\chapter{Predefined simulations, test cases and performance}

In CAT different series of predefined simulations are implemented. 
They comprise simple idealized examples allowing the study of basic 
propeties of 2D and rotating balanced flows. Further simulations of
previous studies are included  allowing the reproduction   reference cases. 

\section{Initial Value Problems in Physical Space}

Initial value problems in physical space simulate the time evolution
of vorticity (potential vorticity) distributions prescribed in physical 
space under the action of dissipation. The predefined simulations can
be seen on the one hand as illustrative examples for teaching purposes 
and on the other hand as starting point for new and more general 
simulations.

\subsection{Top Hat Jet: Option {\tt sim = "jet01"}}

\subsection{Gaussian Jet: Option {\tt sim = "jet02"}}

\subsection{Fourier Jet: Option {\tt sim = "jet03"}}

\subsection{Circular Top Hat Jet: Option {\tt sim = "jet04"}}

\subsection{Circular Gaussian Jet: Option {\tt sim = "jet05"}}

\subsection{Circular Fourier Jet: Option {\tt sim = "jet06"}}

\subsection{Elliptical Vortex Patches: Option {\tt sim = "vor01"}}

\subsection{Elliptical Gaussian Vortices: Option {\tt sim = "vor02"}}


\section{Initial Value Problems in Spectral Space}

Initial value problems in spectral space simulate the time evolution
of vorticity (potential vorticity) distributions prescribed in spectral
space under the action of dissipation. This class of simulations
contains as a special case the classical decaying turbulence
experiments.


\subsection{discs in Fourier Space: Option {\tt sim = "dec01"}}

\subsection{Rings in Fourier Space: Option {\tt sim = "dec01"}}


\section{Forced decaying flows}