Changeset 11225 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex
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 20190708T14:42:50+02:00 (5 years ago)
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex
r11213 r11225 512 512 513 513 The surface and bottom boundary condition on both $\bar{e}$ and $\psi$ can be calculated thanks to Dirichlet or 514 Neumann condition through \np{nn\_ tkebc\_surf} and \np{nn\_tkebc\_bot}, resp.514 Neumann condition through \np{nn\_bc\_surf} and \np{nn\_bc\_bot}, resp. 515 515 As for TKE closure, the wave effect on the mixing is considered when 516 \np{ ln\_crban}\forcode{ = .true.} \citep{craig.banner_JPO94, mellor.blumberg_JPO04}.516 \np{rn\_crban}\forcode{ > 0.} \citep{craig.banner_JPO94, mellor.blumberg_JPO04}. 517 517 The \np{rn\_crban} namelist parameter is $\alpha_{CB}$ in \autoref{eq:ZDF_Esbc} and 518 518 \np{rn\_charn} provides the value of $\beta$ in \autoref{eq:ZDF_Lsbc}. … … 770 770 771 771 The turbulent closure schemes presented in \autoref{subsec:ZDF_tke}, \autoref{subsec:ZDF_gls} and 772 \autoref{subsec:ZDF_osm} (\ie \np{ln\_zdftke} or \np{ln\_zdf tke} or \np{ln\_zdfosm} defined) deal, in theory,772 \autoref{subsec:ZDF_osm} (\ie \np{ln\_zdftke} or \np{ln\_zdfgls} or \np{ln\_zdfosm} defined) deal, in theory, 773 773 with statically unstable density profiles. 774 774 In such a case, the term corresponding to the destruction of turbulent kinetic energy through stratification in … … 984 984 c_b^T =  r 985 985 \] 986 When \forcode{ln_lin = .true.}, the value of $r$ used is \np{rn\_Uc0}*\np{rn\_Cd0}. 987 Setting \forcode{ln_OFF = .true.} (and \forcode{ln_lin = .true.}) is equivalent to setting $r=0$ and leads to a freeslip boundary condition. 986 When \np{ln\_lin} \forcode{= .true.}, the value of $r$ used is \np{rn\_Uc0}*\np{rn\_Cd0}. 987 Setting \np{ln\_OFF} \forcode{= .true.} (and \forcode{ln_lin = .true.}) is equivalent to setting $r=0$ and leads to a freeslip boundary condition. 988 988 989 These values are assigned in \mdl{zdfdrg}. 989 990 Note that there is support for local enhancement of these values via an externally defined 2D mask array … … 1038 1039 In the nonlinear friction case, the drag coefficient, $C_D$, can be optionally enhanced using 1039 1040 a "law of the wall" scaling. This assumes that the model vertical resolution can capture the logarithmic layer which typically occur for layers thinner than 1 m or so. 1040 If \np{ln\_loglayer} = .true., $C_D$ is no longer constant but is related to the distance to the wall (or equivalently to the half of the top/bottom layer thickness):1041 If \np{ln\_loglayer} \forcode{= .true.}, $C_D$ is no longer constant but is related to the distance to the wall (or equivalently to the half of the top/bottom layer thickness): 1041 1042 \[ 1042 1043 C_D = \left ( {\kappa \over {\mathrm log}\left ( 0.5 \; e_{3b} / rn\_{z0} \right ) } \right )^2 … … 1062 1063 \label{subsec:ZDF_drg_stability} 1063 1064 1064 Setting \ forcode{ln_drgimp= .false.} means that bottom friction is treated explicitly in time, which has the advantage of simplifying the interaction with the splitexplicit free surface (see \autoref{subsec:ZDF_drg_ts}). The latter does indeed require the knowledge of bottom stresses in the course of the barotropic subiteration, which becomes less straightforward in the implicit case. In the explicit case, top/bottom stresses can be computed using \textit{before} velocities and inserted in the overall momentum tendency budget. This reads:1065 Setting \np{ln\_drgimp} \forcode{= .false.} means that bottom friction is treated explicitly in time, which has the advantage of simplifying the interaction with the splitexplicit free surface (see \autoref{subsec:ZDF_drg_ts}). The latter does indeed require the knowledge of bottom stresses in the course of the barotropic subiteration, which becomes less straightforward in the implicit case. In the explicit case, top/bottom stresses can be computed using \textit{before} velocities and inserted in the overall momentum tendency budget. This reads: 1065 1066 1066 1067 At the top (below an ice shelf cavity): … … 1155 1156 \label{subsec:ZDF_drg_ts} 1156 1157 1157 With splitexplicit free surface, the substepping of barotropic equations needs the knowledge of top/bottom stresses. An obvious way to satisfy this is to take them as constant over the course of the barotropic integration and equal to the value used to update the baroclinic momentum trend. Provided \forcode{ln_drgimp = .false.} and a centred or \textit{leapfrog} like integration of barotropic equations is used (\ie \forcode{ln_bt_fw = .false.}, cf \autoref{subsec:DYN_spg_ts}), this does ensure that barotropic and baroclinic dynamics feel the same stresses during one leapfrog time step. However, if \forcode{ln_drgimp = .true.}, stresses depend on the \textit{after} value of the velocities which themselves depend on the barotropic iteration result. This cyclic dependency makes difficult obtaining consistent stresses in 2d and 3d dynamics. Part of this mismatch is then removed when setting the final barotropic component of 3d velocities to the time splitting estimate. This last step can be seen as a necessary evil but should be minimized since it interferes with the adjustment to the boundary conditions. 1158 1158 With splitexplicit free surface, the substepping of barotropic equations needs the knowledge of top/bottom stresses. An obvious way to satisfy this is to take them as constant over the course of the barotropic integration and equal to the value used to update the baroclinic momentum trend. Provided \np{ln\_drgimp}\forcode{= .false.} and a centred or \textit{leapfrog} like integration of barotropic equations is used (\ie \forcode{ln_bt_fw = .false.}, cf \autoref{subsec:DYN_spg_ts}), this does ensure that barotropic and baroclinic dynamics feel the same stresses during one leapfrog time step. However, if \np{ln\_drgimp}\forcode{= .true.}, stresses depend on the \textit{after} value of the velocities which themselves depend on the barotropic iteration result. This cyclic dependency makes difficult obtaining consistent stresses in 2d and 3d dynamics. Part of this mismatch is then removed when setting the final barotropic component of 3d velocities to the time splitting estimate. This last step can be seen as a necessary evil but should be minimized since it interferes with the adjustment to the boundary conditions. 1159 1159 1160 1160 The strategy to handle top/bottom stresses with splitexplicit free surface in \NEMO is as follows:
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