Changeset 3022 for branches/2011/dev_r2855_CMCC3_divd/DOC/TexFiles/Chapters
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- 2011-10-28T12:20:17+02:00 (13 years ago)
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branches/2011/dev_r2855_CMCC3_divd/DOC/TexFiles/Chapters/Chap_ASM.tex
r2483 r3022 86 86 87 87 %========================================================================== 88 % Divergence damping description %%% 89 \section{Divergence damping initialisation} 90 \label{ASM_details} 91 92 The velocity increments may be initialized by the iterative application of 93 a divergence damping operator. In iteration step $n$ new estimates of 94 velocity increments $u^{n}_I$ and $v^{n}_I$ are updated by: 95 \begin{equation} \label{eq:asm_dmp} 96 \left\{ \begin{aligned} 97 u^{n}_I = u^{n-1}_I + \frac{1}{e_{1u} } \delta _{i+1/2} \left( {A_D 98 \;\chi^{n-1}_I } \right) \\ 99 \\ 100 v^{n}_I = v^{n-1}_I + \frac{1}{e_{2v} } \delta _{j+1/2} \left( {A_D 101 \;\chi^{n-1}_I } \right) \\ 102 \end{aligned} \right, 103 \end{equation} 104 where 105 \begin{equation} \label{eq:asm_div} 106 \chi^{n-1}_I = \frac{1}{e_{1t}\,e_{2t}\,e_{3t} } 107 \left( {\delta _i \left[ {e_{2u}\,e_{3u}\,u^{n-1}_I} \right] 108 +\delta _j \left[ {e_{1v}\,e_{3v}\,v^{n-1}_I} \right]} \right). 109 \end{equation} 110 By the application of \eqref{eq:asm_dmp} and \eqref{eq:asm_dmp} the divergence is filtered 111 in each iteration, and the vorticity is left unchanged. In the presence of coastal boundaries 112 with zero velocity increments perpendicular to the coast the divergence is strongly damped. 113 This type of the initialisation reduces the vertical velocity magnitude and alleviates the 114 problem of the excessive unphysical vertical mixing in the first steps of the model 115 integration \citep{Talagrand_JAS72, Dobricic_al_OS07}. Diffusion coefficients are defined as 116 $A_D = \alpha e_{1t} e_{2t}$, where $\alpha = 0.2$. The divergence damping is activated by 117 assigning to \textit{ndivdmp} in the \textit{nam\_asminc} namelist a value greater than zero. 118 By choosing this value to be of the order of 100 the increments in the vertical velocity will 119 be significantly reduced. 120 121 122 %========================================================================== 88 123 89 124 \section{Implementation details}
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