the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 Jun 2024
The ratio of transverse to longitudinal turbulent velocity statistics for aircraft measurements
Abstract. The classical theory of homogeneous isotropic turbulence predicts the ratio of transverse to longitudinal structure functions or power spectra equal to 4/3 in the inertial subrange. For the typical turbulence cascade in the inertial subrange, it also predicts a power law scaling with an exponent of +2/3 and −5/3 for the structure functions and the power spectra, respectively.
We estimate those ratios and exponents from in-situ high-rate turbulence measurements collected by three research aircraft during four field experiments in two regimes of the marine atmospheric boundary layer: shallow trade-wind convection and subtropical stratocumulus. The results were derived by fitting power law formulas to the structure functions and power spectra computed separately for the three components of the turbulent wind velocity measured in horizontal flight segments.
The variability in the results can be attributed to how the wind velocity components are measured on an individual aircraft. The differences related to environmental conditions, e.g. between characteristic levels and regimes of the boundary layer, are of secondary importance.
Experiment-averaged transverse-to-longitudinal ratios are 23–46 % smaller than predicted by the theory. The deviations of average scaling exponents with respect to the theoretical values range from −35 to +47 % for structure functions and from −25 to +22 % for power spectra, depending on experiment and velocity component. The reason for the disagreement in transverse-to-longitudinal ratios between the observations and the theory remains uncertain.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(5113 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(5113 KB) - Metadata XML
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-1366', Anonymous Referee #1, 26 Jun 2024
Review of “The ratio of transverse to longitudinal turbulent velocity statistics for aircraft measurements” by Jakub L Nowak et al
The manuscript describes the ratio of transverse to longitudinal structure functions and power spectra in the inertial subrange, as measured by aircraft, and how the derived ratios and scaling exponents deviate from the classical theory of homogeneous and isotropic turbulence. Derived ratios are closer to ¾ than to the theoretical 4/3 value. The authors conclude that the derived ratios and exponents mainly depend on how the velocity components were measured on the aircraft compared to a minor influence of ABL regimes and across different field experiments.
General remarks
The manuscript provides a profound and insightful analysis of the spectra and structure functions, with a rigorous and detailed description of methods used to derive the ratios and scaling exponents, including uncertainty analysis and sensitivity to the fitting range of the spectra. I only have a few suggestions for improving clarity and better contextualizing the work within the existing literature.
Specific comments
- It would be helpful to the reader if the abstract could clearly state the overall aim of the manuscript before outlining the methodological details. Is it to document the derived ratios and exponents and their deviation from theoretical values?
- I think the introduction could be re-structured to lead from a broad scope to the specific purpose of this paper. For example, the second paragraph is a rather technical explanation of turbulence measurements on aircraft, which I find hard to contextualize when reading for the first time.
- The introduction (L. 63ff) mentions a few studies of isotropy from ground-based measurements. It would be interesting to mention what these studies find, since they exclude aircraft-specific errors. Also, are there studies available from tall towers (several hundreds of meters high), reaching above the surface layer?
- L. 72: Could you explain what the upwash distortion is? (Since it is mentioned several times.)
- L. 134: Could you still briefly mention TAS and sampling frequency for the ATR?
- It would be helpful to add an explanation about the applicability of the findings to the undisturbed ABL (and reference coordinate system along the mean wind), since the longitudinal and transversal components refer to the aircraft-referenced coordinate system (L. 136ff), including aircraft heading and pitch if I understand correctly.
- L. 139: Add the reference coordinate system.
- L. 142: “Note that both vertical and lateral wind components are considered transverse.” It might be helpful to mention this earlier, since both terms are used multiple times before.
- L. 210: Does the ¾ value have a special meaning, or is it just by coincidence the closest value for the ratios?
- Looking at Fig.3-Fig.5, one could interpret that filled symbols show less scatter than open circles. Could one conclusion of the study be that wind-parallel flight legs provide statistically more robust results than wind-perpendicular flight legs?
- L. 289ff: To investigate aircraft-specific errors leading to the deviation from theoretical values: What about a comparison to tall tower measurements or airborne Sonic anemometer measurements? Would the spatial distance between aircraft and reference measurement hinder a direct comparison?
- Appendix C: Does the conclusion of appendix C mean that the insensitivity to the included scales extends beyond the inertial subrange, meaning that even the larger scales are close to anisotropy in the ABL? It would be interesting to see if measured anisotropy in the inertial subrange is related to anisotropy at larger scales. Were strongly anisotropic cases (at larger scales) considered in the analysis?
Technical comments
- The figure labels are very small and hard to read, especially Fig. 1, 2, B1 and C1. Would it be possible to plot fewer cases, but increase label sizes?
- L. 22: Maybe rather use “turbulence strength” than “turbulence intensity” to not confuse it with the actual variable TI.
- L. 59: boundaries of what?
Citation: https://doi.org/10.5194/egusphere-2024-1366-RC1 - AC1: 'Reply on RC1', Jakub Nowak, 10 Oct 2024
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RC2: 'Comment on egusphere-2024-1366', Anonymous Referee #2, 04 Jul 2024
- AC2: 'Reply on RC2', Jakub Nowak, 10 Oct 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-1366', Anonymous Referee #1, 26 Jun 2024
Review of “The ratio of transverse to longitudinal turbulent velocity statistics for aircraft measurements” by Jakub L Nowak et al
The manuscript describes the ratio of transverse to longitudinal structure functions and power spectra in the inertial subrange, as measured by aircraft, and how the derived ratios and scaling exponents deviate from the classical theory of homogeneous and isotropic turbulence. Derived ratios are closer to ¾ than to the theoretical 4/3 value. The authors conclude that the derived ratios and exponents mainly depend on how the velocity components were measured on the aircraft compared to a minor influence of ABL regimes and across different field experiments.
General remarks
The manuscript provides a profound and insightful analysis of the spectra and structure functions, with a rigorous and detailed description of methods used to derive the ratios and scaling exponents, including uncertainty analysis and sensitivity to the fitting range of the spectra. I only have a few suggestions for improving clarity and better contextualizing the work within the existing literature.
Specific comments
- It would be helpful to the reader if the abstract could clearly state the overall aim of the manuscript before outlining the methodological details. Is it to document the derived ratios and exponents and their deviation from theoretical values?
- I think the introduction could be re-structured to lead from a broad scope to the specific purpose of this paper. For example, the second paragraph is a rather technical explanation of turbulence measurements on aircraft, which I find hard to contextualize when reading for the first time.
- The introduction (L. 63ff) mentions a few studies of isotropy from ground-based measurements. It would be interesting to mention what these studies find, since they exclude aircraft-specific errors. Also, are there studies available from tall towers (several hundreds of meters high), reaching above the surface layer?
- L. 72: Could you explain what the upwash distortion is? (Since it is mentioned several times.)
- L. 134: Could you still briefly mention TAS and sampling frequency for the ATR?
- It would be helpful to add an explanation about the applicability of the findings to the undisturbed ABL (and reference coordinate system along the mean wind), since the longitudinal and transversal components refer to the aircraft-referenced coordinate system (L. 136ff), including aircraft heading and pitch if I understand correctly.
- L. 139: Add the reference coordinate system.
- L. 142: “Note that both vertical and lateral wind components are considered transverse.” It might be helpful to mention this earlier, since both terms are used multiple times before.
- L. 210: Does the ¾ value have a special meaning, or is it just by coincidence the closest value for the ratios?
- Looking at Fig.3-Fig.5, one could interpret that filled symbols show less scatter than open circles. Could one conclusion of the study be that wind-parallel flight legs provide statistically more robust results than wind-perpendicular flight legs?
- L. 289ff: To investigate aircraft-specific errors leading to the deviation from theoretical values: What about a comparison to tall tower measurements or airborne Sonic anemometer measurements? Would the spatial distance between aircraft and reference measurement hinder a direct comparison?
- Appendix C: Does the conclusion of appendix C mean that the insensitivity to the included scales extends beyond the inertial subrange, meaning that even the larger scales are close to anisotropy in the ABL? It would be interesting to see if measured anisotropy in the inertial subrange is related to anisotropy at larger scales. Were strongly anisotropic cases (at larger scales) considered in the analysis?
Technical comments
- The figure labels are very small and hard to read, especially Fig. 1, 2, B1 and C1. Would it be possible to plot fewer cases, but increase label sizes?
- L. 22: Maybe rather use “turbulence strength” than “turbulence intensity” to not confuse it with the actual variable TI.
- L. 59: boundaries of what?
Citation: https://doi.org/10.5194/egusphere-2024-1366-RC1 - AC1: 'Reply on RC1', Jakub Nowak, 10 Oct 2024
-
RC2: 'Comment on egusphere-2024-1366', Anonymous Referee #2, 04 Jul 2024
- AC2: 'Reply on RC2', Jakub Nowak, 10 Oct 2024
Peer review completion
Journal article(s) based on this preprint
Interactive computing environment
The ratio of transverse to longitudinal turbulent velocity statistics for aircraft measurements: software Jakub L. Nowak, Marie Lothon, Donald H. Lenschow, and Szymon P. Malinowski https://doi.org/10.5281/zenodo.11127723
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Marie Lothon
Donald H. Lenschow
Szymon P. Malinowski
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(5113 KB) - Metadata XML