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arxiv: 2605.17560 · v1 · pith:QLYD7LUTnew · submitted 2026-05-17 · ⚛️ physics.flu-dyn

Spatio-Temporal Signatures of Intermittency in Helically Rotating Turbulence through Topological Data Analysis

Snigdhashree Mallick , Yashwanth Ramamurthi , Shiva Kumar Malapaka , Amit Chattopadhyay (International Institute of Information Technology , Bangalore , India) This is my paper

Pith reviewed 2026-05-19 22:28 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords topological data analysisturbulence intermittencyhelically rotating flowspersistence diagramsWasserstein distancevorticity magnitudeeddy length scalespatiotemporal signatures
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The pith

Topological data analysis detects space-time locations of strong turbulent fluctuations in helically rotating flows via changes in persistence diagrams of vorticity and eddy-size fields.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies a topological data analysis framework to low-resolution simulations of helically rotating turbulence to pinpoint when and at which scales strong turbulent fluctuations emerge and turn into intermittent events. It treats vorticity magnitude and length-scale fields as scalar observables, extracts their persistence diagrams, and measures how those diagrams evolve using Wasserstein distances. This produces heatmaps that highlight localized, short-lived variations more clearly than conventional statistical tools. The central result is that pronounced shifts in the Wasserstein-distance heatmaps serve as direct markers of the fluctuations that drive intermittency.

Core claim

In 128^3 simulations of helically rotating turbulence, the topology of vorticity-magnitude and length-scale scalar fields, tracked through persistence diagrams and Wasserstein-distance metrics, produces space-time heatmaps whose pronounced variations mark the emergence of strong turbulent fluctuations that lead to intermittency.

What carries the argument

Persistence diagrams computed on vorticity-magnitude and eddy-size scalar fields, with Wasserstein distances between successive diagrams forming heatmaps that localize intermittent activity.

If this is right

  • TDA can reveal intermittent events that remain hidden in conventional statistical diagnostics.
  • The method works at modest 128^3 resolution, making it practical for large parameter surveys.
  • Vorticity tracks rotational multiscale structures while length-scale tracks the sizes at which intermittency occurs.
  • Wasserstein-distance heatmaps supply a spatiotemporal map of strong fluctuations across the domain.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same pipeline could be applied to non-rotating or magnetohydrodynamic turbulence to test whether the signatures generalize.
  • Combining TDA heatmaps with machine-learning classifiers might automate real-time detection of extreme events in flow data.
  • Extending the scalar observables to include enstrophy or dissipation rate could sharpen the localization of intermittent bursts.

Load-bearing premise

The vorticity-magnitude and length-scale fields, together with their persistence-diagram summaries, isolate genuine intermittent events rather than grid artifacts or features specific to the helical forcing.

What would settle it

Repeating the analysis on a higher-resolution simulation or a non-helically forced flow and checking whether the same pattern of pronounced Wasserstein-distance variations appears would test whether the signatures truly track intermittency.

Figures

Figures reproduced from arXiv: 2605.17560 by Amit Chattopadhyay (International Institute of Information Technology, Bangalore, India), Shiva Kumar Malapaka, Snigdhashree Mallick, Yashwanth Ramamurthi.

Figure 1
Figure 1. Figure 1: Schematic overview of our approach 3 Results We now present our analysis for a single representative case, namely highrotminhel (entry no. 7 in table 1), to maintain clarity and focus on the techniques and results discussed herein. For the remaining cases, presented in the same order as described in the subse￾quent sections, are included in the appendix. 3.1 Identification of STFs leading to intermittent e… view at source ↗
Figure 2
Figure 2. Figure 2: Persistence diagrams for selected timesteps of the [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of Wasserstein distance heatmaps for the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Length scale hierarchy used for classification, reflecting Richardson’s cascade model [21]. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Temporal evolution of the absolute change in the number of binned [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Temporal evolution of the number of persistence features for the [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Differences in the energy dissipation rate between consecutive timesteps. The left panel (2 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Differences in kinetic energy between consecutive timesteps. The left panel (2 [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Differences in kinetic helicity between consecutive timesteps. The left panel (2 [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Contour trees computed from the length scale scalar field of the [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: (a) Energy versus time for seven different configurations. (b) Same energy curves shown individually for clarity. (c) Corresponding kurtosis curves indicating [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Schematic persistence diagram; points away from [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: 1st-order Wasserstein distance matrices for curl components in the dataset. [PITH_FULL_IMAGE:figures/full_fig_p026_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Number of topological features as a function of timestep. The top row shows sublevel set filtrations, while the bottom row shows superlevel set filtrations, for [PITH_FULL_IMAGE:figures/full_fig_p026_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Maxhelmaxrot case 28 [PITH_FULL_IMAGE:figures/full_fig_p028_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Maxhelmaxrot case 29 [PITH_FULL_IMAGE:figures/full_fig_p029_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Maxrotminhel case 30 [PITH_FULL_IMAGE:figures/full_fig_p030_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Maxrotminhel case 31 [PITH_FULL_IMAGE:figures/full_fig_p031_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Nohelmaxrot case 32 [PITH_FULL_IMAGE:figures/full_fig_p032_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Nohelmaxrot case 33 [PITH_FULL_IMAGE:figures/full_fig_p033_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Nohelnorot case 34 [PITH_FULL_IMAGE:figures/full_fig_p034_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Nohelnorot case 35 [PITH_FULL_IMAGE:figures/full_fig_p035_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Norotmaxhel case 36 [PITH_FULL_IMAGE:figures/full_fig_p036_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Norotmaxhel case 37 [PITH_FULL_IMAGE:figures/full_fig_p037_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Norotminhel case 38 [PITH_FULL_IMAGE:figures/full_fig_p038_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Norotminhel case 39 [PITH_FULL_IMAGE:figures/full_fig_p039_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: 4th order WD 40 [PITH_FULL_IMAGE:figures/full_fig_p040_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: 4th order WD 41 [PITH_FULL_IMAGE:figures/full_fig_p041_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: 0D and 2D WD heatmaps 42 [PITH_FULL_IMAGE:figures/full_fig_p042_29.png] view at source ↗
read the original abstract

A central challenge in hydrodynamic turbulence is identifying precisely when, and at which length scales, strong turbulent fluctuations (STFs) emerge and develop into intermittent events, which are often obscured by conventional statistical diagnostics. We address this problem by applying a Topological Data Analysis (TDA) framework to reveal the spatiotemporal signatures of intermittency in low-resolution ($128^3$) helically rotating turbulent flows. Vorticity magnitude and length-scale (eddy size) fields are used as scalar observables for TDA: vorticity characterizes rotational dynamics that generate multiscale flow structures, while length-scale fields encode the scales at which intermittent activity arises. Their evolving topology is quantified using persistence diagrams and Wasserstein-distance metrics. Compared with traditional statistical approaches, this framework is more sensitive to localized and short-lived flow variations, enabling clearer detection of intermittent behavior. Pronounced variations in Wasserstein-distance heatmaps provide direct signatures of STFs across space and time. Together, these results demonstrate that TDA offers an effective complementary tool for detecting STFs that lead to intermittency within turbulent regime.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript applies topological data analysis (TDA) via persistence diagrams and Wasserstein distances to vorticity-magnitude and length-scale scalar fields from 128³ simulations of helically forced rotating turbulence. It claims that pronounced variations in the resulting Wasserstein-distance heatmaps constitute direct spatio-temporal signatures of strong turbulent fluctuations (STFs) that drive intermittency, and that the TDA framework is more sensitive to localized, short-lived events than conventional statistical diagnostics.

Significance. If the claimed signatures can be shown to correspond to genuine physical intermittency rather than resolution or forcing artifacts, the work would supply a useful complementary diagnostic for identifying when and at which scales intermittent events emerge in rotating turbulence. The study is an empirical application of existing TDA tools with no free parameters or self-referential definitions.

major comments (3)
  1. [Abstract] Abstract and results presentation: the assertion that the TDA framework 'is more sensitive to localized and short-lived flow variations' and enables 'clearer detection of intermittent behavior' is not supported by any quantitative comparison to classical intermittency measures (e.g., flatness factors, structure-function scaling exponents) or by error bars/validation against known diagnostics.
  2. [Numerical Setup] Numerical setup and results sections: the 128³ grid is employed without discussion of its consequences for the persistence diagrams; at this resolution the inertial range is narrow and numerical dissipation is strong, raising the possibility that birth-death pairs and Wasserstein distances reflect grid artifacts or helical-forcing imprints rather than physical STFs.
  3. [Results] Results section on Wasserstein-distance heatmaps: the interpretation of heatmap variations as 'direct signatures of STFs across space and time' rests on the untested assumption that the chosen scalar fields (vorticity magnitude and length-scale) and their persistence diagrams isolate genuine intermittent events; no control simulations (higher resolution, non-helical forcing) or cross-checks with traditional diagnostics are reported.
minor comments (2)
  1. [Introduction] The manuscript would benefit from explicit references to prior TDA applications in fluid dynamics to better situate the novelty of the helical-rotating case.
  2. [Figures] Figure captions for the Wasserstein-distance heatmaps should include quantitative scale bars or color-bar ranges to allow readers to assess the magnitude of the reported variations.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their constructive and detailed comments. We agree that strengthening the quantitative validation, discussing resolution limitations, and providing additional cross-checks will improve the manuscript. We have revised the abstract, numerical setup, and results sections to address these points and respond below to each major comment.

read point-by-point responses

  1. Referee: [Abstract] Abstract and results presentation: the assertion that the TDA framework 'is more sensitive to localized and short-lived flow variations' and enables 'clearer detection of intermittent behavior' is not supported by any quantitative comparison to classical intermittency measures (e.g., flatness factors, structure-function scaling exponents) or by error bars/validation against known diagnostics.

    Authors: We accept this point. In the revised manuscript we have added a dedicated subsection and accompanying figure that quantitatively compares Wasserstein-distance variations against flatness factors and structure-function exponents computed on the same vorticity-magnitude and length-scale fields. The TDA heatmaps exhibit sharper temporal peaks aligned with known STF events, while classical measures require longer averaging and show weaker localization. Error bars derived from five independent realizations have also been included to support the sensitivity claim. revision: yes

  2. Referee: [Numerical Setup] Numerical setup and results sections: the 128³ grid is employed without discussion of its consequences for the persistence diagrams; at this resolution the inertial range is narrow and numerical dissipation is strong, raising the possibility that birth-death pairs and Wasserstein distances reflect grid artifacts or helical-forcing imprints rather than physical STFs.

    Authors: We agree that explicit discussion of the 128³ resolution is required. We have inserted a new paragraph in the Numerical Setup section noting the limited inertial range and the role of numerical dissipation. We explain that persistence diagrams are constructed on the resolved scales and that Wasserstein distances measure relative topological changes rather than absolute feature sizes; these changes remain consistent across variations in rotation rate and helical forcing amplitude, supporting a physical origin. A forward-looking statement on the value of higher-resolution follow-up studies has been added. revision: yes

  3. Referee: [Results] Results section on Wasserstein-distance heatmaps: the interpretation of heatmap variations as 'direct signatures of STFs across space and time' rests on the untested assumption that the chosen scalar fields (vorticity magnitude and length-scale) and their persistence diagrams isolate genuine intermittent events; no control simulations (higher resolution, non-helical forcing) or cross-checks with traditional diagnostics are reported.

    Authors: The vorticity-magnitude and length-scale fields were selected because they directly encode the rotational multiscale structures and eddy-size distributions central to helical rotating turbulence. In revision we have added cross-checks that overlay Wasserstein-distance peaks with peaks in the flatness factor of the same fields, demonstrating temporal coincidence. We have also clarified in the text that the helical forcing is an intrinsic part of the physical regime under study rather than an artifact. We do not present new control runs in this work. revision: partial

standing simulated objections not resolved
  • Performing additional higher-resolution (e.g., 512³) or non-helical control simulations to further exclude numerical artifacts, which would require new computational resources beyond the present study.

Circularity Check

0 steps flagged

Empirical TDA application shows no circular derivation

full rationale

The paper applies standard persistence diagrams and Wasserstein distances to vorticity-magnitude and length-scale fields extracted from 128^3 helical turbulence simulations. The central claim—that pronounced variations in the resulting heatmaps constitute direct signatures of STFs and intermittency—is presented as an empirical observation from the computed diagrams, not as a mathematical derivation that reduces to its own inputs by construction. No equations define a quantity in terms of itself, no fitted parameters are relabeled as predictions, and no load-bearing uniqueness theorems or ansatzes are imported via self-citation. The methodology remains self-contained against external benchmarks (existing TDA libraries and turbulence diagnostics) and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on standard TDA constructions with no new free parameters, axioms beyond basic topology, or invented entities described in the abstract.

axioms (1)
  • standard math Persistence diagrams and Wasserstein distance are well-defined and stable for scalar fields on a discrete grid
    Invoked implicitly when converting vorticity and length-scale fields into topological summaries

pith-pipeline@v0.9.0 · 5746 in / 1238 out tokens · 39492 ms · 2026-05-19T22:28:04.012893+00:00 · methodology

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    Relation between the paper passage and the cited Recognition theorem.

    We address this problem by applying a Topological Data Analysis (TDA) framework to reveal the spatiotemporal signatures of intermittency in low-resolution (128^3) helically rotating turbulent flows. Vorticity magnitude and length-scale (eddy size) fields are used as scalar observables for TDA... Their evolving topology is quantified using persistence diagrams and Wasserstein-distance metrics.

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