
\def\V{{\bf v}}
\def\ave#1{\overline{#1}}
\def\mave#1{\tilde{#1}}
\def\q{c}

\begin{frame}
 \frametitle{Limitations of turbulent diffusion}

Idealized view of the dry convective boundary layer.

\begin{columns}
\column{0.4\textwidth}
\includegraphics[bb= -40 -40 480 600,clip,height=6cm]{/home/hourdin/PRESENTATIONS/IMAGES/PBL/PDF/cbl2.pdf}
\column{0.6\textwidth}

{\bf In the mixed layer}

\begin{itemize}
\item Diffusive formulation
\begin{equation}\nonumber
\ave{w'\theta'}=-K_z\der{\theta}{z}=0 \mbox{\ \ \  or slightly }<0
\end{equation}
\item
Uniform heating by the surface
\begin{equation}\nonumber
\der{\theta}{t}\simeq \frac{\ave{w'\theta'}_0}{z_i} (\mbox{Cste}>0)
\end{equation}
\begin{equation}\nonumber
\ave{w'\theta'} \simeq \frac{z-z_i}{z_i}\ \ave{w'\theta'}_0 >0
\end{equation}
\end{itemize}

\end{columns}
\end{frame}
