
\documentclass[a4paper,12pt]{article}
    \usepackage{amsmath}
    \usepackage{amssymb}
    \usepackage{breqn}
\usepackage{graphicx}
\usepackage{color}
\usepackage{float}
\usepackage[numbers]{natbib}

\def\apj{ApJ}
\def\apss{Ap{\&}SS}
\def\mnras{MNRAS}
\def\aap{A\&A}
\def\apjl{ApJ}
\def\gafd{Geophys.\ Astrophys.\ Fluid Dyn.}
\def\jfm{JFM}
\def\physrep{PhR}
\def\pre{PRE}
\def\prl{PRL}
\def\apjs{ApJS}
\def\pasa{PASA}
\def\pasj{PASJ}
\def\nat{Natur}
\def\pasp{PASP}
\def\ssr{SSRv}
\def\memsai{Memorie della Societa Astronomica Italiana}
\def\araa{Ann. Rev. of Astron. and Astrophys.}
\newcommand\zhetp{JETP}
\newcommand\jetp{Sov.\ Phys.\ JETP}

	\addtolength{\oddsidemargin}{-.875in}
	\addtolength{\evensidemargin}{-.875in}
	\addtolength{\textwidth}{1.75in}

	\addtolength{\topmargin}{-.875in}
	\addtolength{\textheight}{1.75in}

\input macros.tex

\begin{document}

\section*{Response to Referee B}

We thank the referee for carefully reading and reviewing our manuscript. We have revised certain parts of the paper, 
especially the introductory paragraphs. Here we offer explanations 
to the referee's detailed comments and have pointed to the revisions (marked in blue) pertaining to some of the comments.
We hope that these revisions will satisfy the referee to find our manuscript now suitable for a 
publication in PRL.

\begin{enumerate}
\item \textbf{The authors report the exponential growth of large-scale magnetic
fields after the saturation of small-scale magnetic fields, which was
referred to as ``a novel quasi-kinematic large-scale dynamo". However,
as the authors also noted in their introduction, the saturation of
magnetic fields depends on scales (occurring first on small scales),
so I do not see how their finding is particularly novel.} \\

Yes, as the referee has pointed out, it is correct that saturation of magnetic fields depends on scales, which 
we showed in our previous paper Bhat et. al. (2016) \citep{BSB16}. However, previously it was thought that the large-scale field 
transitioned from the kinematic to the nonlinear growth stage around the same time as the small-scale field on the forcing scale saturated \cite{BSB16}. 
This second growth phase for large-scale field, seen in the present work, was not identified.
In our previous paper mentioned above, we had two major simulations (with $1024^3$ resolution) of the helical dynamo (without shear). 
One run was at Prandtl number of $\Pm=0.1$ and the other was at $\Pm=10$. It is not clear that this second 
phase is there at all in the run with $\Pm=0.1$, as the requirement of separation in growth time scales,
between the small-scale dynamo dominated (first) phase and the large-scale dynamo
dominated (second) phase, is harder to achieve at low $\Pm$.
But there was a hint of the second phase in the run with $\Pm=10$. 
In our current work, the growth rates of the large-scale field
(between the first and second phase),
are well separated in their values and 
thus it was possible to identify the novel second phase distinctly. 

In fact in the literature so far, the large-scale field exponential growth has been referred to theoretically only in the kinematic phase. 
But it is now well-established that for large-$\Rm$ systems, the small-scale dynamo (SSD)
is the dominant driver of the growth of magnetic fields 
at all scales in the kinematic phase \citep{VC92,TC2013,SB14,BSB16}. The worry is whether then the large-scale field is simply overwhelmed by the small-scale fields.
With our new result, it is demonstrated that there is a separate 
large-scale dynamo (LSD) phase, in high $\Rm$ systems, which then
grows large-scale fields to substantial strengths.

We have made some new revisions in the introduction (first three
paragraphs) to better explain the new developments and also to help
clarify the significance/novelty of our result.

\item \textbf{Also, the manuscript presents different simulations depending on the
presence of a prescribed shear, helical/non-helical forcing, etc.
However, I do not find a systematic analysis on the dependence of
their results on shear parameter, magnetic Reynolds number, etc. For
instance, Figures 1 and 2 compare the cases with shear and without it,
but apart from presenting growth rates for different modes against
time, I am unsure what to learn from these two figures in terms of the
role of shear in dynamo. Another example is Figure 5 which shows three
points for three different shear values.} \\ 

In this work, our focus is on addressing the state of large-scale fields in presence of 
rapidly growing small-scale fields and not about the role of the shear in the dynamo. 
Thus we have shown here the operation of a distinctive large-scale dynamo even in presence
of strongly growing small-scale fields, both in helical turbulence with shear and without shear.
%
In our work, we use the variation of shear parameter 
as a proxy to test the agreement of the growth rate of 
this quasi-kinematic LS field against estimates from mean-field theory. 
We find that, while the prediction by the standard theory is for a kinematic large-scale dynamo (one that can be obtained easily at low $\Rm$), 
it agrees reasonably well with this quasi-kinematic LSD at large $\Rm$ also. However, it is clear that the standard mean-field theory
does not explains everything.

The standard theory has traditionally not accounted for the rapid small-scale dynamo in the kinematic phase. 
We find this novel standalone LSD only when SSD has slowed down. This is a different kind of system compared to the one 
from which the standard large-scale (or mean-field) theory is derived, 
and is as yet somewhat unexplored territory for the theory of LSD.

Regarding dependence on other parameters, we have checked for the dependence of the growth rate for a
factor of 2 change in $\Rm$ and the forcing scale. The growth rate seems to be independent of both parameters.

\item \textbf{The discussion is based on the quasi-linear analysis, which obviously
requires the values of turbulent transport coefficients ($\eta_T$,
$\alpha$). I am unsure about the accuracy of their estimated values for
these coefficients to validate the agreement of the quasi-linear
analysis and computational results.} \\

We agree that the estimates are at the zeroth order. But there is a good agreement with the numerical results, with 
an efficiency factor that is of the order unity. While the growth rate and oscillation rate of large-scale field agree
reasonably well with the zeroth order theoretical estimates, 
we still do think that the standard mean-field theory is insufficient to understand our results completely. 
As we have mentioned towards the end, in our discussions, the system is already nonlinear before the second phase of 
large-scale field growth arises. The standard mean-field equations/solutions do not account for this nonlinearity.
However, the reason we think these estimates agree is that the field at large-scales is not affected by Lorentz force yet. 

We have now included a couple of lines to delineate the effects that aren't
included in our model.
These edits are marked in blue on page 4.

\item \textbf{In Figures 3 and 4, the data should be presented for the same range} \\

One is a semi-log plot, so one cannot compare Figs.3 and 4.
The purpose of the two figures is also different and requires
the adopted scales. While Figure 3 shows that the growth 
of the large-scale field in the SSD dominated stage of helical runs 
are the same as as the pure SSD runs, Figure 4 shows the 
extended growth of the small-scale field in the helical run compared
to the non-helical (pure SSD) run. 

\end{enumerate}
\textbf{In summary, I do not find the results not sufficiently significant,
and thus regret that I cannot recommend this manuscript for the
publication in Physical Review Letters.}\\

Our main result in this paper is the numerical demonstration of the quasi-kinematic large-scale dynamo in a large-$\Rm$ system. 
Up until now, we have thought of large-scale fields growing to  significant strengths mainly in the nonlinear growth phase (due to helicity decay 
at small-scales). With this  result, we now already have a kinematic large-scale dynamo at large $\Rm$, after the SSD 
has saturated; rather we call it the ``quasi-kinematic" LSD as the system is already nonlinear on smaller scales. 
Thus, we have shown that we don't have to wait until the fully nonlinear phase for large-scale fields to grow
to significant strengths. 
This result is also important as future numerical studies of large-scale dynamo at large-$\Rm$,
relevant to stars and galaxies, can operate in this regime 
(where there is growth time-scale separation between the subsequent stages) to obtain a 
separate 'kinematic' LSD.   

We hope that our explanations 
convince the reviewer that this result of quasi-kinematic large-scale field growth is of 
high importance and our study is only a preliminary one but nonetheless that which warrants the 
best exposure to the rest of the community. 

\bibliographystyle{phcpc}
\bibliography{reftwody}


\end{document}
