# 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 modesâ€. 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 modesâ€. 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}