Changeset 11225


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Timestamp:
2019-07-08T14:42:50+02:00 (11 months ago)
Author:
jchanut
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#2216, Finalize ZDF chapter - OSMOSIS and Adaptive vertical advection subsections to be updated

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  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex

    r11213 r11225  
    512512 
    513513The 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. 
     514Neumann condition through \np{nn\_bc\_surf} and \np{nn\_bc\_bot}, resp. 
    515515As 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}. 
    517517The \np{rn\_crban} namelist parameter is $\alpha_{CB}$ in \autoref{eq:ZDF_Esbc} and 
    518518\np{rn\_charn} provides the value of $\beta$ in \autoref{eq:ZDF_Lsbc}.  
     
    770770 
    771771The 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\_zdftke} 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,  
    773773with statically unstable density profiles. 
    774774In such a case, the term corresponding to the destruction of turbulent kinetic energy through stratification in 
     
    984984    c_b^T = - r 
    985985\] 
    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 free-slip boundary condition. 
     986When \np{ln\_lin} \forcode{= .true.}, the value of $r$ used is \np{rn\_Uc0}*\np{rn\_Cd0}. 
     987Setting \np{ln\_OFF} \forcode{= .true.} (and \forcode{ln_lin = .true.}) is equivalent to setting $r=0$ and leads to a free-slip boundary condition. 
     988 
    988989These values are assigned in \mdl{zdfdrg}. 
    989990Note that there is support for local enhancement of these values via an externally defined 2D mask array 
     
    10381039In the non-linear friction case, the drag coefficient, $C_D$, can be optionally enhanced using 
    10391040a "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): 
     1041If  \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): 
    10411042\[ 
    10421043  C_D = \left ( {\kappa \over {\mathrm log}\left ( 0.5 \; e_{3b} / rn\_{z0} \right ) } \right )^2 
     
    10621063 \label{subsec:ZDF_drg_stability} 
    10631064 
    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 split-explicit free surface (see \autoref{subsec:ZDF_drg_ts}). The latter does indeed require the knowledge of bottom stresses in the course of the barotropic sub-iteration, 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: 
     1065Setting \np{ln\_drgimp} \forcode{= .false.} means that bottom friction is treated explicitly in time, which has the advantage of simplifying the interaction with the split-explicit free surface (see \autoref{subsec:ZDF_drg_ts}). The latter does indeed require the knowledge of bottom stresses in the course of the barotropic sub-iteration, 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: 
    10651066 
    10661067At the top (below an ice shelf cavity): 
     
    11551156 \label{subsec:ZDF_drg_ts} 
    11561157 
    1157 With split-explicit free surface, the sub-stepping 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{leap-frog} 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  
     1158With split-explicit free surface, the sub-stepping 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{leap-frog} 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.  
    11591159 
    11601160The strategy to handle top/bottom stresses with split-explicit free surface in \NEMO is as follows: 
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