High-resolution temperature profiling in the &Pi; Chamber: variability of statistical properties of temperature fluctuations

Grosz, Robert; Chandrakar, Kamal Kant; Shaw, Raymond A.; Anderson, Jesse C.; Cantrell, Will; Malinowski, Szymon P.

doi:https://doi.org/10.5194/egusphere-2024-2051

Preprints

https://doi.org/10.5194/egusphere-2024-2051

Preprints

16 Oct 2024

| 16 Oct 2024

High-resolution temperature profiling in the Π Chamber: variability of statistical properties of temperature fluctuations

Robert Grosz, Kamal Kant Chandrakar, Raymond A. Shaw, Jesse C. Anderson, Will Cantrell, and Szymon P. Malinowski

Abstract. This study delves into the small-scale temperature structure of Rayleigh-Bénard convection (RBC) generated in the Π Chamber under three temperature differences (10 K, 15 K, and 20 K) at Rayleigh number Ra ~ 10⁹ and Prandtl number Pr ≈ 0.7. We performed high resolution measurements (2 kHz) with the UltraFast Thermometer (UFT) at selected points along the vertical axis. The miniaturized design of the sensor featured with a resistive platinum-coated tungsten wire, 2.5 μm thick and 3 mm long, mounted on a miniature wire probe allowed for undisturbed vertical temperature profiling spanning from 8 cm above the bottom surface to 5 cm below the top surface. The resulting rich dataset comprised both long (19 min) and short (3 min) time series, revealing strong variance and skewness in the temperature distributions near both surfaces and in the bulk (central) region linked with local thermal plume dynamics. We also identified three spectral regimes termed inertial range (slopes of ~ −7/5), transition range (slopes of ~−3) and dissipative range, characterized by slopes varying ~ −7. Furthermore, the analysis showed a robust relationship between the periodicity of large-scale circulation (LSC) and the temperature gradient, describable by an exponential relation. Notably, the experimental findings demonstrate strong agreement with Direct Numerical Simulations (DNS) conducted under similar thermodynamic conditions, illustrating a rare comparative analysis of this nature.

Received: 03 Jul 2024 – Discussion started: 16 Oct 2024

Competing interests: The authors have the following competing interests: Szymon P. Malinowski is a member of the editorial board of Atmospheric Measurement Techniques.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.

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Journal article(s) based on this preprint

20 Jun 2025

High-resolution temperature profiling in the Π Chamber: variability of statistical properties of temperature fluctuations

Robert Grosz, Kamal Kant Chandrakar, Raymond A. Shaw, Jesse C. Anderson, Will Cantrell, and Szymon P. Malinowski

Atmos. Meas. Tech., 18, 2619–2638, https://doi.org/10.5194/amt-18-2619-2025,https://doi.org/10.5194/amt-18-2619-2025, 2025

Short summary

Robert Grosz, Kamal Kant Chandrakar, Raymond A. Shaw, Jesse C. Anderson, Will Cantrell, and Szymon P. Malinowski

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-2051', Anonymous Referee #1, 06 Nov 2024

Please see attached comments in PDF format.

Citation: https://doi.org/10.5194/egusphere-2024-2051-RC1
- AC1: 'Reply on RC1', Robert Grosz, 20 Nov 2024
  
  Please find all our answers in the attached document.
  
  Citation: https://doi.org/10.5194/egusphere-2024-2051-AC1
RC2:
'Comment on egusphere-2024-2051', Anonymous Referee #2, 25 Nov 2024

The manuscript discusses Rayleigh-Bénard type measurements conducted in the Pi chamber, addressing higher-order statistics of temperature fluctuations, including second- and third-order moments and spectra. Evaluating the measurement capabilities of the Pi chamber for this Rayleigh-Benard helps make us aware of the capabilities and limitations of measurements that can be performed with the Pi chamber. I find this aspect of the study helpful and valuable for the community. Unfortunately, this is not well presented in the manuscript. The experimental results are compared with direct numerical simulations of the same system, showing good overall agreement. However, why the simulations do not show symmetry around the mid-plane is not discussed, which should be there unless asymmetries in the setup are also modelled.
The overall impression is that the manuscript lacks rigorous scientific analysis/discussion (see points below), making it unsuitable for publication in this form.
Limitations of the manuscript are:

(i) The manuscript has incorrect analysis and discussions on some of the data. In particular, some of the 3-minute measurement data is misinterpreted. It should be noted that this data is not statistically converged.

(ii) The conclusion and abstract need to indicate more of the limitations of the presented measurements.

(iii) Line 26 states some limitations, but this needs to be mentioned more in the data discussion to explain certain observations.

(iv) See a list of incorrect/inconsistent analyses and statements in the manuscript.

-- Figure 3: Unclear what is learned from this figure.

-- Line 28: Suggest you do measurements in the boundary layer, which is incorrect. Boundary layer thickness is well below 1 cm for Ra=1e9, so the sentence should be removed.

-- Line 52: Fan et al not relevant

-- Line 55: Olsthoorn, 2023 not relevant

-- Line 71: Brown and Ahlers's most famous model on LSC is not cited, and not all given references are relevant.

-- Line 77: See Annu. Rev. Fluid Mech. 2010. 42:335–64

-- Line 143: Deteremination --> Determination

-- Line 155-156: Why are no differences observed near the top plate? Roughness should still affect the flow.

-- Line 172: "All these effects are beyond the scope of this investigation, but the raw measurements give clear evidence of changing oscillations near both plates." --> This statement is incorrect. The fluctuations shown in Figure 4 cannot be compared to the LSC measured as performed in the RB community.

-- Scatter in these figures indicates that longer measurement data would be required. Performing measurements longer than 19 minutes would reduce fluctuations in statistical data.

-- Figure A1 and Figure A2: Temporal comparison between experiments and simulations is misleading as no one-to-one comparison of the same flow state is performed.

-- line 195 and further: Discussion incorrect as the data are not converged. This data is not converged, and that discussion is meaningless. The 19-minute-long measurements do not show such an increase.

-- line 211: Indeed 3, minute measurements are too short.

-- Figure 7: Vertical variability of the LSC period with respect to --> LSC is the coherent large scale flow structure in the cell, so it should not vertically vary. The discussion should be adjusted accordingly.

-- Provide details on how Pearson correlation coefficients are calculated.

-- Line 252: "relatively small variability of PSD slopes." --> The variations in the slopes are very large. Scaling exponents vary by as much as 20 to 30%. This severely limits how much one can learn from this data. That is recognized in line 254 ("Our analysis provides no clear answer,")

-- line 257-291: What main point do you want to explain to the reader?

-- line 339: It should be discussed that both measurement times are too short, especially the 3-minute data, which even leads to misleading discussions in the manuscript.

-- line 341: How this improves our understanding of atmospheric flow is not discussed.

-- line 368: Scheel et al. is a numerical study with no theory on heat transport.

-- Figure 11: Why is DNS not symmetric around the mid-plane?

-- Appendix B: "and display greater symmetry compared" --> Incorrect. Normalising the temperature difference between the plates does not affect symmetry around the midplane.

-- Figure C1: What does it mean that velocity in the centre is always positive? Is this a velocity magnitude?

-- Figure C2: What are all the numbers in the legend?

-- Figure D1: The data are visibly deviating from the presented lines. Difficult to see how this corresponds to Pearson correlation coefficients of -1.

Citation: https://doi.org/10.5194/egusphere-2024-2051-RC2
- AC2: 'Reply on RC2', Robert Grosz, 23 Dec 2024
  
  Please find all our answers in the attached document.
  
  Citation: https://doi.org/10.5194/egusphere-2024-2051-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-2051', Anonymous Referee #1, 06 Nov 2024

Please see attached comments in PDF format.

Citation: https://doi.org/10.5194/egusphere-2024-2051-RC1
- AC1: 'Reply on RC1', Robert Grosz, 20 Nov 2024
  
  Please find all our answers in the attached document.
  
  Citation: https://doi.org/10.5194/egusphere-2024-2051-AC1
RC2:
'Comment on egusphere-2024-2051', Anonymous Referee #2, 25 Nov 2024

The manuscript discusses Rayleigh-Bénard type measurements conducted in the Pi chamber, addressing higher-order statistics of temperature fluctuations, including second- and third-order moments and spectra. Evaluating the measurement capabilities of the Pi chamber for this Rayleigh-Benard helps make us aware of the capabilities and limitations of measurements that can be performed with the Pi chamber. I find this aspect of the study helpful and valuable for the community. Unfortunately, this is not well presented in the manuscript. The experimental results are compared with direct numerical simulations of the same system, showing good overall agreement. However, why the simulations do not show symmetry around the mid-plane is not discussed, which should be there unless asymmetries in the setup are also modelled.
The overall impression is that the manuscript lacks rigorous scientific analysis/discussion (see points below), making it unsuitable for publication in this form.
Limitations of the manuscript are:

(i) The manuscript has incorrect analysis and discussions on some of the data. In particular, some of the 3-minute measurement data is misinterpreted. It should be noted that this data is not statistically converged.

(ii) The conclusion and abstract need to indicate more of the limitations of the presented measurements.

(iii) Line 26 states some limitations, but this needs to be mentioned more in the data discussion to explain certain observations.

(iv) See a list of incorrect/inconsistent analyses and statements in the manuscript.

-- Figure 3: Unclear what is learned from this figure.

-- Line 28: Suggest you do measurements in the boundary layer, which is incorrect. Boundary layer thickness is well below 1 cm for Ra=1e9, so the sentence should be removed.

-- Line 52: Fan et al not relevant

-- Line 55: Olsthoorn, 2023 not relevant

-- Line 71: Brown and Ahlers's most famous model on LSC is not cited, and not all given references are relevant.

-- Line 77: See Annu. Rev. Fluid Mech. 2010. 42:335–64

-- Line 143: Deteremination --> Determination

-- Line 155-156: Why are no differences observed near the top plate? Roughness should still affect the flow.

-- Line 172: "All these effects are beyond the scope of this investigation, but the raw measurements give clear evidence of changing oscillations near both plates." --> This statement is incorrect. The fluctuations shown in Figure 4 cannot be compared to the LSC measured as performed in the RB community.

-- Scatter in these figures indicates that longer measurement data would be required. Performing measurements longer than 19 minutes would reduce fluctuations in statistical data.

-- Figure A1 and Figure A2: Temporal comparison between experiments and simulations is misleading as no one-to-one comparison of the same flow state is performed.

-- line 195 and further: Discussion incorrect as the data are not converged. This data is not converged, and that discussion is meaningless. The 19-minute-long measurements do not show such an increase.

-- line 211: Indeed 3, minute measurements are too short.

-- Figure 7: Vertical variability of the LSC period with respect to --> LSC is the coherent large scale flow structure in the cell, so it should not vertically vary. The discussion should be adjusted accordingly.

-- Provide details on how Pearson correlation coefficients are calculated.

-- Line 252: "relatively small variability of PSD slopes." --> The variations in the slopes are very large. Scaling exponents vary by as much as 20 to 30%. This severely limits how much one can learn from this data. That is recognized in line 254 ("Our analysis provides no clear answer,")

-- line 257-291: What main point do you want to explain to the reader?

-- line 339: It should be discussed that both measurement times are too short, especially the 3-minute data, which even leads to misleading discussions in the manuscript.

-- line 341: How this improves our understanding of atmospheric flow is not discussed.

-- line 368: Scheel et al. is a numerical study with no theory on heat transport.

-- Figure 11: Why is DNS not symmetric around the mid-plane?

-- Appendix B: "and display greater symmetry compared" --> Incorrect. Normalising the temperature difference between the plates does not affect symmetry around the midplane.

-- Figure C1: What does it mean that velocity in the centre is always positive? Is this a velocity magnitude?

-- Figure C2: What are all the numbers in the legend?

-- Figure D1: The data are visibly deviating from the presented lines. Difficult to see how this corresponds to Pearson correlation coefficients of -1.

Citation: https://doi.org/10.5194/egusphere-2024-2051-RC2
- AC2: 'Reply on RC2', Robert Grosz, 23 Dec 2024
  
  Please find all our answers in the attached document.
  
  Citation: https://doi.org/10.5194/egusphere-2024-2051-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Robert Grosz on behalf of the Authors (20 Jan 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (28 Jan 2025) by Wiebke Frey

RR by Anonymous Referee #2 (10 Feb 2025)

Suggestions for revision or reasons for rejection

In the response the general aspects of my report have not been commented. For example, I indicated that the manuscript "lacks rigorous scientific analysis/discussion". In the updated manuscript, this aspect has not been appropriately addressed. My previous report indicated that data convergence has not been fully addressed. Around line 119, this is commented on shortly, stating that data are converged within "Data are within 10% of the true value". However, it should be noted that this Lenschow et al. (1994) criterium, of more than 30 years ago, of a convergence of 10% within the value does not at all reflect standards of the Rayleigh-Benard community [as I had indicated in my previous report]. In the Rayleigh-Benard community, convergence to 1% or even up to 0.1% is standard in state-of-the-art studies. Correspondingly, statements like good convergence in abstract and conclusions do not reflect readers' expectations.

As previously indicated, evaluating the measurement capabilities of the Pi chamber for Rayleigh-Benard helps us to be aware of the capabilities and limitations of measurements that can be performed with the Pi chamber. This aspect of the study is helpful and valuable for the community. Ideally, measurements would be performed longer [as suggested in my previous report]. The response does not indicate why longer measurements are impossible or why the 3-minute measurement data could not be removed from the manuscript. However, at least, the manuscript should avoid (qualitative) statements like "high convergence" and "tiny deviation", as the obtained convergence does not reflect modern standards by the Rayleigh-Bénard community (see attached). Instead, an uncertainty analysis should be provided to report the uncertainties in the data. Even scaling exponents have significant uncertainty (see Figure 10), which should already be clarified to the reader in the abstract and conclusions. The reader should not have to look in the manuscript in detail to find this information. Again, the Rayleigh-Benard community (first line of the abstract) has different criteria and reads qualitative statements like "high convergence" differently. This is avoided by reporting uncertainty values in abstracts and conclusions.

The motivation for the study is better articulated in the updated manuscript version. Unfortunately, not all information provided in the responses to the referees is included in the manuscript. Two key examples include the discussion on asymmetry. Additionally, the descriptions with temporal development of experiments and DNS are compared (Appendix A). In the response, it is indicated that this is indeed not a direct comparison. However, this information is not incorporated in the manuscript. I still find that plotting the temporal evolution of experimental and simulation data in the same figure, suggesting direct comparison, is misleading [especially because zoom-ins of certain time frames are provided]. However, at the very least, what is done should be clarified.

Additional points:
* The abstract and conclusions should also clarify that there are significant uncertainties in the obtained scaling exponents. The asymmetry and large fluctuations in the data clearly show that the scaling exponents are not converged, which is not reflected by the very small error in the power law fits.
* Line 119: Data are within 10% of the true value --> For which statistic does this hold (first-order moments, second-order moments, higher-order statistics)
* Line 123: indicating good convergence --> In the RB community, the criteria for good convergence are at least one order of magnitude stricter. This should be clearer in the abstract/conclusion.
* Line 144: homogeneous horizontal grid spacing --> Does this mean boundary layers closer to the vertical sidewall are not explicitly resolved?
* Line 145: How many points are in the boundary layers close to the plates?
* Line 165: On what is the statement that previous studies had "limited temporal resolution" based?
* Figure 6: The scatter in the data reveals that the error bars are too small to capture the uncertainty in the measurements.
* Line 208: High convergence --> not quantitative provide actual uncertainties
* Line 214: "Then, at the 20 cm level, there is a subtle indication of possible " --> What is meant?
* Line 220: "However, not all thermal plumes could be fully averaged out" --> incorrect terminology
* Line 232: "However, recent numerical work by Zhang et al. (2018)" --> "recent" --> It is 2025 now
* Line 323: "dissipative regime slopes are approximately −7" --> Seems more like -7.5 (see also line 389); again, there is significant uncertainty
* Line 338: "As presented in Fig. 5, standard deviation distribution in the chamber is almost symmetrical with respect to the center with a small bias near the ceiling." --> No; this does not reflect the discussion on the asymmetry as indicated in my previous report and the answer to the referee. Please update the discussion as indicated in the response to the referee
* Line 343: "with a tiny bias in the vicinity of the upper plate." --> Not a tiny deviation.
* Line 409: What is meant here? There is no explanation?

Hide

RR by Anonymous Referee #1 (12 Feb 2025)

RR by Anonymous Referee #3 (21 Feb 2025)

Suggestions for revision or reasons for rejection

The authors discuss experimental results in the Pi chamber, a closed vessel to conduct cloud microphysics experiments. The main purpose of the represent publications is to extract statistical information from the temperature field in the chamber, obtained from Ultrafast Thermometers (UFTs).

The present manuscript thus presents temperature statistics, such as temperature fluctuations and Fourier spectra, which are obtained for this particular experimental platform and which are necessary to define operating points of future cloud microphysics experiments. Three different outer temperature differences are applied and time series at the probe (which can be moved vertically up and down) are collected. The experiments are backed up with DNS of the same configuration. The Rayleigh numbers are 1.1e9, 1.6e9 and 2.1e9.

The results which the authors extracted are interesting and deserve to my view a publication. They help to understand the convective turbulence in the Pi chamber better and thus are necessary for future studies of the cloud microphysics in this device. Here, I ask the authors to clarify a few minor points before a publication:

1) The temperature fluctuation profiles in Fig. 5 (and Fig. 11) look meaningful to me. The authors cannot resolve the near-wall regions such that they miss the profile maximum at the height of the thermal boundary layer thickness. Shouldn’t the third-order moment in Fig. 6 be more or less mirror-symmetric (about half-height)? It might be that 19 min of measurement time are still too short. Could the authors comment on this. For example, how much does the LSC change in this time period, can this be detected in the experiment?

2) On the spectra: a Bolgiano scaling should appear for scales above the Bolgiano scale L_B (which might be translated into a Bolgiano frequency f_B = u_rms L_B. Is it possible to extract such a scale (e.g. from the DNS) that separates the lowest frequencies from the rest of the spectrum? Otherwise, one might conclude that it is simply a Kolmogorov-type scaling. Bolgiano scaling is typically found in stratified turbulence, not in unstably stratified flows.

3) The discussion of the -3 range of the spectrum: can we really see fingerprints of a helicity cascade in the spectrum. The spectra are taken along (or close to) the centerline. Perhaps it just might be a crossover into the dissipative range. Please comment.

Hide

ED: Publish subject to minor revisions (review by editor) (21 Feb 2025) by Wiebke Frey

AR by Robert Grosz on behalf of the Authors (03 Mar 2025) Author's response Author's tracked changes Manuscript

ED: Publish subject to technical corrections (07 Mar 2025) by Wiebke Frey

AR by Robert Grosz on behalf of the Authors (15 Mar 2025) Author's response Manuscript

Journal article(s) based on this preprint

20 Jun 2025

High-resolution temperature profiling in the Π Chamber: variability of statistical properties of temperature fluctuations

Robert Grosz, Kamal Kant Chandrakar, Raymond A. Shaw, Jesse C. Anderson, Will Cantrell, and Szymon P. Malinowski

Atmos. Meas. Tech., 18, 2619–2638, https://doi.org/10.5194/amt-18-2619-2025,https://doi.org/10.5194/amt-18-2619-2025, 2025

Short summary

Robert Grosz, Kamal Kant Chandrakar, Raymond A. Shaw, Jesse C. Anderson, Will Cantrell, and Szymon P. Malinowski

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Short summary

Our objective was to enhance understanding of thermally-driven convection in terms of small-scale variations in the temperature scalar field. We conducted a small-scale study on the temperature field in the Π Chamber using three different temperature differences (10 K, 15 K, and 20 K). Measurements were carried out using a miniaturized UltraFast Thermometer operating at 2 kHz, allowing undisturbed vertical temperature profiling from 8 cm above the floor to 5 cm below the ceiling.


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