% $Id: notes3.tex,v 1.16 2016/01/26 13:11:03 illa Exp $
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\input macros
\title{}
\author{}
\date{\today,~ $ $Revision: 1.16 $ $}
\begin{document}
%\maketitle

%\section{Setup}

%\begin{equation}
%\pmatrix{\emf}
%\end{equation}

%-rw-r--r-- 1 brandenb brandenb 1336477 2014-04-30 11:51 fig/216k30_45_B002_Om002.ps
%-rw-r--r-- 1 brandenb brandenb 1136690 2014-04-30 11:38 fig/216k30_45_B002_Om01_theta0.ps
%-rw-r--r-- 1 brandenb brandenb 1377363 2014-04-30 11:50 fig/216k30_45_B002_Om05_theta0.ps

% bfilt002_theta.png
% bfilt002_theta_smooth.png
% bfilt01_theta.png
% bfilt01_theta_smooth.png

\section{Timeseries}
Timeseries for the different field components. The data is Fourier filtered ($k/2$) and smoothed.


\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{Om002_th0_bfilt_smooth}
\end{center}\caption[]{
0.002, $0^\circ$
}\label{Om002_th0_bfilt_smooth}\end{figure}

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{Om002_th30_bfilt_smooth}
\end{center}\caption[]{
0.002, $30^\circ$
}\label{Om002_th30_bfilt_smooth}\end{figure}

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{Om002_th60_bfilt_smooth}
\end{center}\caption[]{
0.002, $60^\circ$
}\label{Om002_th60_bfilt_smooth}\end{figure}

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{Om002_th90_bfilt_smooth}
\end{center}\caption[]{
0.002, $90^\circ$
}\label{Om002_th90_bfilt_smooth}\end{figure}

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{Om01_th0_bfilt_smooth}
\end{center}\caption[]{
0.01, $0^\circ$
}\label{Om01_th0_bfilt_smooth}\end{figure}

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{Om01_th30_bfilt_smooth}
\end{center}\caption[]{
0.01, $30^\circ$
}\label{Om01_th30_bfilt_smooth}\end{figure}

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{Om01_th60_bfilt_smooth}
\end{center}\caption[]{
0.01, $60^\circ$
}\label{Om01_th60_bfilt_smooth}\end{figure}

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{Om01_th90_bfilt_smooth}
\end{center}\caption[]{
0.01, $90^\circ$
}\label{Om01_th90_bfilt_smooth}\end{figure}

\newpage
\newpage
\pagebreak 

\section{Maximum vs theta for different Co.}

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{bfilt002_theta_smooth}
\end{center}\caption[]{
Summary for 0.002.
Note that $\meanB_y=\max$ at $\theta=0^\circ$,
and $\meanB_z=\max$ at $\theta=30^\circ$.
}\label{bfilt002_theta_smooth}\end{figure}

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{bfilt01_theta_smooth}
\end{center}\caption[]{
Summary for 0.01.
Note that $\meanB_y=\max$ at $\theta=30^\circ$,
and $\meanB_z=\max$ at $\theta=60^\circ$.
}\label{bfilt01_theta_smooth}\end{figure}

\begin{table}[htb]\caption{
$\theta$ values where $\meanB_y$ and $\meanB_z$ are maximum
for different values of $\Co$.
}\vspace{12pt}\centerline{\begin{tabular}{lccccccc}
$\Co$ & 0.0015 & 0.0075 \\
\hline
$\meanB_y$ & $0^\circ$ & $30^\circ$ \\
$\meanB_z$ & $30^\circ$ & $60^\circ$ \\
\label{Ttimescale}\end{tabular}}\end{table}

Note that the amplitude of NEMPI structures are similar for
these two values of $\Co$.


\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{bzVStheta}
\end{center}\caption[]{
Dependence of $\bar{B}_z/B_{eq}$ with the colatitude for two different values of the Coriolis
number and at two different heights.
}\label{bzVStheta}\end{figure}

\section{Structures}

\begin{figure*}[h!]
\begin{center}
\includegraphics[width=0.49\textwidth]{Om002_th0_bb3_xy22}
\includegraphics[width=0.49\textwidth]{Om002_th30_bb3_xy18}
\includegraphics[width=0.49\textwidth]{Om002_th60_bb3_xy30}
\includegraphics[width=0.49\textwidth]{Om002_th90_bb3_xy34}
\end{center}\caption[]{
$B_z/B_{eq}$ for $Co = 0.0015$
}\label{bb3_xy002}
\end{figure*}

\begin{figure*}[h!]\begin{center}
\includegraphics[width=0.49\textwidth]{Om01_th0_bb3_xy082}
\includegraphics[width=0.49\textwidth]{Om01_th30_bb3_xy35}
\includegraphics[width=0.49\textwidth]{Om01_th60_bb3_xy40}
\includegraphics[width=0.49\textwidth]{Om01_th90_bb3_xy51}
\end{center}\caption[]{
$B_z/B_{eq}$ for $Co = 0.0075$
}\label{bb3_xy01}\end{figure*}


\begin{verbatim}
\end{verbatim}

\section{Different resolution}

\subsection{Structures}
\begin{figure*}[h!]
\begin{center}
\includegraphics[width=0.4\textwidth]{256joernbb3_xy32}
\includegraphics[width=0.4\textwidth]{192bb3_xy20}
\includegraphics[width=0.4\textwidth]{216bb3_xy12}
\includegraphics[width=0.4\textwidth]{240abiskobb3_xy20}
\includegraphics[width=0.4\textwidth]{384beskowbb3_xy20}
\includegraphics[width=0.4\textwidth]{384abiskobb3_xy20}
\includegraphics[width=0.4\textwidth]{576bb3_xy20}
\includegraphics[width=0.4\textwidth]{768bb3_xy25}
\end{center}\caption[]{
$B_z$ at the surface for different resolution runs
}\label{pspec}
\end{figure*}


\subsection{Power spectrum}

\begin{figure*}[h!]
\begin{center}
\includegraphics[width=0.49\textwidth]{pBz_spec2_V256k30VF_Bz002_corona_hor}
\includegraphics[width=0.49\textwidth]{pBz_spec2_192k30_B002_Om0}
\includegraphics[width=0.49\textwidth]{pBz_spec2_216k30_B002_Om0}
\includegraphics[width=0.49\textwidth]{pBz_spec2_240k30_B002_Om0}
\includegraphics[width=0.49\textwidth]{pBz_spec2_384k30_Bz002_beskow}
\includegraphics[width=0.49\textwidth]{pBz_spec2_384k30_Bz002_abisko}
\includegraphics[width=0.49\textwidth]{pBz_spec2_576k30_Bz002}
\includegraphics[width=0.49\textwidth]{pBz_spec2_768k30_Bz002}
\end{center}\caption[]{
Power spectrum for different resolution runs
}\label{pspec}
\end{figure*}


\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.49\textwidth]{maxEmVSres}
\end{center}\caption[]{
Maximum of the magnetic power spectrum for $k_{\perp} H_{\rho}=2$ for different
resolution and the two machines
}\label{pspec}
\end{figure}
%\begin{itemize}
%\item
%\end{itemize}

%r e f
%\begin{thebibliography}{}

%\bibitem[Biskamp \& M\"uller(1999)]{BM99}
%Biskamp, D., \& M\"uller, W.-C.\yprl{1999}{83}{2195}

%\end{thebibliography}

\vfill\bigskip\noindent\tiny\begin{verbatim}
$Header: /var/cvs/brandenb/tex/illa/rotCorona/notes3.tex,v 1.16 2016/01/26 13:11:03 illa Exp $
\end{verbatim}

\newpage

\begin{landscape}% Landscape page
        \centering % Center table
        {\renewcommand{\arraystretch}{3}
        \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline
          $\Omega$ & $Co$   & $\theta$ &  run name & status & 
          VAR max  & t max  & tstart   &  t end    & xypic  &  
          yzpic    & pBBeq  & pBBeq\_one&  maxBz    & maxBy  &
          max $\bar{B_z}$ & max $\bar{B_y}$ & max $\bar{B_z}$ smoot & max $\bar{B_y}$ smooth\\ \hline
           0  &  0   & 0 & 216k30\_B002\_Om0              &&&&&&&&&&&&&&& \\ \hline \hline
          .002&0.0015& 0 &216k30\_45\_B002\_Om002         &&&&&&&&&&&&&&& \\ \hline
          .002&0.0015& 30&216k30\_45\_B002\_Om002\_theta30&&&&&&&&&&&&&&& \\\hline
          .002&0.0015& 60&216k30\_45\_B002\_Om002\_theta60&&&&&&&&&&&&&&& \\\hline
          .002&0.0015& 90&216k30\_45\_B002\_Om002\_theta90&&&&&&&&&&&&&&& \\\hline \hline
          .01 &0.0075& 0 &216k30\_45\_B002\_Om01\_theta0  &&&&&&&&&&&&&&& \\\hline
          .01 &0.0075& 30&216k30\_45\_B002\_Om01\_theta30 &&&&&&&&&&&&&&& \\\hline
          .01 &0.0075& 60&216k30\_45\_B002\_Om01\_theta60 &&&&&&&&&&&&&&& \\\hline
          .01 &0.0075& 90&216k30\_45\_B002\_Om01\_theta90 &&&&&&&&&&&&&&& \\\hline \hline
          .015&0.011 & 0 &216k30\_B002\_Om015\_theta0     &&&&&&&&&&&&&&& \\ \hline
          .015&0.011 & 30&216k30\_B002\_Om015\_theta30    &&&&&&&&&&&&&&& \\\hline
          .015&0.011 & 60&216k30\_B002\_Om015\_theta60    &&&&&&&&&&&&&&& \\\hline
          .015&0.011 & 90&216k30\_B002\_Om015\_theta90    &&&&&&&&&&&&&&& \\\hline \hline
          .02 &0.015 & 0 &216k30\_B002\_Om02\_theta0      &&&&&&&&&&&&&&& \\ \hline
          .02 &0.015 & 30&216k30\_B002\_Om02\_theta30     &&&&&&&&&&&&&&& \\\hline
          .02 &0.015 & 60&216k30\_B002\_Om02\_theta60     &&&&&&&&&&&&&&& \\\hline
          .02 &0.015 & 90&216k30\_B002\_Om02\_theta90     &&&&&&&&&&&&&&& \\\hline \hline
          
        \end{tabular}
%        \captionof{table}{Table caption}% Add 'table' caption
}
    \end{landscape}
 
\newpage
\normalsize
Resolution (beskow) 

\begin{center}
\begin{tabular}{lllllllll} \hline
Resolution & run name & urms & $\nu_3$ & $\delta x$ & $\delta z$ & $k_{N_y}^x$ & $k_{N_y}^z$  & $\Rey_{grid}$ \\ \hline
192x192x384 & 192k30\_B002\_Om0\_beskow\_gnu & 0.087 & 6e-10  & 0.033 & 0.024&96 &192&0.018\\
384x384x768 & 384k30\_B002\_Om0\_beskow\_gnu & 0.087 & 1.8e-11 & 0.016& 0.012&192&384&0.018\\
384x384x768 & 384k30\_B002\_Om0\_abisko      & 0.087 & 1.8e-11 & 0.016& 0.012&192&384&0.018 \\
576x576x1152& 576k30\_B002\_Om0\_beskow\_gnu & 0.088 & 6e-13  & 0.011 & 0.008&288&576&0.074\\  %576k30_B002_Om0_beskow_gnu
768x758x1536 & 768k30\_B002\_Om0\_beskow\_gnu& 0.089 & 6e-13  & 0.008 & 0.006&384&768&0.0005\\ %768k30_B002_Om0_beskow_gnu
1152x1152x2304& 1152k30\_B002\_Om0\_beskow\_gnu2&0.088& 9e-15 & 0.005 & 0.004&576&1152&0.004
\end{tabular}
\end{center}

We are using hyperdiffusion $D_3 = \nu_3 / 30$
\EQ
\delta x = { 2\pi \over resolution}
\EN
Nyquist wavenumber
\EQ
k_{N_y} = {\pi \over \delta x}
\EN

\EQ
\Rey_{grid} = {\urms \over \nu_n k_{N_y}^{2n-1}}
\EN

\begin{table*}[t!]\caption{
Summary of runs, all of them with $g H_\rho/\csq=1$,$\Beqz/B_0$, size $(2\pi)^2\times3\pi$
%AB: should move the second part of caption to table notes.
%IL: do you mean the general quantities like size of the box and so?
%AB: Also, I think we should now add Ta_t^{1/2} as well.
% IL: remove name of the runs, add growth rate
% IL: Rey is not necesary. It's 28-29 for all runs. urms is 0.085-0.089
% IL: also remove \Pm 
% IL: add Ta_t
}\vspace{10pt}
\centerline{
\begin{tabular}{lcccccccccccc}
Run &  Resolution  & $B_0/\Beqz$& $\Co$ & $\theta$ 
   %&$\Rey$& $\Pm$ & $B_z^{\rm max}/B_0$&$\tautdm$&$\Rey_grid$& $k_{diff}$ &BR\\
   %& $\Tat^{1/2}$ & $B_z^{\rm max}/B_0$&$\Bfm/B_0$&$\tautdm$&$\Rey_{grid}$& $k_{\rm d}$
   %IL: Changed \Rey_{grid} to k_Nyquist
   & $\Tat^{1/2}$ & $B_z^{\rm max}/B_0$&$\Bfm/B_0$&$\tautdm$&$k_{N_y}^x$ = $2 k_{N_y}^z$ 
   & $k_{\rm \nu}$ & $k_{\rm \eta}$ &$\lambda/\tautd$ &BR\\
\hline
\hline
A1 & $192^2\times384$  && 0 & 0 & 0 & & & & 96  & & &$0.84 \pm 0.13$ & YES \\%
A2 & $384^2\times768$  && 0 & 0 & 0 & & & & 192 & 270 & 66 &$1.49 \pm 0.15$ & YES \\%from logrho
A3 & $576^2\times1152$ && 0 & 0 & 0 & & & & 288 & & &$1.49 \pm 0.17$ & YES \\%
A4 & $768^2\times1536$ && 0 & 0 & 0 & & & & 384 & 280 & 60 & $1.58 \pm 0.17$ & YES \\%
A5 & $1152^2\times2304$&& 0 & 0 & 0 & & & & 576 & & &$1.53 \pm 0.14$ & YES \\%
\hline
% 384k30_B002_Om002_theta0
B1 & $384^2\times768$  &0.025& 0.0015 & 0  & 4.0& & & & & &&$1.66\pm 0.26$ & YES \\
B2 & $384^2\times768$  &0.025& 0.0015 & 30 & 4.0& & & & & &&$1.74\pm 0.15$ &YES \\
B3 & $384^2\times768$  &0.025& 0.0015 & 60 & 4.0& & & & & &&$1.79\pm 0.23$ &YES \\
B4 & $384^2\times768$  &0.025& 0.0015 & 90 & 4.0& & & & & &&$0.73\pm 0.07$ &YES \\
\hline
% 384k30_B002_Om004_theta0
C1 & $384^2\times768$  && 0.003 & 0 & 8.0& & & & & &&$1.30\pm 0.09$ &  YES\\
C2 & $384^2\times768$  && 0.003 & 30& 8.0& & & & & &&$1.71\pm 0.22$ & YES\\
%C3 & $384^2\times768$  && 0.003 & 50& 8.0& & & & & &$ \pm $ & YES\\ 
C4 & $384^2\times768$  && 0.003 & 60& 8.0& & & & & &&$0.82\pm 0.08$ & YES\\
C5 & $384^2\times768$  && 0.003 & 70& 8.0& & & & & &&$0.31\pm 0.06$&  YES\\
C6 & $384^2\times768$  && 0.003 & 90& 8.0& & & & & &&$0.73\pm 0.07$ & YES\\ 
\hline
% 384k30_B002_Om005_theta0
D1 & $384^2\times768$ && 0.0037 & 0 & 10 & & & & & &&$1.78\pm 0.18$ & YES\\ 
D2 & $384^2\times768$ && 0.0037 & 60& 10 & & & & & &&$0.44\pm 0.05$ & YES\\ 
\hline
% 384k30_B002_Om006_theta
E1 & $384^2\times768$  && 0.0044 & 0 & 12 & & & & & &&$0.92\pm 0.24$ &  YES\\ 
E2 & $384^2\times768$  && 0.0044 & 60& 12 & & & & & &&$0.75\pm 0.14$ & WEAK \\
\hline
% 384k30_B002_Om01_theta0
F1 & $384^2\times768$  && 0.007 & 0 & 20 & & & & & &&$0.48\pm 0.12$ & NO\\
F2 & $384^2\times768$  && 0.007 & 30& 20 & & & & & &&$0.21\pm 0.06$  & NO\\
F3 & $384^2\times768$  && 0.007 & 60& 20 & & & & & &&$0.19\pm 0.15$  & NO\\
F4 & $384^2\times768$  && 0.007 & 90& 20 & & & & & &&$0.74\pm 0.19$  & WEAK \\
\hline
\hline
\label{runs}
\end{tabular}}
%\tablefoot{Different runs, $g H_\rho/\csq=1$,$\Beqz/B_0$, size $(2\pi)^2\times3\pi$}
\end{table*}

\end{document}
