Changeset 11225

Timestamp:

2019-07-08T14:42:50+02:00 (5 years ago)

Author:

jchanut

Message:

#2216, Finalize ZDF chapter - OSMOSIS and Adaptive vertical advection subsections to be updated

File:

• NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex (modified) (6 diffs)

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

@@ -512 +512 @@
 
 The surface and bottom boundary condition on both $\bar{e}$ and $\psi$ can be calculated thanks to Dirichlet or
-Neumann condition through \np{nn\_tkebc\_surf} and \np{nn\_tkebc\_bot}, resp.
+Neumann condition through \np{nn\_bc\_surf} and \np{nn\_bc\_bot}, resp.
 As for TKE closure, the wave effect on the mixing is considered when
-\np{ln\_crban}\forcode{ = .true.} \citep{craig.banner_JPO94, mellor.blumberg_JPO04}.
+\np{rn\_crban}\forcode{ > 0.} \citep{craig.banner_JPO94, mellor.blumberg_JPO04}.
 The \np{rn\_crban} namelist parameter is $\alpha_{CB}$ in \autoref{eq:ZDF_Esbc} and
 \np{rn\_charn} provides the value of $\beta$ in \autoref{eq:ZDF_Lsbc}. 
@@ -770 +770 @@
 
 The turbulent closure schemes presented in \autoref{subsec:ZDF_tke}, \autoref{subsec:ZDF_gls} and
-\autoref{subsec:ZDF_osm} (\ie \np{ln\_zdftke} or \np{ln\_zdftke} or \np{ln\_zdfosm} defined) deal, in theory, 
+\autoref{subsec:ZDF_osm} (\ie \np{ln\_zdftke} or \np{ln\_zdfgls} or \np{ln\_zdfosm} defined) deal, in theory, 
 with statically unstable density profiles.
 In such a case, the term corresponding to the destruction of turbulent kinetic energy through stratification in
@@ -984 +984 @@
     c_b^T = - r
 \]
-When \forcode{ln_lin = .true.}, the value of $r$ used is \np{rn\_Uc0}*\np{rn\_Cd0}.
-Setting \forcode{ln_OFF = .true.} (and \forcode{ln_lin = .true.}) is equivalent to setting $r=0$ and leads to a free-slip boundary condition.
+When \np{ln\_lin} \forcode{= .true.}, the value of $r$ used is \np{rn\_Uc0}*\np{rn\_Cd0}.
+Setting \np{ln\_OFF} \forcode{= .true.} (and \forcode{ln_lin = .true.}) is equivalent to setting $r=0$ and leads to a free-slip boundary condition.
+
 These values are assigned in \mdl{zdfdrg}.
 Note that there is support for local enhancement of these values via an externally defined 2D mask array
@@ -1038 +1039 @@
 In the non-linear friction case, the drag coefficient, $C_D$, can be optionally enhanced using
 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.
-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):
+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):
 \[
   C_D = \left ( {\kappa \over {\mathrm log}\left ( 0.5 \; e_{3b} / rn\_{z0} \right ) } \right )^2
@@ -1062 +1063 @@
  \label{subsec:ZDF_drg_stability}
 
-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:
+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 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:
 
 At the top (below an ice shelf cavity):
@@ -1155 +1156 @@
  \label{subsec:ZDF_drg_ts}
 
-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. 
-
+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 \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. 
 
 The strategy to handle top/bottom stresses with split-explicit free surface in \NEMO is as follows: