\section{Carrier-Greenspan periodic solution}

The Carrier-Greenspan periodic solution for flows on a sloping beach. References: [1]. Carrier and Greenspan, Journal of Fluid Mechanics, 1958 and [2]. Mungkasi and Roberts, International Journal for Numerical Methods in Fluids, 2012.

\subsection{Results}


We should see excellent agreement between the analytical and numerical solutions.

\begin{figure}[h]
\begin{center}
\includegraphics[width=0.9\textwidth]{stage_plot.png}
\end{center}
\caption{Stage results}
\end{figure}

\begin{figure}[h]
\begin{center}
\includegraphics[width=0.9\textwidth]{xmom_plot.png}
\end{center}
\caption{Momentum results}
\end{figure}

\begin{figure}[h]
\begin{center}
\includegraphics[width=0.9\textwidth]{xvel_plot.png}
\end{center}
\caption{Velocity results}
\end{figure}


\endinput