Changeset 817 for trunk/DOC/BETA/Chapters/Chap_LDF.tex

Timestamp:

2008-02-09T15:13:48+01:00 (16 years ago)

Author:

gm

Message:

trunk - update including Steven correction of the first 5 chapters (until DYN) and activation of Appendix A & B

File:

• trunk/DOC/BETA/Chapters/Chap_LDF.tex (modified) (4 diffs)

trunk/DOC/BETA/Chapters/Chap_LDF.tex

@@ -22 +22 @@
 % Lateral Mixing Coefficients
 % ================================================================
-\section{Lateral Mixing Coefficient (key\_ldftra\_c.d and key\_ldfdyn\_c.d)}
+\section{Lateral Mixing Coefficient (\textbf{key\_ldftra\_c.d} - \textbf{key\_ldfdyn\_c.d)} }
 \label{LDF_coef}
 
@@ -61 +61 @@
 \quad \text{comments}
 \end{equation}
-where $e_{max}$ is the max of $e_1$ and $e_2$ taken over the whole masked ocean domain, and $A_o^l$ is \np{ahm0} (momentum) or \np{aht0} (tracer) namelist parameters. This variation is intended to reflect the lesser need for subgrid scale eddy mixing where the grid size is smaller in the domain. It was introduced in the context of the DYNAMO modelling project \citep{Willebrand2001}. %gm  not only that! stability reasons: with non uniform grid size, it is common to face a blow up of the model due to to large diffusive coefficient compare to the smallest grid size... this is especially true for bilaplacian (to be added in the text!)  
-
-Other formulations can be introduced by the user for a given configuration. For example, in the ORCA2 global ocean model (\key{orca\_r2}), the laplacian viscous operator uses \np{ahm0}~=~$4.10^4 m^2.s^{-1}$ poleward of 20$^{\circ}$ north and south and decreases to \np{aht0}~=~$2.10^3 m^2.s^{-1}$ at the equator \citep{Madec1996, Delecluse2000}. This specification can be found in \rou{ldf\_dyn\_c2d\_orca} routine defined in \mdl{ldfdyn\_c2d}. Similar specific horizontal variation can be found for Antarctic or Arctic sub-domain of ORCA2 and ORCA05 (\key{antarctic} or \key{arctic} defined, see \hf{ldfdyn\_antarctic} and \hf{ldfdyn\_arctic}).
+where $e_{max}$ is the max of $e_1$ and $e_2$ taken over the whole masked ocean domain, and $A_o^l$ is \np{ahm0} (momentum) or \np{aht0} (tracer) namelist parameters. This variation is intended to reflect the lesser need for subgrid scale eddy mixing where the grid size is smaller in the domain. It was introduced in the context of the DYNAMO modelling project \citep{Willebrand2001}. 
+%%%
+\gmcomment { not only that! stability reasons: with non uniform grid size, it is common to face a blow up of the model due to to large diffusive coefficient compare to the smallest grid size... this is especially true for bilaplacian (to be added in the text!)  }
+
+Other formulations can be introduced by the user for a given configuration. For example, in the ORCA2 global ocean model (\key{orca\_r2}), the laplacian viscous operator uses \np{ahm0}~=~$4.10^4 m^2.s^{-1}$ poleward of 20$^{\circ}$ north and south and decreases to \np{aht0}~=~$2.10^3 m^2.s^{-1}$ at the equator \citep{Madec1996, Delecluse_Madec_Bk00}. This specification can be found in \rou{ldf\_dyn\_c2d\_orca} routine defined in \mdl{ldfdyn\_c2d}. Similar specific horizontal variation can be found for Antarctic or Arctic sub-domain of ORCA2 and ORCA05 (\key{antarctic} or \key{arctic} defined, see \hf{ldfdyn\_antarctic} and \hf{ldfdyn\_arctic}).
 
 \subsubsection{Space Varying Mixing Coefficients (\key{ldftra\_c3d} and \key{ldfdyn\_c3d})}
@@ -97 +99 @@
 % Direction of lateral Mixing
 % ================================================================
-\section{Direction of Lateral Mixing (\mdl{ldfslp})}
+\section  [Direction of Lateral Mixing (\textit{ldfslp})]
+      {Direction of Lateral Mixing (\mdl{ldfslp})}
 \label{LDF_slp}
 
-%gm%  we should emphasize here that the implementation is a rather old one. Better work can be achieved by using \citet{Griffies1998, Griffies2004} iso-neutral scheme.
+%%%
+\gmcomment{  we should emphasize here that the implementation is a rather old one. Better work can be achieved by using \citet{Griffies1998, Griffies2004} iso-neutral scheme. }
 
 
@@ -270 +274 @@
 % Eddy Induced Mixing
 % ================================================================
-\section{Eddy Induced Velocity (\mdl{traadv\_eiv}, \mdl{ldfeiv})}
+\section  [Eddy Induced Velocity (\textit{traadv\_eiv}, \textit{ldfeiv})]
+      {Eddy Induced Velocity (\mdl{traadv\_eiv}, \mdl{ldfeiv})}
 \label{LDF_eiv}
-
 
 When Gent and McWilliams [1990] diffusion is used (\key{traldf\_eiv} defined), an eddy induced tracer advection term is added, the formulation of which depends on the slopes of iso-neutral surfaces. Contrary to iso-neutral mixing, the slopes use here are referenced to the geopotential surfaces, i.e. \eqref{Eq_ldfslp_geo} is used in $z$-coordinates, and the sum \eqref{Eq_ldfslp_geo}  + \eqref{Eq_ldfslp_iso} in $s$-coordinates. The eddy induced velocity is given by: