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\title{Assessing magnetic bihelicity near the surface of the dynamo}
\author{}
\date{\today,~ $ $Revision: 1.3 $ $}
\begin{document}
\maketitle

\section{Introduction}

The detailed properties of the magnetic field near the surface of
dynamos in stars with outer convection zones is not normally regarded
an important aspect.
One expects the magnetic field to decline smoothly toward the surface.
However, the structure of the convection zone has a very
discontinuous behavior toward the surface, because the convective length
scale, which is expected to be proportional to the pressure scale height,
decreases sharply toward the surface layers.
Above the surface, the pressure scale height increases rapidly as the
temperature reaches coronal values.
The velocity here is insignificant and strongly controlled by the
magnetic field.
The effect on the dynamo-generated magnetic field is not obvious and
may be rather counter-intuitive, if it has any effect at all.

Here we are interested in the scale dependence of the magnetic field
in the proximity of the surface.
What is meant by scale-dependence can be very much a matter of definition.
If we think of a Fourier spectrum as a function of the inverse wavenumber,
the location of the peaks in wavenumber may give us one answer,
but if we think of scales being the typical scale in a wavelet
decomposition, we may get another answer.
Which of the two decompositions is better depends on circumstances.

In a completely homogeneous system, when the turbulent intensity and
perhaps the kinetic helicity are statistically uniform, a Fourier
decomposition is the most appropriate tool.
On the other hand, near the surface, when the properties of the turbulence
change drastically over scales short compared with the typical scale of
the turbulence, a Fourier decomposition is prone to develop Gibbs phenomena
and is therefore probably the worst possibly method.
Wavelet transforms may then be more appropriate.
Assessing the difference between these two treatments is the goal of the
present paper.

The system we choose to study here is a turbulent dynamo driven by
a random forcing function, whose amplitude is modulated by a tophat
function.
This means that the turbulent intensity falls off abruptly outside the
dynamo-active region.
Here we are particularly interested in the question of how the magnetic
energy and helicity spectra change near the surface.
In particular, we want to know how the relative importance of large and
small length scales changes as we cross the surface.
This may have important consequences for understanding the apparent sign
change of magnetic helicity with height, which has been found
both in the solar wind \citep{BSBG11} and in various dynamo modes
\citep{BCC09,WBM11,WBM12}.

%\begin{equation}
%{\cal H}(\xx,\yy)=\int \xx\curl^{-1}\yy\,\dd V
%\end{equation}

%\begin{figure}[t!]\begin{center}
%\includegraphics[width=\columnwidth]{ponset_576e}
%\end{center}\caption[]{
%Onset of vorticity and GW energy.
%}\label{pencil}\end{figure}

%\begin{table}[htb]\caption{
%}\vspace{12pt}\centerline{\begin{tabular}{lccccccc}
%\hline
%\label{Ttimescale}\end{tabular}}\end{table}

\begin{verbatim}
1. compute horizontal spectra at different heights
2. expansion in terms of other polynomials.
\end{verbatim}

%r e f
\begin{thebibliography}{}

\bibitem[Brandenburg et al.(2009)]{BCC09}
Brandenburg, A., Candelaresi, S., \& Chatterjee, P.\ymn{2009}{398}{1414}
%{1422}{Small-scale magnetic helicity losses from a mean-field dynamo}

\bibitem[Brandenburg et al.(2011)]{BSBG11}
Brandenburg, A., Subramanian, K., Balogh, A., \& Goldstein, M. L.\yapj{2011}{734}{9}
%Brandenburg, A., Subramanian, K., Balogh, A., \& Goldstein, M. L.\yapjN{2011}{734}{9}
%{Scale-dependence of magnetic helicity in the solar wind}

%\bibitem[Matthaeus et al.(1982)]{MGS82}
%Matthaeus, W. H., Goldstein, M. L., \& Smith, C.\yprl{1982}{48}{1256}
%{1259}{Evaluation of magnetic helicity in homogeneous turbulence}

\bibitem[Warnecke et al.(2011)]{WBM11}
Warnecke, J., Brandenburg, A., \& Mitra, D.\yana{2011}{534}{A11}
%Warnecke, J., Brandenburg, A., \& Mitra, D.\yanaN{2011}{534}{A11}
%{Dynamo-driven plasmoid ejections above a spherical surface}

\bibitem[Warnecke et al.(2012)]{WBM12}
Warnecke, J., Brandenburg, A., \& Mitra, D.\yjour{2012}{J. Spa.\ Weather Spa.\ Clim.}{2}{A11}
%Warnecke, J., Brandenburg, A., \& Mitra, D.\yjourN{2012}{J. Spa.\ Weather Spa.\ Clim.}{2}{A11}
%{Magnetic twist: a source and property of space weather}

\end{thebibliography}

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