Changeset 6347 for branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_ZDF.tex

Timestamp:

2016-02-24T08:56:48+01:00 (8 years ago)

Author:

gm

Message:

#1683: SIMPLIF-1 : Phase with the v3.6_Stable (DOC+ZDF+traqsr+lbedo)

File:

• branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_ZDF.tex (modified) (9 diffs)

branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_ZDF.tex

@@ -262 +262 @@
 \end{equation}
 
-At the ocean surface, a non zero length scale is set through the  \np{rn\_lmin0} namelist 
+At the ocean surface, a non zero length scale is set through the  \np{rn\_mxl0} namelist 
 parameter. Usually the surface scale is given by $l_o = \kappa \,z_o$ 
 where $\kappa = 0.4$ is von Karman's constant and $z_o$ the roughness 
 parameter of the surface. Assuming $z_o=0.1$~m \citep{Craig_Banner_JPO94} 
-leads to a 0.04~m, the default value of \np{rn\_lsurf}. In the ocean interior 
+leads to a 0.04~m, the default value of \np{rn\_mxl0}. In the ocean interior 
 a minimum length scale is set to recover the molecular viscosity when $\bar{e}$ 
 reach its minimum value ($1.10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$ ).
@@ -295 +295 @@
 As the surface boundary condition on TKE is prescribed through $\bar{e}_o = e_{bb} |\tau| / \rho_o$, 
 with $e_{bb}$ the \np{rn\_ebb} namelist parameter, setting \np{rn\_ebb}~=~67.83 corresponds 
-to $\alpha_{CB} = 100$. further setting  \np{ln\_lsurf} to true applies \eqref{ZDF_Lsbc} 
-as surface boundary condition on length scale, with $\beta$ hard coded to the Stacet's value.
+to $\alpha_{CB} = 100$. Further setting  \np{ln\_mxl0} to true applies \eqref{ZDF_Lsbc} 
+as surface boundary condition on length scale, with $\beta$ hard coded to the Stacey's value.
 Note that a minimal threshold of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) 
 is applied on surface $\bar{e}$ value.
@@ -852 +852 @@
 The bottom friction represents the friction generated by the bathymetry. 
 The top friction represents the friction generated by the ice shelf/ocean interface. 
-As the friction processes at the top and bottom are represented similarly, only the bottom friction is described in detail below.\\
+As the friction processes at the top and bottom are represented similarly, 
+only the bottom friction is described in detail below.
 
 
@@ -926 +927 @@
 $H = 4000$~m, the resulting friction coefficient is $r = 4\;10^{-4}$~m\;s$^{-1}$. 
 This is the default value used in \NEMO. It corresponds to a decay time scale 
-of 115~days. It can be changed by specifying \np{rn\_bfric1} (namelist parameter).
+of 115~days. It can be changed by specifying \np{rn\_bfri1} (namelist parameter).
 
 For the linear friction case the coefficients defined in the general 
@@ -936 +937 @@
 \end{split}
 \end{equation}
-When \np{nn\_botfr}=1, the value of $r$ used is \np{rn\_bfric1}. 
+When \np{nn\_botfr}=1, the value of $r$ used is \np{rn\_bfri1}. 
 Setting \np{nn\_botfr}=0 is equivalent to setting $r=0$ and leads to a free-slip 
 bottom boundary condition. These values are assigned in \mdl{zdfbfr}. 
@@ -943 +944 @@
 in the \ifile{bfr\_coef} input NetCDF file. The mask values should vary from 0 to 1. 
 Locations with a non-zero mask value will have the friction coefficient increased 
-by $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfric1}.
+by $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri1}.
 
 % -------------------------------------------------------------------------------------------------------------
@@ -963 +964 @@
 $e_b = 2.5\;10^{-3}$m$^2$\;s$^{-2}$, while the FRAM experiment \citep{Killworth1992} 
 uses $C_D = 1.4\;10^{-3}$ and $e_b =2.5\;\;10^{-3}$m$^2$\;s$^{-2}$. 
-The CME choices have been set as default values (\np{rn\_bfric2} and \np{rn\_bfeb2} 
+The CME choices have been set as default values (\np{rn\_bfri2} and \np{rn\_bfeb2} 
 namelist parameters).
 
@@ -978 +979 @@
 \end{equation}
 
-The coefficients that control the strength of the non-linear bottom friction are 
-initialised as namelist parameters: $C_D$= \np{rn\_bfri2}, and $e_b$ =\np{rn\_bfeb2}. 
-Note for applications which treat tides explicitly a low or even zero value of 
-\np{rn\_bfeb2} is recommended. From v3.2 onwards a local enhancement of $C_D$ 
-is possible via an externally defined 2D mask array (\np{ln\_bfr2d}=true). 
-See previous section for details.
+The coefficients that control the strength of the non-linear bottom friction are
+initialised as namelist parameters: $C_D$= \np{rn\_bfri2}, and $e_b$ =\np{rn\_bfeb2}.
+Note for applications which treat tides explicitly a low or even zero value of
+\np{rn\_bfeb2} is recommended. From v3.2 onwards a local enhancement of $C_D$ is possible
+via an externally defined 2D mask array (\np{ln\_bfr2d}=true).  This works in the same way
+as for the linear bottom friction case with non-zero masked locations increased by
+$mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri2}.
+
+% -------------------------------------------------------------------------------------------------------------
+%       Bottom Friction Log-layer
+% -------------------------------------------------------------------------------------------------------------
+\subsection{Log-layer Bottom Friction enhancement (\np{nn\_botfr} = 2, \np{ln\_loglayer} = .true.)}
+\label{ZDF_bfr_loglayer}
+
+In the non-linear bottom friction case, the drag coefficient, $C_D$, can be optionally
+enhanced using a "law of the wall" scaling. If  \np{ln\_loglayer} = .true., $C_D$ is no
+longer constant but is related to the thickness of the last wet layer in each column by:
+
+\begin{equation}
+C_D = \left ( {\kappa \over {\rm log}\left ( 0.5e_{3t}/rn\_bfrz0 \right ) } \right )^2
+\end{equation}
+
+\noindent where $\kappa$ is the von-Karman constant and \np{rn\_bfrz0} is a roughness
+length provided via the namelist.
+
+For stability, the drag coefficient is bounded such that it is kept greater or equal to
+the base \np{rn\_bfri2} value and it is not allowed to exceed the value of an additional
+namelist parameter: \np{rn\_bfri2\_max}, i.e.:
+
+\begin{equation}
+rn\_bfri2 \leq C_D \leq rn\_bfri2\_max
+\end{equation}
+
+\noindent Note also that a log-layer enhancement can also be applied to the top boundary
+friction if under ice-shelf cavities are in use (\np{ln\_isfcav}=.true.).  In this case, the
+relevant namelist parameters are \np{rn\_tfrz0}, \np{rn\_tfri2}
+and \np{rn\_tfri2\_max}.
 
 % -------------------------------------------------------------------------------------------------------------
@@ -1267 +1299 @@
 
 % ================================================================
+% Internal wave-driven mixing
+% ================================================================
+\section{Internal wave-driven mixing (\key{zdftmx\_new})}
+\label{ZDF_tmx_new}
+
+%--------------------------------------------namzdf_tmx_new------------------------------------------
+\namdisplay{namzdf_tmx_new}
+%--------------------------------------------------------------------------------------------------------------
+
+The parameterization of mixing induced by breaking internal waves is a generalization 
+of the approach originally proposed by \citet{St_Laurent_al_GRL02}. 
+A three-dimensional field of internal wave energy dissipation $\epsilon(x,y,z)$ is first constructed, 
+and the resulting diffusivity is obtained as 
+\begin{equation} \label{Eq_Kwave}
+A^{vT}_{wave} =  R_f \,\frac{ \epsilon }{ \rho \, N^2 }
+\end{equation}
+where $R_f$ is the mixing efficiency and $\epsilon$ is a specified three dimensional distribution 
+of the energy available for mixing. If the \np{ln\_mevar} namelist parameter is set to false, 
+the mixing efficiency is taken as constant and equal to 1/6 \citep{Osborn_JPO80}. 
+In the opposite (recommended) case, $R_f$ is instead a function of the turbulence intensity parameter 
+$Re_b = \frac{ \epsilon}{\nu \, N^2}$, with $\nu$ the molecular viscosity of seawater, 
+following the model of \cite{Bouffard_Boegman_DAO2013} 
+and the implementation of \cite{de_lavergne_JPO2016_efficiency}.
+Note that $A^{vT}_{wave}$ is bounded by $10^{-2}\,m^2/s$, a limit that is often reached when the mixing efficiency is constant.
+
+In addition to the mixing efficiency, the ratio of salt to heat diffusivities can chosen to vary 
+as a function of $Re_b$ by setting the \np{ln\_tsdiff} parameter to true, a recommended choice). 
+This parameterization of differential mixing, due to \cite{Jackson_Rehmann_JPO2014}, 
+is implemented as in \cite{de_lavergne_JPO2016_efficiency}.
+
+The three-dimensional distribution of the energy available for mixing, $\epsilon(i,j,k)$, is constructed 
+from three static maps of column-integrated internal wave energy dissipation, $E_{cri}(i,j)$, 
+$E_{pyc}(i,j)$, and $E_{bot}(i,j)$, combined to three corresponding vertical structures 
+(de Lavergne et al., in prep):
+\begin{align*}
+F_{cri}(i,j,k) &\propto e^{-h_{ab} / h_{cri} }\\
+F_{pyc}(i,j,k) &\propto N^{n\_p}\\
+F_{bot}(i,j,k) &\propto N^2 \, e^{- h_{wkb} / h_{bot} }
+\end{align*} 
+In the above formula, $h_{ab}$ denotes the height above bottom, 
+$h_{wkb}$ denotes the WKB-stretched height above bottom, defined by
+\begin{equation*}
+h_{wkb} = H \, \frac{ \int_{-H}^{z} N \, dz' } { \int_{-H}^{\eta} N \, dz'  } \; ,
+\end{equation*}
+The $n_p$ parameter (given by \np{nn\_zpyc} in \ngn{namzdf\_tmx\_new} namelist)  controls the stratification-dependence of the pycnocline-intensified dissipation. 
+It can take values of 1 (recommended) or 2.
+Finally, the vertical structures $F_{cri}$ and $F_{bot}$ require the specification of 
+the decay scales $h_{cri}(i,j)$ and $h_{bot}(i,j)$, which are defined by two additional input maps. 
+$h_{cri}$ is related to the large-scale topography of the ocean (etopo2) 
+and $h_{bot}$ is a function of the energy flux $E_{bot}$, the characteristic horizontal scale of 
+the abyssal hill topography \citep{Goff_JGR2010} and the latitude.
+
+% ================================================================
+
+
+