Pith. sign in

REVIEW 3 major objections 6 minor 47 references

Circulation statistics in Rayleigh-Bénard convection follow the vortex-gas/area-rule phenomenology of homogeneous isotropic turbulence, but with thermal-boundary-layer vortices that are plume-borne and elongated.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-01 23:12 UTC pith:VMD4KT6O

load-bearing objection A genuinely new application of circulation statistics to Rayleigh–Bénard convection, with a real gap in the claim that vortex spots dominate circulation fluctuations. the 3 major comments →

arxiv 2607.15489 v1 pith:VMD4KT6O submitted 2026-07-16 physics.flu-dyn cond-mat.stat-mech

Circulation Statistics in Rayleigh-B\'enard Convection

Giovanni Saisse , Roshan J. Samuel , Luca Moriconi , J\"org Schumacher , Katepalli R. Sreenivasan This is my paper
classification physics.flu-dyn cond-mat.stat-mech
keywords Rayleigh–Bénard convectionvelocity circulation statisticsvortex gas modelarea rulethermal boundary layerelementary vorticesswirling strengthturbulence intermittency
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper asks whether the circulation statistics discovered in homogeneous isotropic turbulence (HIT)—the area rule linking circulation to minimal surfaces, and the dominance of localized vortex structures—also hold in buoyancy-driven Rayleigh-Bénard convection. Using direct numerical simulations at Rayleigh number 10^9 and Prandtl number 0.7, it finds that they largely do: circulation probability density functions in wall-parallel planes satisfy the area rule, and circulation fluctuations are dominated by the circulation of identified elementary vortices, exactly as in the vortex gas model. The novelty is inside the thermal boundary layer, where these vortices are preferentially embedded in hot plumes and are more elongated than their HIT counterparts; away from the wall, the statistics recover HIT-like behavior. The paper argues that the vortex-gas picture is a central ingredient in convection as well, with temperature replacing dissipation as the spatial organizer of small-scale vorticity near the wall.

Core claim

The central claim is that the vortex gas model (VGM) of circulation statistics, originally developed for homogeneous isotropic turbulence, extends to turbulent Rayleigh-Bénard convection. In DNS fields at Ra=10^9 and Pr=0.7, the authors identify 'vortex spots' via a swirling-strength criterion and show (i) that their distribution inside the thermal boundary layer is strongly correlated with the temperature field—hot vortices are denser near the boundary-layer edge—and (ii) that their aspect-ratio distributions become increasingly elongated closer to the wall, approaching the HIT distribution in the bulk. They then show that circulation fluctuations around planar square and rectangular contou

What carries the argument

The central objects are 'vortex spots'—two-dimensional cross-sections of elementary vortices—identified by the swirling-strength criterion: positions where the 2D velocity-gradient tensor has complex eigenvalues λ_R ± i λ_I, filtered by a threshold λ_th = σ_λ/8. Their statistics (distribution, number density, aspect ratio from covariance-matrix ellipses) are used to reconstruct circulation PDFs and test the vortex gas model. The Area Rule is the key identity tested: contours of equal enclosed area, regardless of shape, should yield the same standardized circulation distribution. The vortex gas model provides the analytical form of the elementary-vortex circulation PDF, Eq. (4.1), used to com

Load-bearing premise

The load-bearing premise is that the swirling-strength threshold λ_th = σ_λ/8 correctly identifies the physical 'elementary vortices'; if it admits spurious structures or misses real vortex tubes, the distribution, shape, and circulation-dominance conclusions would shift, and the paper itself flags that the 4δ_T anomalies could reflect insufficient statistical convergence as much as a real transitional layer, and that finite-resolution effects contaminate the fine structure o

What would settle it

Recompute the same circulation statistics from the same DNS fields while varying the swirling-strength threshold (e.g., λ_th = σ_λ/4 and σ_λ/16): if the reconstructed circulation PDFs in Fig. 3 stop matching the exact PDFs, or if the aspect-ratio tails in Fig. 2 change shape inside the TBL, then the identification of elementary vortices is not robust and the central HIT comparison is not well grounded. Additionally, measure the standardized circulation PDFs for equal-area contours with extreme aspect ratios at heights well inside the TBL (e.g., δ_T/4): if they fail to collapse, the area rule i

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • The area rule for circulation statistics, previously established in HIT, remains valid in a buoyancy-driven wall-bounded flow, extending the universality of circulation phenomenology across flow classes.
  • Circulation fluctuations inside the thermal boundary layer are dominated by localized vortex spots, meaning the vortex-gas framework can be used to interpret (and possibly predict) circulation statistics in convection without tracking full velocity fields.
  • Inside the thermal boundary layer, thermal plumes—not the energy dissipation field—set the spatial distribution of elementary vortices, coupling the small-scale vorticity statistics to the temperature field.
  • The recovery of HIT-like aspect-ratio and circulation statistics in the bulk suggests that coherent vortex morphology and circulation intermittency become universal away from boundary-layer effects.
  • The apparent transitional regime near 4δ_T, where the area rule weakens and hot-vortex fractions dip non-monotonically, identifies a distinct layer between the thermal boundary layer and the bulk that merits separate study.

Where Pith is reading between the lines

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

  • Editorial inference: The observed vortex–plume correlation suggests a dust-devil-like mechanism for vortex formation inside the thermal boundary layer; a time-resolved tracking of plumes and vortex spots could directly test this causal link, which the paper leaves as an analogy.
  • Editorial inference: The analysis hinges on a single swirling-strength threshold λ_th = σ_λ/8; if the statistics are sensitive to this choice, the quantitative comparison with HIT could shift, so a threshold-sensitivity scan would bound the robustness of the central claim.
  • Editorial inference: The area rule may be a generic property of any turbulent flow where circulation fluctuations are carried by sparse, coherent vortex structures; proving this from the Navier–Stokes equations would unify HIT, channel, pipe, and convective flows, but that proof is not yet available.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper studies velocity circulation statistics in direct numerical simulations of Rayleigh–Bénard convection (Ra=10^9, Pr=0.7, domain 4×4×1 with 1350×1350×864 collocation points). It identifies two-dimensional 'vortex spots' in wall-parallel planes using a swirling-strength criterion with threshold λ_th=σλ/8, and compares their temperature correlations, aspect-ratio statistics, and circulation contributions with homogeneous isotropic turbulence (HIT) results, including the Johns Hopkins Turbulence Database. The central claims are: (i) inside the thermal boundary layer, vortex spots are preferentially located in hot plumes and are more elongated than in HIT; (ii) circulation PDFs on wall-parallel square and rectangular contours follow the 'area rule' and are approximately self-similar within the TBL, except for a possible transitional region near 4δ_T; (iii) the circulation carried by localized vortex spots dominates circulation fluctuations, extending the vortex-gas model (VGM) phenomenology to RBC; and (iv) away from the TBL, statistics return to HIT-like behavior. An appendix presents a heuristic statistical-mechanics model for exponential tails in the aspect-ratio distributions.

Significance. If substantiated, the paper is significant because it extends the VGM/area-rule framework beyond HIT to buoyancy-driven convection and identifies thermal plumes as the organizing field for elementary vortices, in contrast to the dissipation field in HIT. The paper benefits from a high-resolution spectral DNS, a systematic comparison with HIT database results, 20 independent flow realizations for the vortex-temperature correlations, and explicit acknowledgments of its own limitations. However, the quantitative support for the VGM-dominance claim rests on standardized PDF comparisons, the vortex identification depends on an untested threshold, and the statistical convergence of the transitional-region anomaly is admittedly incomplete. These issues are addressable within the paper's scope.

major comments (3)
  1. [Sec. IV, Fig. 3] The claim that 'the dominant contribution to circulation fluctuations arises from the circulation carried by the vortex spots' is not supported by the standardized comparison. The text states that exact and spot-based circulations differ by an a priori unknown multiplicative factor of order unity; standardizing both PDFs removes that factor. If Γ_spots = c Γ_exact deterministically, the standardized PDFs coincide for any c. The shape agreement only shows a functional relationship, not dominance in variance. Please quantify the scale: report ⟨Γ_spots^2⟩/⟨Γ_exact^2⟩, fit c and show it is O(1), or compare unstandardized moments. Without this, the VGM 'guiding principle' conclusion remains an inference gap.
  2. [Sec. II, Eq. (2.4)] All vortex-spot statistics (Table I, Fig. 2, Fig. 3) depend on the identification threshold λ_th = σλ/8. The text acknowledges that spurious structures can arise from vortex packing, shear, and resolution, but no sensitivity analysis is reported. This threshold was adopted from HIT VGM studies; its transfer to the RBC boundary layer, where shear and thermal plumes are strong, is not automatic. Please vary λ_th (e.g., σλ/16, σλ/8, σλ/4) and show that hot-vortex fractions, aspect-ratio tails, and spot-based circulation PDFs are stable, or state which conclusions are threshold-dependent.
  3. [Sec. III / Conclusions, Table I and Fig. 7] The paper is based on a single DNS parameter set (Ra=10^9, Pr=0.7, L/H=4) and, while 20 realizations are used for Table I, no uncertainty estimates are given for the circulation PDFs or scaling exponents. The conclusions acknowledge that the 4δ_T anomaly 'cannot rule out insufficient statistical convergence' and that higher-order moments require larger ensembles. Because the abstract highlights a possible transitional region where the area rule fails, this caveat should be carried into the abstract, and the exception should be substantiated with bootstrap confidence intervals or additional data. As written, the quantitative claims about the scaling exponents and the transitional region are provisional.
minor comments (6)
  1. [Sec. III, Table I] The 'relative number density' is defined as the ratio of the second to the third columns. This equals (N_hot/A_hot)/(N_total/A_total), but this normalization is not explicitly explained. Please state the definition in the text.
  2. [Sec. V] The symbol r is used both for the vortex-spot aspect ratio (Sec. III, Appendix A) and for the contour aspect ratio (Fig. 6). Using different symbols (e.g., α for contour aspect ratio) would reduce confusion.
  3. [Fig. 5 caption] The normalization by the H/2, 50×50 case is clear, but the unlabeled curves in the lower-right panel make the figure hard to parse. Please add height labels to all curves or otherwise distinguish the panels more clearly.
  4. [Appendix A] The sentence 'Substituting (A13) in (A12)' omits the use of (A14) and the subtraction in (A16). Also, the statistical isotropy assumption behind (A13) is strong in the boundary layer; this limitation should be noted.
  5. [Eq. (4.2)] Please specify the range of q used in the parabolic fit and clarify whether Γ̄ denotes a single-spot circulation before standardization. The notation is used in Fig. 4 without a clear definition.
  6. [Sec. III, Fig. 2] The finite-resolution artifacts mentioned in the text are not indicated in the figure. Consider masking or annotating the affected aspect-ratio range.

Circularity Check

0 steps flagged

No significant circularity: main results are empirical DNS comparisons against external HIT benchmarks and exact circulation from the same simulation.

full rationale

The paper's central claims are tested against quantities that are not inputs to the model: exact circulation is computed from the DNS vorticity flux, and HIT comparisons use JHTDB data. The vortex-spot identification threshold λ_th=σλ/8 (Sec. II) is inherited from prior VGM papers by overlapping authors, but it is explicitly stated as an analysis convention, not presented as a prediction or derivation; no result is equivalent to this choice by construction. The one curve in Sec. IV that uses a fitted parameter (Eq. (4.1) with σ obtained from Eq. (4.2)) is transparently a fit, and it is not used to derive the main Area Rule or dominance conclusions. The standardized-PDF comparison in Fig. 3 has an inference gap—standardization removes any multiplicative factor, so shape agreement alone does not quantify the dominance claimed—but that is a logical/statistical limitation, not a circular reduction of a predicted quantity to an input. The Area Rule and VGM comparisons are empirical tests against external data, so no step in the derivation chain is equivalent to its own input.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The empirical core of the paper imports one DNS dataset and a vortex detection threshold; the appendix imports a heuristic two-parameter statistical model. No new physical entities are invented.

free parameters (4)
  • vortex identification threshold λ_th = σ_λ/8
    Chosen by hand following prior VGM studies [18,21]; all vortex statistics depend on this threshold.
  • VGM PDF parameter σ = not reported numerically
    Obtained from a parabolic fit to log-moments in Eq. (4.2); used to compare analytic VGM PDF (Eq. 4.1) with RBC data.
  • inverse temperature β (Appendix A)
    Free parameter in the effective Boltzmann weight P(r)∝exp(-βH(r)) for aspect-ratio fluctuations.
  • shape-function constant κ (Appendix A)
    Introduced in H(r)=κ(r+1/r-2); controls the scale of the exponential tail but is not fitted to data.
axioms (5)
  • domain assumption Boussinesq equations with no-slip, constant-temperature walls describe the simulated convection (Eqs. 2.1-2.3).
    The central claim is about turbulent RBC; the DNS solves these equations, so validity of the Boussinesq approximation is assumed.
  • domain assumption The pre-existing DNS dataset [36] at Ra=10^9, Pr=0.7 is sufficiently resolved for small-scale vortex statistics.
    All statistics use this dataset; resolution claims rely on the stated spectral mesh and smallest resolved spot diameters.
  • domain assumption Vortex spots identified by 2D swirling strength (complex eigenvalues of A in Eq. 2.4) with threshold λ_th=σ_λ/8 correspond to physical elementary vortices.
    This identification underlies Table I, aspect-ratio PDFs, and reconstructed circulation PDFs; threshold sensitivity is not tested.
  • ad hoc to paper Effective shape function H(r)=κ(r+1/r-2) and Boltzmann weight P(r)∝exp(-βH(r)) describe aspect-ratio statistics.
    This is a heuristic model in Appendix A; κ and β are free, and the identification with kinetic energy is approximate.
  • ad hoc to paper Individual vortices approximately conserve circulation and cross-sectional area, and the background strain is statistically isotropic.
    Invoked in Appendix A to derive exponential tails; a modeling assumption, not directly measured.

pith-pipeline@v1.3.0-alltime-deepseek · 10742 in / 14419 out tokens · 147975 ms · 2026-08-01T23:12:05.078395+00:00 · methodology

0 comments
read the original abstract

Important statistical properties of velocity circulation in homogeneous isotropic turbulence (HIT) have been unveiled in recent years, raising the question of whether they persist, or are modified, in other classes of turbulent flows. Motivated by the dominant role of small-scale structures in the circulation fluctuations of HIT, we investigate their relevance in direct numerical simulations of Rayleigh-B\'enard convection at a Rayleigh number of $10^9$ and Prandtl number of $O(1)$. Within the thermal boundary layer (TBL), the distribution of elementary vortices is found to be strongly correlated with the temperature field, while the statistics of their core aspect ratios is significantly altered. Additionally, the probability distribution functions of circulation, computed for planar contours which are parallel to the walls, display salient features closely akin to those observed in HIT, with the {\it Area Rule} (a connection between circulation statistics and minimal surfaces) remaining particularly well satisfied -- except for a possible transitional region at a distance of a few TBL thicknesses. Away from the TBL, as expected, the overall statistical behavior of these structures likewise resembles that of HIT, where the intermittent spatial distribution of small vortex tubes is instead determined by the energy dissipation field.

Figures

Figures reproduced from arXiv: 2607.15489 by Giovanni Saisse, J\"org Schumacher, Katepalli R. Sreenivasan, Luca Moriconi, Roshan J. Samuel.

Figure 1
Figure 1. Figure 1: FIG. 1: Overlay of vortex cross-sections (shown as dark spots) on the temperature field. The [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Aspect-ratio PDFs of the identified vortex spots, with the best-fitting ellipses determined [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Standardized circulation PDFs for square contours of size 50 [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Comparison of the analytical circulation PDFs for elementary vortices (HIT), given by [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Circulation PDFs for square contours of different sizes (side lengths indicated in the upper [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Circulation PDFs for all distances from the walls obtained using rectangular loops of fixed [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: In-plane circulation scaling exponents for different distances from the heated walls. The [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

47 extracted references · 1 linked inside Pith

  1. [1]

    Tennekes and J

    H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, 1972)

    1972

  2. [2]

    Frisch, Turbulence (Cambridge University Press, 1995)

    U. Frisch, Turbulence (Cambridge University Press, 1995)

    1995

  3. [3]

    K. R. Sreenivasan, Fluid turbulence, Rev. Mod. Phys.71, S383 (1999)

    1999

  4. [4]

    Z. S. She, E. Jackson, and S. A. Orszag, Intermittent vortex structures in homogeneous isotropic turbulence, Nature344, 226 (1990)

    1990

  5. [5]

    Farge, G

    M. Farge, G. Pellegrino, and K. Schneider, Coherent Vortex Extraction in 3D Turbulent Flows Using Orthogonal Wavelets, Phys. Rev. Lett.87, 054501 (2001)

    2001

  6. [6]

    Kaneda, T

    Y. Kaneda, T. Ishihara, M. Yokokawa, K. Itakura, and A. Uno, Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box, Phys. Fluids15, L21 (2003)

    2003

  7. [7]

    Ishihara, T

    T. Ishihara, T. Gotoh, and Y. Kaneda, Study of High–Reynolds Number Isotropic Turbulence by Direct Numerical Simulation, Annu. Rev. Fluid Mech.41, 165 (2009)

    2009

  8. [8]

    Ishihara, Y

    T. Ishihara, Y. Kaneda, and J. C. R. Hunt, Thin Shear Layers in High Reynolds Number Turbulence—DNS Results, Flow Turbul. Combust.91, 895 (2013)

    2013

  9. [9]

    Schumacher, J

    J. Schumacher, J. D. Scheel, D. Krasnov, D. A. Donzis, V. Yakhot, and K. R. Sreenivasan, Small-scale universality in fluid turbulence, Proc. Natl. Acad. Sci. U.S.A.111, 10961 (2014)

    2014

  10. [10]

    A. A. Ghira, G. E. Elsinga, and C. B. da Silva, Characteristics of the intense vorticity struc- tures in isotropic turbulence at high Reynolds numbers, Phys. Rev. Fluids7, 104605 (2022)

    2022

  11. [11]

    A. A. Ghira, G. E. Elsinga, and C. B. da Silva, Lifetime of the intense vorticity structures in isotropic turbulence, J. Fluid Mech.1007, A62 (2025)

    2025

  12. [12]

    A. A. Migdal, Loop Equation and Area Law in Turbulence, Int. J. Mod. Phys. A9, 1197 (1994)

    1994

  13. [13]

    K. P. Iyer, K. R. Sreenivasan, and P. K. Yeung, Circulation in High Reynolds Number Isotropic Turbulence is a Bifractal, Phys. Rev. X9, 041006 (2019)

    2019

  14. [14]

    K. P. Iyer, S. S. Bharadwaj, and K. R. Sreenivasan, The area rule for circulation in three- dimensional turbulence, Proc. Natl. Acad. Sci. U.S.A.118, e2114679118 (2021)

    2021

  15. [15]

    G. B. Apolin´ ario, L. Moriconi, R. M. Pereira, and V. J. Valad˜ ao, Vortex gas modeling of 19 turbulent circulation statistics, Phys. Rev. E102, 041102 (2020)

    2020

  16. [16]

    Moriconi, Multifractality breaking from bounded random measures, Phys

    L. Moriconi, Multifractality breaking from bounded random measures, Phys. Rev. E103, 062137 (2021)

    2021

  17. [17]

    Moriconi, R

    L. Moriconi, R. M. Pereira, and V. J. Valad˜ ao, Circulation statistics and the mutually exclud- ing behavior of turbulent vortex structures, Phys. Rev. E106, L023101 (2022)

    2022

  18. [18]

    Moriconi and R

    L. Moriconi and R. M. Pereira, Statistics of extreme turbulent circulation events from multi- fractality breaking, Phys. Rev. E106, 054121 (2022)

    2022

  19. [19]

    Moriconi, R

    L. Moriconi, R. M. Pereira, and V. J. Valad˜ ao, Vortex polarization and circulation statistics in isotropic turbulence, Phys. Rev. E109, 045106 (2024)

    2024

  20. [20]

    K. P. Iyer and L. Moriconi, Contour shape dependency of circulation statistics in homogeneous and isotropic turbulence, Phys. Fluids36, 085139 (2024)

    2024

  21. [21]

    Moriconi and R

    L. Moriconi and R. M. Pereira, Circulation Fluctuations of Elementary Turbulent Vortices, Phil. Trans. R. Soc. A384, 20250016 (2026)

    2026

  22. [22]

    Moriconi, Optimal surfaces for turbulent circulation statistics (2025), arXiv:2509.07903

    L. Moriconi, Optimal surfaces for turbulent circulation statistics (2025), arXiv:2509.07903

    Pith/arXiv arXiv 2025

  23. [23]

    H. S. Lima, R. M. Pereira, L. Moriconi, K. R. Sreenivasan, and C. Tsallis, Superstatistics approach to turbulent circulation fluctuations, Proc. Natl. Acad. Sci. U.S.A.123, e2612658123 (2026)

    2026

  24. [24]

    N. P. M¨ uller and G. Krstulovic, Lack of self-similarity in transverse velocity increments and circulation statistics in two-dimensional turbulence, Phys. Rev. Fluids10, L012601 (2025)

    2025

  25. [25]

    Xie, T.-S

    B.-J. Xie, T.-S. Zhou, and J.-H. Xie, Area rule of velocity circulation in two-dimensional instability-driven turbulence beyond the inertial range, Phys. Rev. Fluids11, 064607 (2026)

    2026

  26. [26]

    Mugundhan and S

    V. Mugundhan and S. T. Thoroddsen, Circulation in turbulent flow through a contraction, J. Turbul.24, 577 (2023)

    2023

  27. [27]

    P. Y. Duan, X. Chen, and K. R. Sreenivasan, Multiscale circulation in wall-parallel planes of turbulent channel flows, J. Fluid Mech.1009, R4 (2025)

    2025

  28. [28]

    Song and D

    B. Song and D. Xu, Uni/bifractality of velocity circulation in wall-parallel concentric shells of turbulent pipe flow, J. Fluid Mech.1034, A1 (2026)

    2026

  29. [29]

    N. P. M¨ uller, J. I. Polanco, and G. Krstulovic, Intermittency of Velocity Circulation in Quan- tum Turbulence, Phys. Rev. X11, 011053 (2021)

    2021

  30. [30]

    J. I. Polanco, N. P. M¨ uller, and G. Krstulovic, Vortex clustering, polarisation and circulation intermittency in classical and quantum turbulence, Nat. Commun.12, 7090 (2021). 20

    2021

  31. [31]

    N. P. M¨ uller, Y. Tang, W. Guo, and G. Krstulovic, Velocity circulation intermittency in finite-temperature turbulent superfluid helium, Phys. Rev. Fluids7, 104604 (2022)

    2022

  32. [32]

    N. P. M¨ uller and G. Krstulovic, Exploring the Equivalence between Two-Dimensional Classi- cal and Quantum Turbulence through Velocity Circulation Statistics, Phys. Rev. Lett.132, 094002 (2024)

    2024

  33. [33]

    Chill` a and J

    F. Chill` a and J. Schumacher, New perspectives in turbulent Rayleigh-B´ enard convection, Eur. Phys. J. E35, 58 (2012)

    2012

  34. [34]

    P. P. Shevkar, R. J. Samuel, G. Zinchenko, M. Bode, J. Schumacher, and K. R. Sreenivasan, Hierarchical network of thermal plumes and their dynamics in turbulent Rayleigh–B´ enard convection, Proc. Natl. Acad. Sci. U. S. A.122, e2502972122 (2025)

    2025

  35. [35]

    M. K. Verma, Physics of Buoyant Flows: From Instabilities to Turbulence (World Scientific, Singapore, 2018)

    2018

  36. [36]

    R. J. Samuel, M. Bode, J. D. Scheel, K. R. Sreenivasan, and J. Schumacher, No sustained mean velocity in the boundary region of plane thermal convection, J. Fluid Mech.996, A49 (2024)

    2024

  37. [37]

    N. O. Renn´ o, M. L. Burkett, and M. P. Larkin, A Simple Thermodynamical Theory for Dust Devils, J. Atmos. Sci.55, 3244 (1998)

    1998

  38. [38]

    J. Zhou, R. J. Adrian, S. Balachandar, and T. M. Kendall, Mechanisms for generating coherent packets of hairpin vortices in channel flow, J. Fluid Mech.387, 353 (1999)

    1999

  39. [39]

    Herpin, M

    S. Herpin, M. Stanislas, and J. Soria, The organization of near-wall turbulence: a comparison between boundary layer SPIV data and channel flow DNS data, J. Turb.11, N47 (2010)

    2010

  40. [40]

    J. H. Elsas and L. Moriconi, Vortex identification from local properties of the vorticity field, Phys. Fluids29, 015101 (2017)

    2017

  41. [41]

    Y. Li, E. Perlman, M. Wan, Y. Yang, C. Meneveau, R. Burns, S. Chen, A. Szalay, and G. Eyink, A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence, J. Turb.9, N31 (2008)

    2008

  42. [42]

    Johns Hopkins Turbulence Database, https://turbulence.pha.jhu.edu/

  43. [43]

    A. M. Obukhov, Some specific features of atmospheric tubulence, J. Fluid Mech.13, 77 (1962)

    1962

  44. [44]

    A. N. Kolmogorov, A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, J. Fluid Mech.13, 82 (1962). 21

    1962

  45. [45]

    Rhodes and V

    R. Rhodes and V. Vargas, Gaussian multiplicative chaos and applications: A review, Probab. Surv.11, 315 (2014)

    2014

  46. [46]

    The two-dimensionalization hypothesis is even more compelling in the thermal boundary layer, where the vortices are observed to be columnar, as can be inferred from the three upper panels of Fig. 1

  47. [47]

    Actually, a constantψ 0 =ψ b 0 +ψ v 0 does not contribute to the energy of an infinitely extended, finite-energy vortex system, which necessarily has vanishing total circulation. 22