Changeset 3032 for branches/2011/dev_CMCC/DOC/TexFiles/Chapters/Chap_ASM.tex

Timestamp:

2011-10-31T15:48:12+01:00 (13 years ago)

Author:

vichi

Message:

ticket #881. Step 2: Added changes from dev_r2855_CMCC3_divd branch

File:

• branches/2011/dev_CMCC/DOC/TexFiles/Chapters/Chap_ASM.tex (modified) (1 diff)

branches/2011/dev_CMCC/DOC/TexFiles/Chapters/Chap_ASM.tex

@@ -86 +86 @@
 
 %==========================================================================
+% Divergence damping description %%%
+\section{Divergence damping initialisation}
+\label{ASM_details}
+
+The velocity increments may be initialized by the iterative application of 
+a divergence damping operator. In iteration step $n$ new estimates of 
+velocity increments $u^{n}_I$ and $v^{n}_I$ are updated by:
+\begin{equation} \label{eq:asm_dmp}
+\left\{ \begin{aligned}
+ u^{n}_I = u^{n-1}_I + \frac{1}{e_{1u} } \delta _{i+1/2} \left( {A_D
+\;\chi^{n-1}_I } \right) \\
+\\
+ v^{n}_I = v^{n-1}_I + \frac{1}{e_{2v} } \delta _{j+1/2} \left( {A_D
+\;\chi^{n-1}_I } \right) \\
+\end{aligned} \right,
+\end{equation}
+where
+\begin{equation} \label{eq:asm_div}
+\chi^{n-1}_I = \frac{1}{e_{1t}\,e_{2t}\,e_{3t} }
+                \left( {\delta _i \left[ {e_{2u}\,e_{3u}\,u^{n-1}_I} \right]
+                       +\delta _j \left[ {e_{1v}\,e_{3v}\,v^{n-1}_I} \right]} \right).
+\end{equation}
+By the application of \eqref{eq:asm_dmp} and \eqref{eq:asm_dmp} the divergence is filtered
+in each iteration, and the vorticity is left unchanged. In the presence of coastal boundaries
+with zero velocity increments perpendicular to the coast the divergence is strongly damped.
+This type of the initialisation reduces the vertical velocity magnitude  and alleviates the
+problem of the excessive unphysical vertical mixing in the first steps of the model 
+integration \citep{Talagrand_JAS72, Dobricic_al_OS07}. Diffusion coefficients are defined as 
+$A_D = \alpha e_{1t} e_{2t}$, where $\alpha = 0.2$. The divergence damping is activated by
+assigning to \textit{ndivdmp} in the \textit{nam\_asminc} namelist a value greater than zero. 
+By choosing this value to be of the order of 100 the increments in the vertical velocity will 
+be significantly reduced.
+
+
+%==========================================================================
 
 \section{Implementation details}