\frametitle{}\framesubtitle {}
\begin{center}\begin{tikzpicture}[xscale=2,yscale=1.5]
	\node (E) at (0,0) {\Euler};
	\node (SW) at (3,-1) {\SW};
	\draw[->] (E.south east)-- (SW.north west) node[midway,above,sloped]{\tiny\Hu and \Hp};
\only<1>{\draw(3.3,-1.5)node[below right]{\includegraphics[width=.4\linewidth,height=2.7cm,clip,trim=30 65 270 0]{Pictures/JumpSW}};}

\only<2->{\node (GN) at (0,-1) {\GN};
	\node (NH) at (2,-1) {\NH};
	\draw[->] (E.south)-- (GN.north) node[midway,above,sloped]{\tiny\Hu};
	\draw[->] (GN.east)-- (NH.west) node[midway,below,sloped]{\tiny\Hq};
	\draw[->] (NH.east)-- (SW.west) node[midway,below,sloped]{\tiny\Hp};}
\only<2>{\draw(3.3,-1.5)node[below right]{\includegraphics[width=.4\linewidth,height=2.7cm,clip,trim=30 65 270 0]{Pictures/JumpGN}};}

\only<3->{\node (SWL) at (3,0) {\SWL};
	\draw[->] (E.east)-- (SWL.west) node[midway,above,sloped]{\tiny\Hp};
	\draw[->] (SWL.south)-- (SW.north) node[midway,above,sloped]{\tiny\Hu};}

\only<4->{	\node (GNL) at (1,.4) {\color{red}\GNL};
	\node (NHL) at (2,.4) {\color{red}\NHL};
	\draw[->,red] (E.north east)-- (GNL.west) node[midway,above,sloped,red]{\tiny regul.};
	\draw[->,red] (GNL.east)-- (NHL.west) node[midway,above,sloped,red]{\tiny\Hq};
	\draw[->,red] (NHL.east)-- (SWL.north west) node[midway,above,sloped,red]{\tiny\Hp};}

\only<5>{
	\draw[->,red] (GNL.south)-- (GN.north east) node[midway,above,sloped]{\tiny L=1};
	\draw[->,red] (NHL.south)-- (NH.north) node[midway,above,sloped]{\tiny L=1};}


\begin{scope}[yshift=-1.7cm]
\draw(0,0)node[above right]{\color{bleu}\sc\underline{Models:}};
\draw(.5,-.1)node[left]{{\color{bleu}\Euler}} node[right]{Euler eq. with {\bf monovalued} free surface};
\draw(.5,-.4)node[left]{{\color{bleu}\SW}} node[right]{Shallow water model \only<1-2>{\color{bleu}[Saint-Venant'1871]}};
\only<2->{\draw(.5,-.7)node[left]{{\color{bleu}\NH}} node[right]{Non-hydrostatic model \only<2>{\color{bleu}[Sainte-Marie'11]}};
\draw(.5,-1)node[left]{{\color{bleu}\GN}} node[right]{Green-Naghdi model \only<2>{\color{bleu}[Serre'53]}};}
\only<3->{\draw(2.8,-.4)node[left]{{\color{bleu}\SWL}} node[right]{Layerwise shallow water model {\color{bleu}[ABPS{\sc m}'11]}};}
\only<4->{\draw(2.8,-.7)node[left]{{\color{bleu}\NHL}} node[right]{Layerwise non-hydrostatic model {\color{bleu}[F{\sc n}PPS{\sc m}]}};
\draw(2.8,-1)node[left]{{\color{bleu}\GNL}} node[right]{Layerwise Green-Naghdi model {\color{bleu}[F{\sc n}PPS{\sc m}]}};}

\draw(0,-1.7)node[above right]{\color{bleu}\sc\underline{Assumptions:}};
\draw(.5,-1.8)node[left]{{\color{bleu}\Hp}} node[right]{{\bf Hydrostatic} pressure: \qquad $p\(t,x,z\)=P\(t,x\)+g\(\eta\(t,x\)-z\)$};
\draw(.5,-2.1)node[left]{{\color{bleu}\Hu}} node[right]{{\bf Homogeneity} of the {\bf horizontal} velocity in the column:\qquad$u\(t,x,z\)=\u\(t,x\)$};
\only<2->{\draw(.5,-2.4)node[left]{{\color{bleu}\Hq}} node[right]{{\bf Homogeneity} of the {\bf vertical} velocity in the column:\qquad$w\(t,x,z\)=\w\(t,x\)$};}
\end{scope}

\begin{scope}[xshift=4.1cm,yshift=-1.4cm,xscale=.25,yscale=.4]
\only<1-2>{\def\LM{1}}\only<3->{\def\LM{3}}
	\newcommand\Bottom[1]{(.5-.2*cos(50*#1))+.2*sin(100*#1)-.05*#1)}
	\newcommand\etaM[1]{(5+.1*(1+sin(200*#1)))}
	\newcommand\zetaM[2]{{(\Bottom{#2}+(#1)/\LM*(\etaM{#2}-(\Bottom{#2})))}}
	\newcommand\qb[2]{{#2-14*(\LM-#1)/\LM+30*(\LM-#1)/\LM*(\LM-#1)/\LM-20*(\LM-#1)/\LM*(\LM-#1)/\LM*(\LM-#1)/\LM}}
	\newcommand\qz[1]{\qei+(#1-\ei)*((\qbi-\qei)/(\bi-\ei)+.2*(-1)^(\i)*(#1-\bi))}
\only<1-2>{
	\draw[thick,smooth,samples=100,domain=-3:6] plot(\x,{\etaM{\x}}) node[right]{\footnotesize$\eta$};
	\fill[fill=black!30,smooth,samples=100,domain=-3:6] (-3,-.2)--plot(\x,{\Bottom{\x}})--(6,-.2);
	\draw[thick,smooth,samples=100,domain=-3:6] plot(\x,{\Bottom{\x}}) node[right]{\footnotesize$B$};

	\def\x{2.25}
	\draw[thick,<->] (\x,{\etaM{\x}})--(\x,{\Bottom{\x}}) node[midway,left]{\footnotesize$h$};
	\pgfmathsetmacro{\xi}{\x+1.5}\foreach \i in {1,...,\LM}{
		\pgfmathsetmacro{\bi}{\zetaM{\i-1}{\x}}\pgfmathsetmacro{\ei}{\zetaM{\i}{\x}}
		\pgfmathsetmacro{\qbi}{\qb{(\i-1)}{\x}}\pgfmathsetmacro{\qei}{{\qb{\i}{\x}}}
		\draw[thick,->] ({\xi},{(\bi+\ei)/2})--({\xi+1},{(\bi+\ei)/2}) node[midway,below]{\footnotesize$\u$};
\only<2>{\draw[thick,->] ({\xi},{(\bi+\ei)/2})--({\xi},{(\bi+\ei)/2+1}) node[midway,left]{\footnotesize$\w$};
		\draw[thick,>-<] ({\xi+.25},{(\bi+\ei)/2+.75})--({\xi+.25},{(\bi+\ei)/2+1.25}) node[midway,right]{\footnotesize$\sigma$};
		\draw[thick,dashed] ({\qei},{\ei})--({\qbi},{\bi});
		\draw[thick,domain=\zetaM{\i-1}{\x}:\zetaM{\i}{\x},variable=\t] plot({\qz{\t}},\t);}}
\only<2>{\def\i{1}\pgfmathsetmacro{\im}{1}\pgfmathsetmacro{\qbi}{\qb{0}{\x}}\pgfmathsetmacro{\qei}{\qb{1}{\x}}\pgfmathsetmacro{\bi}{\zetaM{0}{\x}}\pgfmathsetmacro{\ei}{\zetaM{1}{\x}}
		\draw({(\qbi+\qei)/2},{(\bi+\ei)/2}) node[left]{\footnotesize$\q$} ({\qbi},{\bi}) node[xshift=-7]{\footnotesize$q_{B}$};}}

\only<3->{
	\draw[thick,smooth,samples=100,domain=-3:6] plot(\x,{\etaM{\x}}) node[right]{\footnotesize$\eta$};
	\fill[fill=black!30,smooth,samples=100,domain=-3:6] (-3,-.2)--plot(\x,{\Bottom{\x}})--(6,-.2);
	\draw[thick,smooth,samples=100,domain=-3:6] plot(\x,{\Bottom{\x}}) node[right]{\footnotesize$B$};
	\pgfmathsetmacro{\Lm}{\LM-1}
	\foreach \i in {1,...,\Lm}{\pgfmathsetmacro{\ip}{2*\i+1}\draw[very thick,dotted,smooth,samples=100,domain=-3:6] plot(\x,\zetaM{\i}{\x}) node[right,black]{\footnotesize$\zeta_{\sfrac{\pgfmathprintnumber\ip}2}$};}

	\def\x{2.25}
	\draw[thick,<->] (\x,{\etaM{\x}})--(\x,{\Bottom{\x}}) node[midway,left]{\footnotesize$h$};
	\pgfmathsetmacro{\xi}{\x+1.5}\foreach \i in {1,...,\LM}{
		\pgfmathsetmacro{\bi}{\zetaM{\i-1}{\x}}\pgfmathsetmacro{\ei}{\zetaM{\i}{\x}}
		\pgfmathsetmacro{\qbi}{\qb{(\i-1)}{\x}}\pgfmathsetmacro{\qei}{{\qb{\i}{\x}}}
		\draw[thick,->] ({\xi},{(\bi+\ei)/2})--({\xi+1},{(\bi+\ei)/2}) node[midway,below]{\footnotesize$u_\i$};
\only<4->{\draw[thick,->] ({\xi},{(\bi+\ei)/2})--({\xi},{(\bi+\ei)/2+.5}) node[midway,left]{\footnotesize$w_\i$};
		\draw[thick,>-<] ({\xi+.25},{(\bi+\ei)/2+.25})--({\xi+.25},{(\bi+\ei)/2+.75}) node[midway,right]{\footnotesize$\sigma_\i$};
		\draw[thick,dashed] ({\qei},{\ei})--({\qbi},{\bi});
		\draw[thick,domain=\zetaM{\i-1}{\x}:\zetaM{\i}{\x},variable=\t] plot({\qz{\t}},\t);}}
\only<4->{\def\i{1}\pgfmathsetmacro{\im}{2*\i-1}\pgfmathsetmacro{\qbi}{\qb{(\i-1)}{\x}}\pgfmathsetmacro{\qei}{\qb{\i}{\x}}\pgfmathsetmacro{\bi}{\zetaM{(\i-1)}{\x}}\pgfmathsetmacro{\ei}{\zetaM{\i}{\x}}
		\draw({(\qbi+\qei)/2},{(\bi+\ei)/2}) node[left]{\footnotesize$q_\i$} ({\qbi},{\bi}) node[xshift=-7]{\footnotesize$q_{\sfrac{\pgfmathprintnumber\im}2}$};
	\def\i{2}\pgfmathsetmacro{\im}{2*\i-1}\pgfmathsetmacro{\qbi}{\qb{(\i-1)}{\x}}\pgfmathsetmacro{\qei}{\qb{\i}{\x}}\pgfmathsetmacro{\bi}{\zetaM{(\i-1)}{\x}}\pgfmathsetmacro{\ei}{\zetaM{\i}{\x}}
		\draw({(\qbi+\qei)/2},{(\bi+\ei)/2}) node[right]{\footnotesize$q_\i$} ({\qbi},{\bi}) node[xshift=7,yshift=-5]{\footnotesize$q_{\sfrac{\pgfmathprintnumber\im}2}$};
	\def\i{3}\pgfmathsetmacro{\im}{2*\i-1}\pgfmathsetmacro{\qbi}{\qb{(\i-1)}{\x}}\pgfmathsetmacro{\qei}{\qb{\i}{\x}}\pgfmathsetmacro{\bi}{\zetaM{(\i-1)}{\x}}\pgfmathsetmacro{\ei}{\zetaM{\i}{\x}}
		\draw({(\qbi+\qei)/2},{(\bi+\ei)/2}) node[left]{\footnotesize$q_\i$} ({\qbi},{\bi}) node[xshift=-7,yshift=5]{\footnotesize$q_{\sfrac{\pgfmathprintnumber\im}2}$};}}

\end{scope}

\draw(-.2,.7)node{~};
\draw(10,-10)node{~};
\end{tikzpicture}\end{center}