
\def\V{{\bf v}}
\def\ave#1{\overline{#1}}
\def\mave#1{\tilde{#1}}
\def\q{c}
\def\redf{{\color{red} f}}
\def\rede{{\color{red} e}}
\def\redd{{\color{red} d}}
\def\redKz{{\color{red} K_z}}

\begin{frame}
 \frametitle{Mass flux schemes combined with turbulent diffusion}

\begin{columns}

\column{0.6\textwidth}
\includegraphics[width=\textwidth]{/home/hourdin/PRESENTATIONS/IMAGES/PBL/PDF/cbl2.pdf}


\column{0.4\textwidth}
{\small
Separation into 2 sub-colums :
\begin{equation}\nonumber
X=\alpha X_u + (1-\alpha X_d)
\end{equation}
ascending plume of mass flux
\begin{eqnarray}\nonumber
\redf&=&\alpha \rho w_u\\\nonumber
\der{\redf}{z}&=&\rede-\redd\\\nonumber
\der{\redf\q_u}{z}&=&\rede \q_d -\redd \q_u
\end{eqnarray}
}
%\end{columns}\end{frame}\end{document}
\end{columns}

\begin{equation}
\rho \ave{w'\q'}=-\rho \redKz\der{\q}{z} + \redf \dep{\q_u-\q_d}
\end{equation}

{\footnotesize
Chatfield and Brost, 1987, Hourdin et. al., 2002, Siebesma, Soarez et al, 2004 
}

\end{frame}
