption{   \label{Fig_TimeStep_flowchart}
 Sketch of the leapfrog time stepping sequence in \NEMO from \citet{Leclair_Madec_OM09}. 
@@ -209 +219 @@
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 %}
-
-The range of stability of the Leap-Frog scheme can be extended by a factor of two
-by introducing a semi-implicit computation of the hydrostatic pressure gradient term
-\citep{Brown_Campana_MWR78}. Instead of evaluating the pressure at $t$, a linear 
-combination of values at $t-\rdt$, $t$ and $t+\rdt$ is used (see \S~\ref{DYN_hpg_imp}).  
-This technique, controlled by the \np{nn\_dynhpg\_rst} namelist parameter, does not 
-introduce a significant additional computational cost when tracers and thus density 
-is time stepped before the dynamics. This time step ordering is used in \NEMO 
-(Fig.\ref{Fig_TimeStep_flowchart}).
-
-
-This technique, used in several GCMs (\NEMO, POP or MOM for instance), 
-makes the Leap-Frog scheme as efficient 
-\footnote{The efficiency is defined as the maximum allowed Courant number of the time 
-stepping scheme divided by the number of computations of the right-hand side per time step.} 
-as the Forward-Backward scheme used in MOM \citep{Griffies_al_OS05} and more 
-efficient than the LF-AM3 scheme (leapfrog time stepping combined with a third order
-Adams-Moulthon interpolation for the predictor phase) used in ROMS 
-\citep{Shchepetkin_McWilliams_OM05}. 
-
-In fact, this technique is efficient when the physical phenomenon that 
-limits the time-step is internal gravity waves (IGWs). Indeed, it is 
-equivalent to applying a time filter to the pressure gradient to eliminate high 
-frequency IGWs. Obviously, the doubling of the time-step is achievable only 
-if no other factors control the time-step, such as the stability limits associated 
-with advection, diffusion or Coriolis terms. For example, it is inefficient in low resolution
-global ocean configurations, since inertial oscillations in the vicinity of the North Pole 
-are the limiting factor for the time step. It is also often inefficient in very high 
-resolution configurations where strong currents and small grid cells exert 
-the strongest constraint on the time step.
 
 % -------------------------------------------------------------------------------------------------------------
@@ -288 +268 @@
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 \begin{figure}[!t]     \begin{center}
-\includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_MLF_forcing.pdf}
+\includegraphics[width=0.90\textwidth]{Fig_MLF_forcing}
 \caption{   \label{Fig_MLF_forcing}
 Illustration of forcing integration methods. 
@@ -424 +404 @@
 }
 %%
+\end{document}