Changeset 3057 for branches/2011/dev_r2802_NOCL_bfrimp/DOC/TexFiles
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- 2011-11-08T13:39:35+01:00 (13 years ago)
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branches/2011/dev_r2802_NOCL_bfrimp/DOC/TexFiles/Chapters/Chap_ZDF.tex
r2541 r3057 1 1 % ================================================================ 2 % Chapter ÑVertical Ocean Physics (ZDF)2 % Chapter Vertical Ocean Physics (ZDF) 3 3 % ================================================================ 4 4 \chapter{Vertical Ocean Physics (ZDF)} … … 539 539 the clipping factor is of crucial importance for the entrainment depth predicted in 540 540 stably 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 activated541 with the algebraic model for the turbulent uxes. The clipping is only activated 542 542 if \np{ln\_length\_lim}=true, and the $c_{lim}$ is set to the \np{rn\_clim\_galp} value. 543 543 … … 982 982 983 983 % ------------------------------------------------------------------------------------------------------------- 984 % Implicit Bottom Friction 985 % ------------------------------------------------------------------------------------------------------------- 986 \subsection{Implicit Bottom Friction} 987 \label{ZDF_bfr_imp} 988 989 An Implicit form of bottom friction has been devised in the NEMO to improve 990 model stability. We recommend this option for shelf sea and coastal ocean applications, especially 991 for split-explicit time splitting. This option can be invoked by setting \np{ln\_bfrimp} 992 to \textit{true} in the \textit{nambfr} namelist and \np{ln\_zdfexp} to \textit{false} 993 in the \textit{namzdf} namelist. 994 995 This implementation is realised in \mdl{dynzdf\_imp} and \mdl{dynspg\_ts}. In \mdl{dynzdf\_imp}, the 996 bottom 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 1003 where $mbk$ is the layer number of the bottom layer. superscript $n+1$ means the velocity used in the 1004 friction formulea is to be calculated, so, it is implicit. 1005 1006 If split-explicit time splitting is used, care must be taken to avoid the double counting of 1007 the bottom friction in the 2-D barotropic momentum equations. As NEMO only updates the barotropic 1008 pressure gradient and Coriolis' forcing terms in the 2-D barotropic calculation, we need to remove 1009 the bottom friction induced by these two terms which has been included in the 3-D momentum trend 1010 and update it with the latest value. On the other hand, the bottom friction contributed by the 1011 other terms (e.g. the advection term, viscosity term) has been included in the 3-D momentum equations 1012 and should not be added in the 2-D barotropic mode. 1013 1014 The implementation of the implicit bottom friction in \mdl{dynspg\_ts} is done in two steps as the 1015 following: 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)- 1024 2\Delta t_{bc}c_{b}\left(g\nabla\eta^{'}+f\textbf{k}\times\textbf{u}_{b}\right) 1025 \end{equation} 1026 1027 where $\textbf{T}$ is the vertical integrated 3-D momentum trend. We assume the leap-frog time-stepping 1028 is 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 1030 while $\eta^{'}$ is the sea surface level used in the 3-D baroclinic mode. $\textbf{u}_{b}$ is the bottom 1031 layer horizontal velocity. 1032 1033 1034 1035 1036 % ------------------------------------------------------------------------------------------------------------- 984 1037 % Bottom Friction with split-explicit time splitting 985 1038 % ------------------------------------------------------------------------------------------------------------- … … 1091 1144 The essential goal of the parameterization is to represent the momentum 1092 1145 exchange between the barotropic tides and the unrepresented internal waves 1093 induced by the tidal ßow over rough topography in a stratified ocean.1146 induced by the tidal ow over rough topography in a stratified ocean. 1094 1147 In the current version of \NEMO, the map is built from the output of 1095 1148 the barotropic global ocean tide model MOG2D-G \citep{Carrere_Lyard_GRL03}.
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