Diabatic and Frictional Controls of an Axisymmetric Vortex Using Available Potential Energy Theory with a Non-Resting State

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

suggest publication

Author Response

We thank the referee for their support of our manuscript. 

Reviewer 2 Report

Comments and Suggestions for Authors

Revise el documento adjunto.

Comments for author File: Comments.pdf

Author Response

please see the attachment

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This is a review of the manuscript entitled “Diabatic and Frictional Controls of an Axisymmetric Vortex Using Available Potential Energy Theory with a Non-Resting State” by Harris and Tailleux.

In this manuscript, the authors revisit the energetics of axisymmetric vortex motions by redefining the Available Potential Energy (APE) relative to a non-resting reference state in gradient wind balance, rather than a traditional resting state.

The paper suffers from serious issues of clarity. The main line of reasoning is often difficult to follow, and many of the notations are either insufficiently defined or unjustified. As a result, the manuscript is largely inaccessible to readers who are not already highly specialized in this topic. Significant revision is required to improve readability and to better communicate the authors’ findings to a broader atmospheric science audience.

In particular, I strongly recommend including a comprehensive list of symbols and notations. The manuscript is overloaded with symbols, many of which are similar or overlapping in meaning. For instance, pressure alone is represented by an overwhelming variety of symbols: p, p₀, p_*, p’, p’’, p_c, p_∞, p_m, ^p_m . This creates unnecessary cognitive load and makes the manuscript very difficult to read.

In its current state, the manuscript is nearly impenetrable. I urge the authors to substantially revise the paper with an emphasis on clarity, structure, and accessibility.

Please find below additional feedback and comments:

Eqs. 5–6: Φ is used both for the cylindrical coordinate and for geopotential. Could the authors consider using a different symbol to avoid confusing the reader?

Eq. 18: What are Dₛ and h? Have they been defined anywhere?  

Line 126–127: “However, the existing literature appears to lack a clear explanation…” — please add a reference.

Line 127–128: “lack a clear explanation for how the required radially inward motion is actually driven” — are you certain about this? Isn’t the radially inward motion typically attributed to surface friction?

Line 148: Could you briefly remind the reader what gradient wind balance means?  

Line 149: What does the subscript “m” stand for in these notations?

Line 156: “vortex solution used by Smith et al.” — solution to what exactly? Are you referring to Eqs. 22–23?

Line 162: Why introduce an extended phase space here? What exactly is meant by “extended phase space,” and what is the motivation or necessity for using an extended phase space?

Eq. 22: Could you explain where this equation comes from, or at least provide an interpretation of the different terms involved?

Eq. 27: Why does the gradient of p appear here? Isn’t p a function of Φ through hydrostatic balance? Aren’t χ and Φ the new coordinate variables?

Line 170–178: This passage is extremely unclear and confusing.

Line 181–182: “of V” is repeated twice.

Line 182: “a re-arrangement of mass-conserving µ and η” — What does that mean?

Eq. 33: Where does this equation come from?

Eq. 35: dVr/DPhi = -1. Are you sure of this? Shouldn’t it be 0?

Eqs. 35-36: It is unclear how 35 implies 36.

Line 198: “etc..,”. It is unclear what are the use and meaning of “etc” in this sentence.

Line 211: Could the authors explain what they mean by “positive definite” in this context? Could the authors define positive definiteness?

Line 212–213: Please provide a reference.

Line 216: What are “generalized” buoyancy forces? Could you please define them?

Eq. 57: “It may be verified”. Could you at least explain how you obtain this result?

Line 513: Why p_∞(0)? What is this 0? Is it z = 0? If so, why isn’t p_c a function of height as well?

Line 514: What is the physical interpretation of these constants: x, r_m, z₀, z* ?

Appendix A: Could you provide more context for this formula? Where does it come from, and why is it considered a reasonable model?

Author Response

see attached document

This is a review of the manuscript entitled “Diabatic and Frictional Controls of an Axisymmetric Vortex Using Available Potential Energy Theory with a Non-Resting State” by Harris and Tailleux.

In this manuscript, the authors revisit the energetics of axisymmetric vortex motions by redefining the Available Potential Energy (APE) relative to a non-resting reference state in gradient wind balance, rather than a traditional resting state.

The paper suffers from serious issues of clarity. The main line of reasoning is often difficult to follow, and many of the notations are either insufficiently defined or unjustified. As a result, the manuscript is largely inaccessible to readers who are not already highly specialized in this topic. Significant revision is required to improve readability and to better communicate the authors’ findings to a broader atmospheric science audience.

In particular, I strongly recommend including a comprehensive list of symbols and notations. The manuscript is overloaded with symbols, many of which are similar or overlapping in meaning. For instance, pressure alone is represented by an overwhelming variety of symbols: p, p₀, p_*, p’, p’’, p_c, p_∞, p_m, ^p_m . This creates unnecessary cognitive load and makes the manuscript very difficult to read.

In its current state, the manuscript is nearly impenetrable. I urge the authors to substantially revise the paper with an emphasis on clarity, structure, and accessibility.

We thank the reviewer for their constructive comments. Although our paper is probably too specialised to be readable by the broadest possible audience, we agree that the parts highlighted by the reviewer were needlessly obscure. To address this, we therefore did our best to rewrite the offending parts to make them more pedagogical and hence more accessible to readers with some general theoretical background. We hope that this makes our paper more satisfactory. We did not include a separate list for symbols, as this seems unnecessary to us, since all terms are defined on first introduction.

Please find below additional feedback and comments:

Eqs. 5–6: Φ is used both for the cylindrical coordinate and for geopotential. Could the authors consider using a different symbol to avoid confusing the reader?

The symbols used for the azimuthal angle  and geopotential  are similar but nevertheless distinct. Using a different symbol therefore seems unwarranted to us, especially given the minor role played by the azimuthal angle due to our paper’s focus on axisymmetric motions.

Eq. 18: What are Dₛ and h? Have they been defined anywhere?  

Thanks for flagging these. These symbols are now defined.

Line 126–127: “However, the existing literature appears to lack a clear explanation…” — please add a reference.

This paragraph has been substantially revised and reference added.

Line 127–128: “lack a clear explanation for how the required radially inward motion is actually driven” — are you certain about this? Isn’t the radially inward motion typically attributed to surface friction?

This paragraph has been substantially revised to make it clearer and more specific.

Line 148: Could you briefly remind the reader what gradient wind balance means?  

Gradient wind balance is now defined more explicitly in the text.

Line 149: What does the subscript “m” stand for in these notations?

The subscript ‘m’ denotes the fields in the reference state in gradient wind and hydrostatic balances. This is now explicitly clarified in the revision.

Line 156: “vortex solution used by Smith et al.” — solution to what exactly? Are you referring to Eqs. 22–23?

This is now clarified in the text.

Line 162: Why introduce an extended phase space here? What exactly is meant by “extended phase space,” and what is the motivation or necessity for using an extended phase space?

The generalised local APE relies on the concept of static vortex energy, whose properties can only be understood if it is regarded as a function of 5 variables. The extended phase space is simply the space described by these 5 variables.  

Eq. 22: Could you explain where this equation comes from, or at least provide an interpretation of the different terms involved?

Equation 22 is the expression of gradient-wind balance written in the new coordinate system. We agree that our way of presenting it might have been too abrupt. We revised the manuscript to break down the steps by which Eq. (22) is arrived at.  

Eq. 27: Why does the gradient of p appear here? Isn’t p a function of Φ through hydrostatic balance? Aren’t χ and Φ the new coordinate variables?

This part of the material relates to the full time-dependent behaviour of the system, so that the confusion appears to stem from being placed just after the discussion of gradient wind and hydrostatic balance. To avoid confusion, we moved this material right after the model description, which is probably more natural and logical.

Line 170–178: This passage is extremely unclear and confusing.

Additional explanations and clarifications have been added about this part in the new section 2.2. of the revised version of our manuscript. We hope that this is now much clearer.

Line 181–182: “of V” is repeated twice.

Thanks! Corrected.

Line 182: “a re-arrangement of mass-conserving µ and η” — What does that mean?

We added explanations in the revised version of the manuscript.

Eq. 33: Where does this equation come from?

This equation is the total differential of the preceding equation obtained by holding entropy and angular momentum constant. We added an explanation in the text.

Eq. 35: dVr/DPhi = -1. Are you sure of this? Shouldn’t it be 0?

Eq. (35) is hydrostatic balance so is correct as it is. It should not be equal to zero.

Eqs. 35-36: It is unclear how 35 implies 36.

We have completely rewritten the text here. We agree that our derivations were confusing and tried to make it more logical.

Line 198: “etc..,”. It is unclear what are the use and meaning of “etc” in this sentence.

The etc… have been removed and we have tried to be clearer and more specific.

Line 211: Could the authors explain what they mean by “positive definite” in this context? Could the authors define positive definiteness?

Term defined in revision.

Line 212–213: Please provide a reference.

References added.

Line 216: What are “generalized” buoyancy forces? Could you please define them?

We find this comment a bit puzzling, since defining and discussing such forces is what is addressed in the section following Line 216. We have added one sentence to make that clear.

Eq. 57: “It may be verified”. Could you at least explain how you obtain this result?

Explanations added in revision.

Line 513: Why p_∞(0)? What is this 0? Is it z = 0? If so, why isn’t p_c a function of height as well?

The 0 does indeed refer to z = 0. We originally were reproducing the notation of the original vortex equation by Smith et al. (2005), however we have now altered the equation to read p_c(0) to avoid confusion.

Line 514: What is the physical interpretation of these constants: x, r_m, z₀, z* ?

r_m is the radius of maximum winds. x determines the radial length scale over which the pressure field declines. Similarly z* determines the vertical length scale over which it declines and z₀ the altitude at which it reaches zero. We have rewritten Appendix A to clarify the meaning of each of these constants.

Appendix A: Could you provide more context for this formula? Where does it come from, and why is it considered a reasonable model?

The formula of Smith et al. (2005) is designed to create an analytical pressure field that represents the major features of a hurricane pressure field, i.e. decreasing outwards and with a maximum radial pressure gradient just outside the core. This yields a balanced azimuthal wind field typical to that found in a tropical cyclone, discussed further in Smith et al. (2005). We have added this explanation to the appendix.

 

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The proposed study is based on a review of Carnot's theory applied to tropical cyclones, attempting to investigate, by means of an idealised cyclonic vortex model, the thermodynamic cycle of the cyclone.

The work presents a solid physical thermodynamic treatment with very solid results. The work is at an advanced stage of maturity. I suggest that the authors make a small addition to the materials and methods section. It may be my fault, but I did not fully understand how the experiments were produced. For the purposes of reproducibility of the experiment, it might be important to know the means used for these experiments, or more practical indications of the numerical workflow.

Author Response

We thank the referee for their positive comments. It seems to us that we have provided extensive details about the numerical strategy used, which is similar to that used in the paper by Harris et al. (2023), see also Appendix. We therefore did not add more details, as we could not see what to add.

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have satisfactorily addressed my previous comments. The manuscript is now clearer and more accessible. I believe it meets the standards for publication in Atmosphere.