# HG changeset patch
# User paugier <pierre.augier@univ-grenoble-alpes.fr>
# Date 1695221453 -7200
#      Wed Sep 20 16:50:53 2023 +0200
# Node ID 6e5387a6ef1d58b03212a4768e98be533b75c946
# Parent  88dba473f0604ca3ce97c727e8d71e74128759c7
Format with new formattex

diff --git a/2022strat_polo_proj/review0/rebut1.tex b/2022strat_polo_proj/review0/rebut1.tex
--- a/2022strat_polo_proj/review0/rebut1.tex
+++ b/2022strat_polo_proj/review0/rebut1.tex
@@ -34,134 +34,120 @@
 
 \maketitle
 
-\noindent
-We thank the referee for his critical comments. The answer on all the comments are
-listed below.
+\noindent We thank the referee for his critical comments. The answer on all the
+comments are listed below.
 
 \begin{enumerate}
 
 \itemit{p.5: what is the origin of the 0.8 factor instead of the more classical 2/3
-rule for dealiasing? Is it related to the use of hyperviscosity and
-hyperdiffusion?
-}
+rule for dealiasing? Is it related to the use of hyperviscosity and hyperdiffusion?}
 
-We performed with Jason Reneuve an extensive study on dealiasing methods
-(also with phase shifting). It is not yet published but a notable result is that ... TODO...
+We performed with Jason Reneuve an extensive study on dealiasing methods (also with
+phase shifting). It is not yet published but a notable result is that ... TODO...
 
 
 \itemit{p.5: what is the motivation behind forcing low frequency waves only? Wouldn't
-it be better to increase the wave frequency to better satisfy the timescale
-separation required by WWT?
-}
+it be better to increase the wave frequency to better satisfy the timescale separation
+required by WWT?}
 
-TODO: add in the article + add added text here. (geophysical fluids (for example M2 waves) + temporal spectra)
+TODO: add in the article + add added text here. (geophysical fluids (for example M2
+waves) + temporal spectra)
 
 
-\itemit{
-Why is hyperviscosity added to the regular viscosity? Is it just for
-regularisation purposes, but in that case, the simulations presented cannot be
-labelled as DNS I assume? How important it is in the simulations presented here,
-would they all blow up without it?
-}
+\itemit{Why is hyperviscosity added to the regular viscosity? Is it just for
+regularisation purposes, but in that case, the simulations presented cannot be labelled
+as DNS I assume? How important it is in the simulations presented here, would they all
+blow up without it?}
 
 TODO: add in the article + add added text here.
 
-- Most of the simulations are proper DNS with $\kmax\eta$ larger or close to one. For example (40, 20), $\kmax\eta = 0.99$ and 1.05.
+- Most of the simulations are proper DNS with $\kmax\eta$ larger or close to one. For
+example (40, 20), $\kmax\eta = 0.99$ and 1.05.
 
-- Few simulations are not DNS, but they can be to some extend characterized with the standard Reynolds number.
+- Few simulations are not DNS, but they can be to some extend characterized with the
+standard Reynolds number.
 
 - Without hyperviscosity the simulations would not blow up.
 
 - Dataset which can be later improved...
 
 
-\itemit{
-Shear modes are removed from all simulations, but how is this achieved
-exactly? Is it done via a spectrally localised damping term or simply put to
-zero at every time steps?
-}
+\itemit{Shear modes are removed from all simulations, but how is this achieved exactly?
+Is it done via a spectrally localised damping term or simply put to zero at every time
+steps?}
 
 TODO: add in the article + add added text here.
 
-Put to zeros at each time step. Conserves energy. Similar physically to vertical walls in a tank.
+Put to zeros at each time step. Conserves energy. Similar physically to vertical walls
+in a tank.
 
 
-\itemit{
-It is mentionned that the forcing is not delta-correlated in time but that
-its correlation time is consistent with the dispersion relation of internal
-gravity waves at that particular angle $\theta_k$. Can the authors give more
-details about the forcing scheme? In particular, if there is still a stochastic
-process involved, I guess it means that not all of the energy is injected in the
-form of waves. Do the authors think that using a purely harmonic forcing,
-thereby injecting all of the energy in the form of internal gravity waves, would
-change something to the results presented here?
-}
+\itemit{It is mentionned that the forcing is not delta-correlated in time but that its
+correlation time is consistent with the dispersion relation of internal gravity waves
+at that particular angle $\theta_k$. Can the authors give more details about the
+forcing scheme? In particular, if there is still a stochastic process involved, I guess
+it means that not all of the energy is injected in the form of waves. Do the authors
+think that using a purely harmonic forcing, thereby injecting all of the energy in the
+form of internal gravity waves, would change something to the results presented here?}
 
 TODO: describe better the forcing in the article + add added text here.
 
-- no proper stochastic process involve. Phase and amplitude of the forced wavenumbers random and changed in time ...
+- no proper stochastic process involve. Phase and amplitude of the forced wavenumbers
+random and changed in time ...
 
 - a bit of Python to compute time spectra of such process.
 
-- this aspect of the forcing will be discussed in a paper describing more globally the dataset.
+- this aspect of the forcing will be discussed in a paper describing more globally the
+dataset.
 
 TODO: add the question on possible effect of harmonic forcing. We don't know.
 Interesting open question that could be investigated in future studies.
 
 
-\itemit{
-Figure 7: could you show the spatial structure of the dominant vortical mode
-by filtering the coefficients in Fourier space and transform it back to physical
-space? More generally, some visualisations of the typical flows considered, with
-and without vortical modes, would be helpful in my opinion.
-}
+\itemit{Figure 7: could you show the spatial structure of the dominant vortical mode by
+filtering the coefficients in Fourier space and transform it back to physical space?
+More generally, some visualisations of the typical flows considered, with and without
+vortical modes, would be helpful in my opinion.}
 
 Add a 3D figure...
 
 
-\itemit{
-Figure 9: what is the purpose of the kz=kh line?
-}
+\itemit{Figure 9: what is the purpose of the kz=kh line?}
 
 ?
 
 
-\itemit{
-Figure 16: this is an important plot in my opinion, it might be useful to
-include other studies? In particular, it is rather suprising that [46] is so far
-from the dynamical regime considered in this paper (knowing that both studies
-were looking for traces of WWT in simulations). Are they no other studies
-filling the gap between these two extremes?
-}
+\itemit{Figure 16: this is an important plot in my opinion, it might be useful to
+include other studies? In particular, it is rather suprising that [46] is so far from
+the dynamical regime considered in this paper (knowing that both studies were looking
+for traces of WWT in simulations). Are they no other studies filling the gap between
+these two extremes?}
 
 TODO: which studies with wave forcing? Waite... Lindborg... ???
 
-For studies motivated by geophysical flows, the focus is more on buoyancy Reynolds number large or at least not very small.
+For studies motivated by geophysical flows, the focus is more on buoyancy Reynolds
+number large or at least not very small.
 
-Unfortunately, not always easy to correctly quantify these numbers from the data given in the articles.
+Unfortunately, not always easy to correctly quantify these numbers from the data given
+in the articles.
 
 
-\itemit{
-The shear modes are always suppressed while the vortical modes are either
-left or suppressed. Do the authors expect surprising behaviours with the shear
-modes but without the vortical modes?
-}
+\itemit{The shear modes are always suppressed while the vortical modes are either left
+or suppressed. Do the authors expect surprising behaviours with the shear modes but
+without the vortical modes?}
 
-We know thanks to a study on 2D turbulence (Calpe-linares PhD thesis)
-that shear modes can grow without toroidal modes. Therefore we can anticipate accumulation of energy in shear modes,
-which should become very strong and distore the waves.
+We know thanks to a study on 2D turbulence (Calpe-linares PhD thesis) that shear modes
+can grow without toroidal modes. Therefore we can anticipate accumulation of energy in
+shear modes, which should become very strong and distore the waves.
 
 
-\itemit{
-Note that Le Reun et al. [46] did not have to remove neither shear nor
-vortical modes (while the same authors had to remove the geostrophic flow in
-rotating systems to observe regimes reminiscent of inertial wave turbulence),
-which seems like an important information to recall in the present study
-interested in the role of such slow flows on the dynamics. Similarly to the
-rotating case and the spontaneous emergence of geostrophic flows, there must be
-some threshold below which both shear and vortical modes are stable and won't
-grow if not directly forced?
-}
+\itemit{Note that Le Reun et al. [46] did not have to remove neither shear nor vortical
+modes (while the same authors had to remove the geostrophic flow in rotating systems to
+observe regimes reminiscent of inertial wave turbulence), which seems like an important
+information to recall in the present study interested in the role of such slow flows on
+the dynamics. Similarly to the rotating case and the spontaneous emergence of
+geostrophic flows, there must be some threshold below which both shear and vortical
+modes are stable and won't grow if not directly forced?}
 
 TODO: improve the discussion on the difference between Le Reun et al.
 
@@ -173,8 +159,8 @@
 
 \itemit{Introduction, line 2: typo "aims to provides"}
 \itemit{p.2 second paragraph: typo "difficultly"}
-\itemit{p.4, section II, first sentence: typo "hypervisity", define buoyancy, what
-does "kinematic pressure" mean?}
+\itemit{p.4, section II, first sentence: typo "hypervisity", define buoyancy, what does
+"kinematic pressure" mean?}
 \itemit{Ambiguous notation between real part and Reynolds}
 
 \end{itemize}
diff --git a/2022strat_polo_proj/review0/rebut2.tex b/2022strat_polo_proj/review0/rebut2.tex
--- a/2022strat_polo_proj/review0/rebut2.tex
+++ b/2022strat_polo_proj/review0/rebut2.tex
@@ -37,48 +37,41 @@
 \begin{document}
 \maketitle
 
-\noindent
-The authors thank the referee for his/her useful and constructive comments that helped
-us to improve the paper. Below we have responded to all questions. Corresponding
-corrections are made in blue in the new draft.
+\noindent The authors thank the referee for his/her useful and constructive comments
+that helped us to improve the paper. Below we have responded to all questions.
+Corresponding corrections are made in blue in the new draft.
 
 \subsection*{Major comments}
 
 \begin{enumerate}
 
-\itemit{
-The methods section is vague about the choice of vertical domain size and
-vertical resolution.  It should be stated clearly here how $L_z$ is varied with $N$
-and why, and how $n_z$ is chosen.
-}
+\itemit{The methods section is vague about the choice of vertical domain size and
+vertical resolution.  It should be stated clearly here how $L_z$ is varied with $N$ and
+why, and how $n_z$ is chosen.}
 
 TODO: better describe in the method section.
 
 
-\itemit{
-The poloidal forcing is meant to excite only waves but you do not discuss
-its impact on the potential vorticity (PV), which governs the vortical mode.  In
-fact I was surprised that you do not discuss PV in your paper more generally,
-given how important a concept it is in geophysical fluid mechanics.
-}
+\itemit{The poloidal forcing is meant to excite only waves but you do not discuss its
+impact on the potential vorticity (PV), which governs the vortical mode.  In fact I was
+surprised that you do not discuss PV in your paper more generally, given how important
+a concept it is in geophysical fluid mechanics.}
 
-PV is known to be much less dynamically important in stratified flows than in stratified and rotating flows.
-The Ertel PV $\bomega \cdot \bnabla (N^2 z + b) = \omega_z (N^2 + \partial_z b) + \bomega_h \cdot \bnabla_h b$
-is not quadratic and is not equal to the Charney PV.
-There is no PV cascade like in quasi-geostrophic flows.
+PV is known to be much less dynamically important in stratified flows than in
+stratified and rotating flows. The Ertel PV $\bomega \cdot \bnabla (N^2 z + b) =
+\omega_z (N^2 + \partial_z b) + \bomega_h \cdot \bnabla_h b$ is not quadratic and is
+not equal to the Charney PV. There is no PV cascade like in quasi-geostrophic flows.
 
-The forcing in poloidal velocity produces and removes PV but we do not know what can be deduced from that.
+The forcing in poloidal velocity produces and removes PV but we do not know what can be
+deduced from that.
 
 
-\itemit{
-I felt overwhelmed by the great number of non-dimensional parameters
-introduced here; even with all these definitions one could still invent more, ie
-parameters based on the hyperviscosities.  Basic physical insight is lost for me
-here, in particular as I would like to see parameters based on controllable
-parameters such as the energy input.    It’s a personal choice/failing but I
-lost interest in the detailed numerical diagnostics once this parameter zoo
-unfolded.
-}
+\itemit{I felt overwhelmed by the great number of non-dimensional parameters introduced
+here; even with all these definitions one could still invent more, ie parameters based
+on the hyperviscosities.  Basic physical insight is lost for me here, in particular as
+I would like to see parameters based on controllable parameters such as the energy
+input.    It’s a personal choice/failing but I lost interest in the detailed numerical
+diagnostics once this parameter zoo unfolded.}
 
 - Improve  eq (17)
 
@@ -87,19 +80,15 @@
 - No non-dimensional numbers based on hyper-viscosity ...
 
 
-\itemit{
-You talk of “removing vortical modes”.  How is that done numerically?  Is it
-a similar process as in Holmes-Cerfon et al. in JFM 2013?
-}
+\itemit{You talk of “removing vortical modes”.  How is that done numerically?  Is it a
+similar process as in Holmes-Cerfon et al. in JFM 2013?}
 
 TODO: improve the method section.
 
 
-\itemit{
-In the discussion session you say that the energy conversion rate does not
-fluctuate around zero.  As only the kinetic energy is forced, shouldn’t the
-KE->PE conversion rate be nonzero a priori?
-}
+\itemit{In the discussion session you say that the energy conversion rate does not
+fluctuate around zero.  As only the kinetic energy is forced, shouldn’t the KE->PE
+conversion rate be nonzero a priori?}
 
 For Vincent...
 
@@ -110,43 +99,30 @@
 
 \begin{enumerate}
 
-\itemit{
-(1) why introduce a symbol $k_b$ here, which is non-standard anyway?  This
+\itemit{(1) why introduce a symbol $k_b$ here, which is non-standard anyway?  This
 conditions is $k U_h/N << 1$, which is a standard criterion for horizontal phase
-speeds, not scale separation as stated here.
-}
-
+speeds, not scale separation as stated here.}
 
-\itemit{
-(3) maybe it could be stated how these are derived from each other?  Also,
-the folklore in oceanography is that the internal wave energy flows downscale in
-wavenumber but upscale in frequency.   Do the quoted WWT theories agree with
-that?
-}
+\itemit{(3) maybe it could be stated how these are derived from each other?  Also, the
+folklore in oceanography is that the internal wave energy flows downscale in wavenumber
+but upscale in frequency.   Do the quoted WWT theories agree with that?}
 
-- oceans: forced waves (inertial waves, M2 and spontaneous generation from vortices) $\omega/N$ small.
+- oceans: forced waves (inertial waves, M2 and spontaneous generation from vortices)
+$\omega/N$ small.
 
 - our results also transfers towards slow waves
 
 - open question in ocean and in WWT theories
 
-\itemit{
-typo p4 hyper viscosity
-}
+\itemit{typo p4 hyper viscosity}
 
-\itemit{
-(20) is an interesting definition.  But I don’t understand (20b)
-}
+\itemit{(20) is an interesting definition.  But I don’t understand (20b)}
 
-\itemit{
-Figure 4: I find it surprising that there is no “hump” in the spectrum at the
-injection frequencies, as is typical for turbulent spectra.  Why is that?
-}
+\itemit{Figure 4: I find it surprising that there is no “hump” in the spectrum at the
+injection frequencies, as is typical for turbulent spectra.  Why is that?}
 
-\itemit{
-The forcing renewal time $T_c$ is chosen as a wave period; why is that? Why
-not force with white noise in time?
-}
+\itemit{The forcing renewal time $T_c$ is chosen as a wave period; why is that? Why not
+force with white noise in time?}
 
 \end{enumerate}