% $Id: notes.tex,v 1.6 2021/04/09 14:45:03 brandenb Exp $
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\def\calEE{{\cal E}}
\def\red{\textcolor{red}}
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\title{}
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\date{\today,~ $ $Revision: 1.6 $ $}
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%\section{}

%Use $(r,\phi,z)$ coordinates and

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%\begin{equation}
%\eta=\eta_0\,(1-\epsilon\cos\phi)
%\end{equation}

%1,7M mar 29 09:31 K512irrok6c_rospec/data/power_ro.dat
%1,8M mar 29 09:21 M512sig1_k6_ramp1b_rospec/data/power_ro.dat

Runs B and F from Sayan paper.
Driving during $1<t<2$.
Run B for irrotational turbulence produced by plane wave forcing, and
Run F with magnetic forcing and helicity (black is total energy,
i.e., kinetic and magnetic energies).
Spectra are plotted during $1.9<t<2$.

\begin{table}[t]\caption{
Summary of the runs discussed in the paper.
}\vspace{12pt}\centerline{\begin{tabular}{lccccccccc}
Run&$i$&$\calEE_i^{\max}$&$\sigma$& $\calEE_{\rm GW}^{\rm sat}$ & $q$ \\
\hline
B & Ka &$2.4\times10^{-3}$&0&$1.6\times10^{-8}$& 32 \\%K512irrok6c
F & Mv &$1.7\times10^{-2}$&1&$5.1\times10^{-9}$& 2.5 \\%M512sig1_k6_ramp1b
\label{Tsummary}\end{tabular}}\end{table}

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{pcomp_irro_vs_hel}
\end{center}\caption[]{
Initial growth is very fast, but similar in both cases.
}\label{pcomp_irro_vs_hel}\end{figure}

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{ppower_ro_K512irrok6c_rospec}
\end{center}\caption[]{
Run B kinetic energy spectrum (blue) and
density spectrum (red), but multiplied by 0.14.
}\label{ppower_ro_K512irrok6c_rospec}\end{figure}

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{ppower_ro_M512sig1_k6_ramp1b_rospec}
\end{center}\caption[]{
Run F kinetic energy spectrum (blue) and
density spectrum (red), but multiplied by 2.2.
}\label{ppower_ro_M512sig1_k6_ramp1b_rospec}\end{figure}

\begin{figure}[t!]\begin{center}
\includegraphics[width=\columnwidth]{pSCL2_K512irrok6c}
\includegraphics[width=\columnwidth]{pSCL2_M512sig1_k6_ramp1b}
\end{center}\caption[]{
SVT decomposition for Run B (top) for irrotational
turbulence produced by plane wave forcing, and
Run F (bottom) with magnetic forcing and helicity.
}\label{pencil_hel}\end{figure}

\begin{figure}[t!]\begin{center}
\includegraphics[width=\columnwidth]{pko_K64irrok6c_StT_cont}
\includegraphics[width=\columnwidth]{pko_M64sig1_k6_ramp1b_StT_cont}
\end{center}\caption[]{
$k\omega$ diagram for Run B (top) for irrotational
turbulence produced by plane wave forcing, and
Run F (bottom) with magnetic forcing and helicity.
The fit is proportional to $k^{-3}$ for Run~B and
proportional to $k^{-2}$ for Run~F.
}\label{pencil_hel}\end{figure}

For irrotational turbulence, most of the power comes from the
lowest wavenumbers.
This raises the question how sensitive the results are
to the lowest wavenumber in the domain.

%\begin{table}[htb]\caption{
%}\vspace{12pt}\centerline{\begin{tabular}{lccccccc}
%$R$ & $T$ & $\kf$ & $\omf$ & $\EEGW$ & $\hrms$ & $k_{\rm peak}$ \\
%\hline
%\label{Ttimescale}\end{tabular}}\end{table}

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

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

%\end{thebibliography}

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