Role of Eddies in the Maintenance of Multiple Jets Embedded in Eastward and Westward Baroclinic Shears
Reviewer 1 Report
The manuscript describes classical two-layer numerical simulations of quasigeostrophic beta-plane turbulence forced by uniform eastward (ES) or westeward (WS) baroclinic flows. The study is focused on layer-wise comparison of averaged meridional profiles in order to elucidate the role of eddy fluxes in ES and WS flows. The bottom friction in both cases is an order smaller than can be expected in the ocean , so that zonally averaged alternating jets are predominantly barotropic while the contribution of weak baroclinic component has opposite signs in ES and WS cases. Despite the authors have identified the reversal in the relative roles of the baroclinic Reynolds and form stresses, they conclude in the abstract: ìdynamics are essentially the same in both cases: the relative vorticity fluxes force the jets in the entire fluid column and the eddy buoyancy fluxes transfer momentum from the top to the bottom layer, where it is balanced by bottom friction.î
While the conclusions are important, the manuscript is based mostly on visual comparison of figures with meridional profiles of averaged dimensional flow characteristics which complicates making convincing conclusions. It is not crystal clear why the considered two particular cases look similar in the layer-wise analysis in spite of previous studies (based mostly on the decomposition into barotropic and baroclinic modes) indicated that ìproperties of the jets and ambient eddies, as well as their dynamic interactions, are profoundly different between the east and westward shears.î Therefore, the manuscript is suggested to be essentially revised.
1.Why these particular cases are interesting to study and what part of parameter space in previous studies, e.g., [27, 32], they correspond to? (A table with nondimensional parameters would be useful for comparison).
2.The same snapshots for WS case should be included in contraposition to Fig. 1 like in . The layer-wise kinetic energy evolution would help in panel g to elucidate more energetic bottom layer in WS case (better to be a separate figure).
3.As can be seen from Fig. 2, the maximum of east jet velocity in the top layer is about 3 times larger than absolute value of U_b. Perhaps, some plots at the same figure of properly normalized profiles for WS and ES cases (meridionally shifted to have the same position of maximum jet velocity) might help for more meaningful comparison?
4.In double-periodic simulations the meridional domain size has to be chosen differently to reproduce accurately two major periods in ES and WS cases in order to avoid artificial sub-harmonic features in ES case where the jet scale in slightly less as seen in ,
5.In section 3.1, when analyzing the convergence of fluxes in Eq. (3), itíd be more useful to look first at Fig. 6 to see that Rs and Fs almost balance each other in the top layer as expected with minor role of viscosity. In the bottom layer Rs and Fs have nearly the same sign which clarifies immediately the dominant role of bottom friction. This figure provides the major support to the authors point about similarity of ES and WS cases. (In Fig. 6 profiles of Reynolds and form stress do not look meridionally periodic as other quantities. Also 6a, c would be more easy to read with the same scales like at other figures).
6.At the next step ìlook at the eddy fluxes of relative vorticity and buoyancy in the meridional direction (Figure 3). In both ES and WS cases, eddy fluxes have a major contribution from the buoyancy fluxes, which are uniformly positive/negative in top and bottom layers. On the other hand, eddy vorticity fluxes change sign along the profile and show a strong positive correlation with the mean zonal velocities in the layers. This shows that eddy vorticity fluxes force the jets [for details, refer equation (15.21) in 37] and are up-gradient in the eastward jet cores. This process of up-gradient vorticity fluxes, which is responsible for persistent jets, is generally described as negative viscosity effect [10,38]î.
This common conclusion has to be clarified how it can follow from Eq. (3) (preferably without referring to a textbook) as an arbitrary constant (with no effect on the flux divergence) can be added to fluxes in Eq. (3) and Fig. 3 indicating the sign of fluxes does not matter in eq. (3).
7.Going further to the energy analysis, itíd logical to describe layer-wise energy balance instead of Eq. (4) and to plot the energy exchange between layers to clarify the role of eddy buoyancy fluxes before introducing the heat diffusivity in Fig. 5. (Fig. 4a and b has different scales masking 4 times stronger Rey stress in ES case).
8.Comparison of baroclinic stream function with the bottom stress in Fig. 7 follows from previous results as the later is proportional to the vorticity plotted in Fig. 4 and it just emphasizes reversal of baroclinic contribution which has been already shown in Fig. 2.
The lines 199-207 need more quantitate arguments to make sense.
9.Section 4 is based on some vague and poorly defined arguments (as the authors have emphasized in lines 279-281) in contrast with clearly defunded approach in . It has to be completely rewritten if the authors intend to keep it.
Author Response File: Author Response.pdf
Reviewer 2 Report
Manuscript ID: fluids-375928
Type of manuscript: Article
Title: Role of eddies in the maintenance of multiple jets embedded in eastward and westward baroclinic shears
Authors: Hemant Khatri *, Pavel Berloff
The manuscript addresses a comprehensive discussion on the role of eddies in dynamics of oceanic jets by solving a two-layer QG model. As reviewed by the authors, this baroclinic model have been studied previously in literature, and the present work contributes our understanding how barotropic and baroclinic modes interact each other from a comparative point of view between the eastward and westward zonal shear flows. They found that there is no difference in eddy dynamics in these two cases. They also derived expressions for meridional group velocity of Rossby waves in both lower and upper layers. I believe this study triggers a nice discussion on the dynamics of Reynolds stresses in each layer and I therefore recommend the publication of this work subject to the clarification on the following minor issues. I believe that it is also applicable and interesting for researchers dealing with applications of idealized geophysical flows.
1- In QG modelling, the authors preferred to use a standard bi-harmonic dissipation mechanism. There are extensive discussions on literature as well including a hyperviscosity model in QG2 setups (8th or 16th order dissipation mechanism). They are mostly focused on spectral/preudospectral methods numerics. Maybe authors would consider extending their literature review on QG2 models and mentioned some highly cited papers on these models. A table summarizing the prospectus (historically who used QG2 for what purposes) would be even nicer.
2- What was the rationale for selecting the zonal background flows with 6 cm/s and -4 cm/s for eastward and westward problems, respectively? Why not 6 and -6 or 4 and -4?
3- In Figure 2, meridional profiles are presented (averaged in time). A mathematical description of how they decompose barotropic and baroclinic components would be useful. I think it has been shown on page 11, but it could be nice to provide them before the presentation.
4- Mathematical definitions of u, v and zeta are missing in Equation (3), they can be related to stream function.
5- What is a typical mathematical definition of zonally averaged time-mean quantities, the bar variables in the paper? An integral representation (with time and zonal direction) would be useful. To perform the statistics, how many snapshots are stored/used (all time steps on the fly or subsampled as a post-processing after runs completed)?
6- Initial and boundary conditions have not been presented. For completeness, it would be nicer to document in this paper as well.
Author Response File: Author Response.pdf
Reviewer 1 Report
recommend for publication
Reviewer 2 Report
Thank you for clarifying my comments in your response to my review and revised manuscript. I am mostly satisfied with the clarifications. Therefore, I strongly support publication of this manuscript.