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Changeset 3057 for branches/2011/dev_r2802_NOCL_bfrimp/DOC/TexFiles – NEMO

Ignore:
Timestamp:
2011-11-08T13:39:35+01:00 (13 years ago)
Author:
hliu
Message:

update semi-implicit bottom friction branch, Document has been added in NEMO_book Chapter 10.4.4

File:
1 edited

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  • branches/2011/dev_r2802_NOCL_bfrimp/DOC/TexFiles/Chapters/Chap_ZDF.tex

    r2541 r3057  
    11% ================================================================ 
    2 % Chapter Ñ Vertical Ocean Physics (ZDF) 
     2% Chapter Vertical Ocean Physics (ZDF) 
    33% ================================================================ 
    44\chapter{Vertical Ocean Physics (ZDF)} 
     
    539539the clipping factor is of crucial importance for the entrainment depth predicted in  
    540540stably stratified situations, and that its value has to be chosen in accordance  
    541 with the algebraic model for the turbulent ßuxes. The clipping is only activated  
     541with the algebraic model for the turbulent uxes. The clipping is only activated  
    542542if \np{ln\_length\_lim}=true, and the $c_{lim}$ is set to the \np{rn\_clim\_galp} value. 
    543543 
     
    982982 
    983983% ------------------------------------------------------------------------------------------------------------- 
     984%       Implicit Bottom Friction 
     985% ------------------------------------------------------------------------------------------------------------- 
     986\subsection{Implicit Bottom Friction} 
     987\label{ZDF_bfr_imp} 
     988 
     989An Implicit form of bottom friction has been devised in the NEMO to improve 
     990model stability. We recommend this option for shelf sea and coastal ocean applications, especially  
     991for split-explicit time splitting. This option can be invoked by setting \np{ln\_bfrimp}  
     992to \textit{true} in the \textit{nambfr} namelist and \np{ln\_zdfexp} to \textit{false}  
     993in the \textit{namzdf} namelist.  
     994 
     995This implementation is realised in \mdl{dynzdf\_imp} and \mdl{dynspg\_ts}. In \mdl{dynzdf\_imp}, the  
     996bottom boundary condition is implemented implicitly. 
     997 
     998\begin{equation} \label{Eq_dynzdf_bfr} 
     999\left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{mbk} 
     1000    = \binom{c_{b}^{u}u^{n+1}_{mbk}}{c_{b}^{v}v^{n+1}_{mbk}} 
     1001\end{equation} 
     1002 
     1003where $mbk$ is the layer number of the bottom layer. superscript $n+1$ means the velocity used in the 
     1004friction formulea is to be calculated, so, it is implicit. 
     1005 
     1006If split-explicit time splitting is used, care must be taken to avoid the double counting of 
     1007the bottom friction in the 2-D barotropic momentum equations. As NEMO only updates the barotropic  
     1008pressure gradient and Coriolis' forcing terms in the 2-D barotropic calculation, we need to remove 
     1009the bottom friction induced by these two terms which has been included in the 3-D momentum trend  
     1010and update it with the latest value. On the other hand, the bottom friction contributed by the 
     1011other terms (e.g. the advection term, viscosity term) has been included in the 3-D momentum equations 
     1012and should not be added in the 2-D barotropic mode. 
     1013 
     1014The implementation of the implicit bottom friction in \mdl{dynspg\_ts} is done in two steps as the 
     1015following: 
     1016 
     1017\begin{equation} \label{Eq_dynspg_ts_bfr1} 
     1018\frac{\textbf{U}_{med}-\textbf{U}^{m-1}}{2\Delta t}=-g\nabla\eta-f\textbf{k}\times\textbf{U}^{m}+c_{b} 
     1019\left(\textbf{U}_{med}-\textbf{U}^{m-1}\right) 
     1020\end{equation} 
     1021\begin{equation} \label{Eq_dynspg_ts_bfr2} 
     1022\frac{\textbf{U}^{m+1}-\textbf{U}_{med}}{2\Delta t}=\textbf{T}+ 
     1023\left(g\nabla\eta^{'}+f\textbf{k}\times\textbf{U}^{'}\right)- 
     10242\Delta t_{bc}c_{b}\left(g\nabla\eta^{'}+f\textbf{k}\times\textbf{u}_{b}\right) 
     1025\end{equation} 
     1026 
     1027where $\textbf{T}$ is the vertical integrated 3-D momentum trend. We assume the leap-frog time-stepping 
     1028is used here. $\Delta t$ is the barotropic mode time step and $\Delta t_{bc}$ is the baroclinic mode time step. 
     1029 $c_{b}$ is the friction coefficient. $\eta$ is the sea surface level calculated in the barotropic loops 
     1030while $\eta^{'}$ is the sea surface level used in the 3-D baroclinic mode. $\textbf{u}_{b}$ is the bottom 
     1031layer horizontal velocity. 
     1032 
     1033 
     1034 
     1035 
     1036% ------------------------------------------------------------------------------------------------------------- 
    9841037%       Bottom Friction with split-explicit time splitting 
    9851038% ------------------------------------------------------------------------------------------------------------- 
     
    10911144The essential goal of the parameterization is to represent the momentum  
    10921145exchange between the barotropic tides and the unrepresented internal waves  
    1093 induced by the tidal ßow over rough topography in a stratified ocean.  
     1146induced by the tidal ow over rough topography in a stratified ocean.  
    10941147In the current version of \NEMO, the map is built from the output of  
    10951148the barotropic global ocean tide model MOG2D-G \citep{Carrere_Lyard_GRL03}. 
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