Coherence of Eddy Kinetic Energy Variation during Eddy Life Span to Low-Frequency Ageostrophic Energy

Round 1

Reviewer 1 Report

Coherence of Eddy Kinetic Energy Variation during Eddy Life Span to Low-frequency Ageostrophic Energy

    The authors presented a manuscript  containing the results of studies of the energy structure of oceanic movements. In particular, the authors consider a rather interesting question about the coherence between low-frequency ageostrophic movements and mesoscale vortices in the oceans. Questions related to the understanding of energy interactions between movements of various space-time scales, including the mesoscale range and turbulence are still relevant not only in atmospheric physics, but also for the ocean physics. In this direction, the authors develop an interesting topic.

However, I can point out a few flaws in this manuscript.

In the second sentence of introduction, the authors use the term «energy cascade». I can recommend that the authors, before using the term «energy cascade», designate the range of spatial scales that is of interest, and in general explain what an energy cascade is and what causes it is caused by. What is the role of ageostrophic movements in the energy cascade. In general, it is also necessary to provide references to the works of other authors who have received and analyzed the energy spectra of movements in the scale range you have chosen.

Figure 1. The authors obtain global energy distributions of geostrophic and ageostrophic components of movements. I would like to clarify that the maximum values of both the energy of geostrophic and the energy of the ageostrophic components of movements on the maps are 500 cm^2/s^2? In this case, the values of 500 cm^2/s^2 and minus  500 cm^2/s^2 in Figure 1 (c) correspond to zones of fully geostrophic and ageostrophic movements, respectively ? What factors are associated with the formation of these zones?

Line 126 Figure 1 represents the energy values in cm^2/s^2, in the text you are talking about m^2/s^2. Please correct units.

Figure 5. Please indicate the ordinate axis.

Table2. You use a different number of characters after the dot (for example, 0.123 and 0.07). I suggest leaving two characters after the dot.

Figures 3 and 4. You have given the dimensionless energy characteristics along the ordinate axis. Due to these factors, the curves in Figure 3 (b) coincided, and Figure 4 shows differences in amplitudes. Is the normalization done correctly?

Discussion and Conclusions. Authors found close coherence between the EKE variations and low-frequency ageostrophic motions. The authors should note in the conclusions under which conditions coherence can be enhanced or weakened, and in general, temporal or spatial coherence is in question.

The manuscript makes a twofold impression. On the one hand, the research topic is quite interesting: it is necessary to improve our understanding of the energetic interaction of movements of different spatial and temporal scales in various environments, including the ocean. On the other hand, usually the ageostrophic components of movements should be significantly smaller in comparison with the general flow (at least in the Earth's atmosphere). Nevertheless, the results are quite interesting, although in a certain sense, I would like to see a more detailed analysis of the energy interaction of movements of different spatial and temporal scales, including in comparison with data from other authors. Moreover, I suggest that the authors emphasize the novelty and significance of your research for the atmosphere in the conclusions.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

this paper provides clues concerning the role of ageostrophic motion in the spin up  or spin down of geostrophic eddies ; it is of interest to readers and the methodology is globally sound but a point of theory should be checked

I advocate a moderate revision

Two main points should be addressed

- the first one (main one) concerns equation (5 ) - though it is true that this is a component of the barotropic energy transfer (between geostrophic and ageostrophic motions), it is not the whole transfer ; the symmetrical term should be added

- rho0 [\vec{u}_alp + \vec{u}_0] \cdot \vec{\nabla} [\vec{U}_g x \vec{u}_g]

where x is the tensor product / or external product / of the two vectors.

This may explain why the red curve does not fit the blue curve in figure 5. Obviously, other processes such as HF ageostrophic motions, eddy killing effect by wind, possibly tidal currents... can contribute to this discrepancy, as you mention.

- the second important, though less important, point is that a vortex does not undergo only one spin up and one spin down phase in its lifetime ; usually it interacts with other vortices and may merge ith them, or split; therefore the energy will increase and decrease several times during the eddy life. To me, figures 3 and 4 are averages over a large number of eddies which smooth out these multiple variations. If you study an individual eddy, it may not at all follow this simple evolution.

about this point you can quote several papers

Keppler, Lydi & Cravatte, Sophie & Chaigneau, Alexis & Pegliasco, Cori & Gourdeau, Lionel & Singh, Awnesh. (2018). Observed Characteristics and Vertical Structure of Mesoscale Eddies in the Southwest Tropical Pacific. Journal of Geophysical Research: Oceans. 123. 10.1002/2017JC013712. 

Laxenaire, R., Speich, S., Blanke, B., Chaigneau, A., Pegliasco, C., & Stegner, A. (2018). Anticyclonic eddies connecting the western boundaries of Indian and Atlantic Oceans. Journal of Geophysical Research: Oceans, 123, 7651–7677. https://doi.org/10.1029/2018JC014270

Adam Ayouche, Charly de Marez, Mathieu Morvan, Pierre L’hegaret, Xavier Carton, et al.. Structure and Dynamics of the Ras al Hadd Oceanic Dipole in the Arabian Sea. Oceans, MDPI, 2021, 2 (1), pp.105 - 125. ⟨10.3390/oceans2010007⟩. ⟨hal-03484679⟩

MINOR POINT

end of subsection 2.3

you note that the LF ageostrophic energy is 4 times higher than the HF AG energy; but this is also related to the fact (that you mention in the conclusion) that the data have a daily frequency, so that much of the HF AG energy is lost

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Authors corrected the manuscript and reply to my questions. Results Obtained by authors are significant. There are some blots in the manuscript. But I think that, in whole, the manuscript May be recommended for publication.