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

\begin{frame}
 \frametitle{Extension of diffusive formulations}

\begin{itemize}
\item{\bf Introduction of a countergradient term}

\begin{equation}
\ave{w'\theta'}=K_z\depb{\Gamma-\der{\theta}{z}}=0 \mbox{\ \ \ \ with }\Gamma\simeq 1K/km
\end{equation}
Imposed countergradient Deardorf, 1966\\
Revisited by Troen \& Mart, 1986, Holtzlag \& Boville, 1993, based on a similarity approach.

\item {\bf Non local mixing length} (Bougeault)

\item {\bf Higher order closures}\\
- Mellor \& Yamada 1974, hierarchy at successive orders. Complex and still local.\\
- Abdella \& Mc Farlane, 1997, Introduce a mass flux approach to compute the 3rd order moments in a Mellor and Yamada scheme.


\end{itemize}

\end{frame}
