the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 Feb 2024
Stable and unstable fall motions of plate-like ice crystal analogues
Abstract. The orientation of ice crystals affects their microphysical behaviour, growth, and precipitation. Orientation also affects interaction with electromagnetic radiation, and through this, influences remote sensing signals, in-situ observations, and optical effects. Fall behaviours of a variety of 3D-printed plate-like ice crystal analogues in a tank of water-glycerine mixture are observed with multi-view cameras and digitally reconstructed to simulate falling of ice crystals in the atmosphere.
Four main falling regimes were observed: stable, zigzag, transitional, and spiralling. Stable motion is characterised by no resolvable fluctuations in velocity or orientation, with the maximum dimension oriented horizontally. The zigzagging regime is characterised by a back-and-forth swing, corresponding to a time series of inclination angle approximated by a rectified sine wave. In the spiralling regime, analogues consistently incline at an angle between 7 and 28 degrees, depending on particle shape. Transitional behaviour exhibits motion in between spiral and zigzag, similar to that of a falling spherical pendulum.
The inclination angles that unstable planar ice crystals make with the horizontal plane are found to have a non-zero mode. This observed behaviour does not fit the Gaussian model of inclination angle that is common in the literature. The typical Reynolds number when oscillations start is strongly dependent on shape: solid hexagonal plates begin to oscillate at Re = 237, whereas several dendritic shapes remain stable throughout all experiments, even at Re > 1000.
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AC1: 'Comment on egusphere-2024-319', Jen Stout, 18 Mar 2024
Figure 5 in the preprint is incorrect, and should show a timeseries of inclination angles for each case study (as detailed in the caption). I have attached the corrected version of the figure - apologies for any confusion caused.
Thanks,
Jen Stout
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RC1: 'Comment on egusphere-2024-319', Anonymous Referee #1, 21 Mar 2024
The study by Stout et al. investigates the kinematic behaviour of plate-like ice crystal analogues, as they sediment in a controlled laboratory environment. The study relies on experiments conducted as part of previous published work, and expands upon it by characterizing varying trajectory regimes, and the associated orientation, velocity fluctuations, and projected area fluctuations of the analogues. Among other findings, they show that in certain regimes the commonly adopted assumption of ice crystal orientation being distributed normally around 0° may not be accurate. This finding is highly valuable for a number of sub-disciplines within the cloud physics community, as assumptions on ice crystal orientation are needed for radiative transfer simulations, as well as the interpretation of lidar and radar observables.
I find the manuscript to be of high scientific quality: the motivation behind the study is clearly illustrated, the analysis section is preceded by a comprehensive literature review on the topic, the analysis methods are sound, the figures are clear and polished, and the text is overall very clear and well-written. I did not find any major flaws in the manuscript, and I recommend it for publication in ACP after a round of relatively minor revisions. The revisions I request are mainly to include minor missing details, clarify some ambiguities, and improve the clarity of certain portions of the text.General points
- When fitting sine waves to the particles’ elevation time series, the goodness of the fit should be discussed. I believe a comprehensive discussion is not necessary, as the assumption is supported by previous studies already cited by the authors. However, I would like the goodness of fit to be quantified and discussed at least for the four case studies. As an example, the author could calculate a RMS deviation between the observed and fitted thetas, possibly normalized by the wave amplitude.
- In my opinion the abstract is not very effective at “marketing” the article. The findings of the study are highly relevant for a number of applications, as discussed by the authors in section 4.2, and this could be briefly highlighted in the abstract itself. For example, when mentioning that “the Gaussian model of inclination angle is common in the literature”, another sentence could be added clarifying in what circumstances this assumption is used and in what instances the findings of this study should be taken into account.
- Section 4.2: the considerations made here are quite vague, and I believe it would valuable for the community to include practical recommendations on how to take into account the findings of this study. For example: could the results of this study be directly included in forward simulations to assess the effect of the findings on e.g., radar observations and shortwave reflection? Or is more work needed in this regard? If the results here presented could indeed be directly used in forward simulations, can you describe practical steps on how to do it?
Minor points
- Lines 5-6: when mentioning the zig-zag motions it would be helpful to clarify that it occurs in a constant vertical plane, as this aspect was unclear to me when first reading the manuscript.
- Lines 21-23: upon first reading the introduction it was unclear to me how the different trajectory regimes could affect the orientation distribution. Since it is key that the reader understands this aspect, I believe it is already worth explicitly explaining it here.
- Lines 74-75: upon first reading the article it was unclear to me what “more planar” and “more circular” actually meant. I suggest that the authors rephrase in a clearer way.
- Section 1.2.2: it would be helpful for the reader to have the moment of inertia of a thin disc and of a sphere included here for reference. Alternatively the authors could refer to the precise equations in a classical mechanics textbook.
- Line 104: I suggest that here it is specified that the range is indicated by the hatched area in the figure.
- Line 120: it is unclear to me what “orientation model for falling particle” means, and in what ways it is different from the “models of particle orientation” mentioned in the previous sentence. Can the authors briefly provide more details on the study by Klett (1995) and the assumptions made therein?
- Lines 123-124: I find the sentence “however, these indirect measurements lack the spatial resolution necessary to represent microphysical processes without making many assumptions” very unclear and vague. Can the authors concisely explain the assumptions used by Melnikov and Straka and why these are unrealistic?
- Lines 147-148: since the pendulum assumption is key to the analysis presented later in the article, I believe it would be helpful for the reader here to explicitly describe the functional form of an orientation distribution associated with such pendulum motion.
- Line 241: how is unstable periodic detected? Are all non-stable motions classified as unstable periodic? This should be clarified in the text.
- Line 250 / Fig. 3: I assume that the categorization into zig-zag / transitional / spiral here is made using the epsilon parameter introduced later in the text? Or was it by visual inspection of the cases? This should be briefly stated in the text.
- Lines 391-392: This sentence reads like something is missing, what is separated? Into what? I assume the authors mean something along the lines of: “… separates the cases into the different particle shapes and the zigzag and spiraling regimes, to demonstrate their impact on the distributions.”
- Lines 502-511: I have the impression that these lines don't belong in this section. The current section focuses on summarizing the findings, while these lines seem to introduce a new portion of the analysis. I suggest that these lines are moved earlier in the text, possibly in a new section. After applying this change, the current section could be simply named “summary”, as the current title is vague and not very indicative for the reader.
- Line 532: What does “strong turbulence” mean quantitatively? Can you quantify in terms of eddy dissipation rate and mention cloud types where turbulence could be considered strong?
Stylistic/technical corrections
- I believe that throughout the whole text some figure references are wrong. For example, throughout section 3.2.2 I believe Fig. 5 is referenced instead of Fig. 6, and at line 361 Fig. 7 is referenced instead of Fig. 8. I suggest that the authors double check all figure references.
- I’m wondering if the acronyms used for the different particle analogue shapes could be replaced with more intuitive phrases (e.g., HexPl instead HP, FerDen instead of F, DenAPl instead of DP). As a reader it is quite hard to remember all of them, and I often found myself having to go back to Table 1. In my opinion this change would improve the ease of interpretation of the figures, but of course it is not a necessary change.
- St_theta is sometimes denoted as St, the notation should be kept consistent throughout the whole text and all the figures.
- Line 18: the phrase “produce a trajectory” sounds odd to me, maybe it could be replaced with “follow a trajectory”?
- Line 34: Doppler should be capitalized
- Line 39: The reference to Platt (1977) should be in parentheses
- Line 94: I assume the authors meant to refer to I_a?
- Line 464: “Fig.” is missing
Citation: https://doi.org/10.5194/egusphere-2024-319-RC1 -
RC2: 'Comment on egusphere-2024-319', Anonymous Referee #2, 25 Mar 2024
OVERALL COMMENTS:
The authors reported observed falling motions of plate-like ice crystal analogues. It adds data to fill up the parameter space. The non-zero mode of the inclination angle is not necessary a new idea, but previous works are based on MASC in some air motion (not only Garrett et al. 2015 but also Jiang et al. 2019), so there is value in providing a benchmark behavior in quiescent fluid. I also found the results regarding the broad distribution of instantaneous vertical velocity interesting.
I would recommend this manuscript for publication on ACP after the following comments are addressed.
Regarding writing, there is huge room to reduce redundancy and improve clarity.
MAIN COMMENTS:
The framework (theta and phi) is insufficient to describe the particle orientation. For simplicity, refer to the first plot in https://en.wikipedia.org/wiki/Euler_angles. If I understand correctly, theta and phi are equivalent to beta and alpha, respectively, in Wikipedia's illustration. Then another angle (gamma in this illustration) is required to describe the orientation. The classification is confusing due to the missing angle. For the motion of the spiralling case (see animation in the supplementary materials), if one follow the tip of one branch, it is rotating quite slowly. This is not the case for the two transitional cases, especially the second. In the text, the rotation around the vertical axis is commented on for the transitional cases but omitted for the spiralling cases. It could have be systematically described with Euler angles. The analogue to plane and conical pendulums suffers from the similar issue, that is, it also misses degree of freedom in the true oriention evolution. Please justify the omitting of degree of freedom or add the results regarding this additional angle.
MINOR COMMENTS:
L101: Would you please be explicit about the mass-diameter relationship (from Nakada and Terada 1935) and I* estimation formula (from Kajikawa 1992)? Why do you use these two formulae to provide reference
L237: Do you mean all three Euler agnels fluctuate less than 2.5 deg? You only defined two of them in Figure 1. Is the third one measured?
L252: Also low aspect ratio D
L252-255: The logic in these two sentences is confusing. Is increased CD a cause or a result of the unstable motion?
Figure 5: In the corrected version of this figure, would you please show the fitted theta togethether with the raw theta (which I think is what is currently shown)?
L311: Which figure you are referring to for constant dphi/dt? At least it is not clear in Figure 6. Please clarify.
L316: "the arms of the crystal": Is this the same as the a-axis? Or is it the same as "branch"?
L338: "the angle of the particle": What is this?
Figure 8: It makes sense that, as suggested in the text, the thickness of a particle causes the disagreement between cosine theta and the ratio between the instantaneous and max projected areas. Is there any analysis of actual images that supports this argument? Also, the caption says "modelled projected areas as seen from below". Please explain how it is modelled.
L358: "as drag is minimised in the horizontal plane": What do you mean by this?
L376: What is "v" in the denominator?
Figure 9: What are the values before and after the +/- sign for mean theta amp and mean theta tilt? Also, it helps readers if you can label the distributions with dominant falling sub-types and numbers of cases.
Figure 13: The high epsilon cases in Panel c clearly are not well described by a linear fit. Have you tried to link V/Vmean for these cases to other potential controlling variables?
Subsection 3.3.4 Strouhal numbers: Is there any relationship between the two St numbers and area ratio?
L449: Why do you use data for cylinder as reference while all particles tested are plate-like? Hashino et al. 2014 (doi:10.1016/j.atmosres.2014.07.003) has some simulations on vortex structure around falling plates and may be a useful reference for some of your parameter space.
L462: Doesn't it take both theta_amp and theta_tilt to decide whether a particle is falling in the transitional sub-type?
L479: In the animation for the spiralling case, it seems that the center of mass is rotating around the y-axis but the particle is not rotating around its vertical axis. See main comments. Please clarify.
L495: Please specify that this is consistent with previous work instead of a new result.
L496: What about spiralling or other falling sub-types?
TECHNICAL ISSUES:
Figure 1: the language (an observer "facing parallel" to some plane) is confusing; Panel b does not look like that the observer is facing the a-y plane (actually Panel a looks like it)
Table 1: This table defines most acronyms/abbreviations (TRAIL, CD, PB, and so on) and should be moved to before the first time they are used (mostly in Figure 2).
Section 1.2: It is confusing when the authors simultaneously used terms like "circular discs", "planar discs", and "thin discs", and mixed references for idealized discs and real ice crystals all in one subsection for "circular discs".
L80: Please be specific about which subsection of Pruppacher and Klett the authors are referring to.
L94: There is no 'I' in Eq. 3. Please clarify.
L236: Why is there so much description of unsteady motion in this subsection titled "Crystals which fall steadily"
L243: Unit for moment of inertia seems missing, or do you mean the dimensionless one?
L245 and several other places: "onset of stability": do you mean "onset of unstable motion"?
L265: Please refer to plots (panels) when describing each falling sub-type.
L311: "dphi/dt is constant such that it precesses at a constant rate": this is redundant.
Words like "rock" and "see-saw" are too informal.
Figure 13: Panel c: missing operator before 0.019?
Citation: https://doi.org/10.5194/egusphere-2024-319-RC2 -
EC1: 'Comment on egusphere-2024-319', Ann Fridlind, 31 May 2024
Thank you to reviewers for excellent reviews and to authors for excellent responses to reviewer's comments. In some cases, it appears that very helpful response text was not propagated to the manuscript text in revisions. Please add text revisions so that general readers will have access to the following information within context, from responses to comments:
Regarding unstable motion: "Everything classified in this paper as unstable is also classified as periodic. There was no complex tumbling, or behaviour with any complex, non-sinusoidal motion in it. There are some experiments in the study which have aperiodic motions, or motions that have other, additional modes of motion on top of the sine wave behaviour. Spiralling motion is periodic because it periodically rotates, zigzagging motion is periodic because it periodically swings. For example, the transitional case has another mode of motion (the sine wave grows in amplitude). All cases are periodic in some sense, but the number of frequencies is sometimes above 1."
Regarding particle reconstruction, this very basic explanation would be helpful to general reader understanding: "We note that it would be unreliable to perform analysis based on the raw images, since the particle is not strictly seen from directly beneath by the camera (since the camera may not be perfectly vertical and the particle may not be perfectly centred over the camera); we mitigate these issues through the use of the digital reconstruction. The analysis of the reconstructed trajectories does support this argument, since (at times) the observed projected area exceeds that of the projected area of the particle when horizontal (i.e. the ratio in figure 8(b) exceeds 1); this can only be achieved through the influence of the thickness of the particle."
Re l*: "The I* estimation formula from Kajikawa 1992 was chosen as it offers a practical advantage over more complicated relationships, as it only requires the mass and diameter of the crystal (no detailed knowledge of the full distribution of mass around the snowflake is needed). While alternative mass-dimension relationships could have been chosen, the mass-diameter relationship from Nakada and Terada (1935) was chosen arbitrarily as an illustration of the order of magnitude approximation for reference, so that readers have an estimate of the possible range of values."
Re Figure 13: "Yes – All the variables mentioned in this study were explored, but no other results were worth showing (as results were nonlinear or unconvincing)."
Re Strouhal numbers: Can you please add the figure or explain the finding in the text for other readers who wish to know this?
Re use of cylinders as reference, other readers would benefit from this information: "We chose to use cylinders as a reference in this section due to a lack of available literature discussing the frequency of eddy shedding behind hexagonal plates. We appreciate the provided reference (Hashino et al., 2014) and acknowledge its potential relevance for future investigations. However, since it does not directly address the specific parameters or phenomena explored in our study, we have opted not to cite it in this manuscript. While Hashino et al. (2014) examines flow characteristics and torque distribution around ice columns and hexagonal plates, it does not delve into the frequency of eddy shedding or the parameters central to our analysis, such as I* or onset of different motion subtypes at varying Reynolds numbers. Therefore, we believe our decision aligns with the focus and scope of our research."
Thank you for considering these minor revisions.
Citation: https://doi.org/10.5194/egusphere-2024-319-EC1
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