Changeset 6322 for branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Chap_ZDF.tex

Timestamp:

2016-02-18T08:38:04+01:00 (8 years ago)

Author:

gm

Message:

#1629: DOC of v3.6_stable : update the introduction and Qsr, add new tidal mixing param.

File:

• branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Chap_ZDF.tex (modified) (1 diff)

branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Chap_ZDF.tex

@@ -1313 +1313 @@
 
 % ================================================================
+% 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.
+
+% ================================================================
+
+
+