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REVIEW 4 major objections 5 minor 63 references

Solar Vortices as Conduits for Magnetoacoustic Waves: Multi-Layer Coupling and Their Role in Atmospheric Heating

T0 review · 4 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper reports the first direct evidence that solar vortices act as structured waveguides for magnetoacoustic waves, arguing that these compressive waves—not torsional Alfvén waves—dominate energy transport in the lower chromosphere and

desk verdict The qualitative multi-layer waveguide claim is probably right and is the real contribution; the quantitative heating numbers are inflated by a disclosed boundary artifact and should be tempered. read the letter →

arxiv 2509.02895 v1 pith:4GSXTIU5 submitted 2025-09-02 astro-ph.SR physics.plasm-ph

Suzana S. A. Silva , Ioannis Dakanalis , Luiz A. C. A. Schiavo , Kostas Tziotziou , Istvan Ballai , Shahin Jafarzadeh , Tiago M. D. Pereira , Georgia Tsiropoula
show 5 more authors
Gary Verth Iñaki Esnaola James A. McLaughlin Gert J. J. Botha Viktor Fedun
This is my paper
classification astro-ph.SRphysics.plasm-ph
keywords solarvorticesmagnetoacousticwaveschromosphericheatingMHDwaveguidesspectralproperorthogonaldecompositionwaveenergyfluxmagnetictornadoesmulti-layercoupling
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out to show that solar vortices—swirling plasma structures spanning the photosphere and chromosphere—are not just places where twisted Alfvén waves travel, but three-dimensional waveguides that concentrate and guide magnetoacoustic (sound-like, compressive) waves upward. Using high-resolution Hα and Ca II 8542 Å observations of chromospheric swirls, a realistic radiation-MHD simulation of a coronal-hole region, and synthetic data mimicking vortex waveguides, the authors identify sausage and kink/helical modes at multiple heights within the same vortex and measure photosphere-to-chromosphere connectivity with information-theoretic metrics. They split the wave energy flux into compressive and magnetic parts and report that compressive flux dominates below about 1 Mm, reaching levels on the order of 10^4 W m^-2 near 0.6 Mm—enough to offset chromospheric radiative losses—while the magnetic (Alfvénic) component takes over only higher up. If correct, the lower chromosphere is heated largely by vortex-guided magnetoacoustic waves, overturning the common assumption that solar tornadoes couple to the upper atmosphere mainly through torsional Alfvén waves. This matters because it changes which wave channel and which heights solar-heating models must feed energy into.

What carries the argument

The load-bearing object is the vortex tube itself, treated as a rotating, elliptical MHD waveguide anchored in the photosphere and extending into the chromosphere. The method carrying the wave-mode identification is spectral proper orthogonal decomposition (SPOD), a covariance-filtering technique that isolates spatially coherent modes at single frequencies; the authors use its spatial patterns and temporal coefficients to classify sausage modes (radial width oscillations) and kink/helical modes (transverse or rotating axis displacements), and cross-check with an automated morphological swirl detector tracking the vortex center and radius. The energy argument rests on splitting the wave energ

What would settle it

Run the same simulation with a lower boundary that lets acoustic waves pass through, and recalculate the height-resolved compressive energy flux inside the vortex; if the flux no longer reaches the roughly 200–400 W m^-2 needed to balance radiative losses below 1 Mm, the heating claim fails. Alternatively, measure the compressive flux inside a vortex from high-cadence Fe I 1.56 µm and Ca II 8542 Å spectropolarimetry; if vortex-region compressive flux equals the non-vortex background, the waveguide claim fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that a solar vortex is a vertically coherent MHD waveguide: the same structure connects photospheric bright points to the overlying chromospheric swirl, and it carries magnetoacoustic waves whose thermal signatures appear in both the Hα wing (photosphere) and Hα core/Ca II 8542 Å (chromosphere). The authors report the first quantitative detection of sausage and kink/helical wave modes inside the same vortex across layers, cross-validating spectral proper orthogonal decomposition (SPOD) with independent morphological tracking of the vortex center and radius. They further decompose the wave energy flux into a compressive pressure-driven part, W_p, and a magnetic pa

Load-bearing premise

The energy-balance result depends on the simulation's lower boundary, which reflects acoustic waves and can artificially inflate the compressive wave flux; if that inflation is large, the claim that vortex-guided waves offset radiative losses would be overstated.

Editorial extensions

If this is right

  • Chromospheric-heating models must include vortex-guided compressive flux; without vortices, the modeled acoustic energy supply in the low chromosphere would be too small.
  • SPOD becomes a diagnostic for detecting rotational flow and wave-mode content even where velocity fields are unresolved, such as sunspot umbras and upper-atmosphere layers.
  • The kink-to-helical transition with height implies the vortex axis is a helical, tilted curve, so three-dimensional forward models of vortices should not assume straight vertical tubes.
  • The W_m/W_p crossover near 1 Mm defines a wave-regime boundary: magnetoacoustic waves dominate below it and Alfvénic waves above it, so wave-heating models must switch the dominant channel at that height.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension suggested by the authors' own caveat: rerun the energy-flux analysis with a transmitting (non-reflecting) lower boundary; if compressive flux still exceeds radiative-loss thresholds below 1 Mm, the heating conclusion survives the boundary artifact.
  • The crossover height where W_m/W_p crosses unity should depend on magnetic field strength and geometry; mapping vortices in plage or sunspot regions would reveal where vortex-guided compressive dominance ends.
  • The finding probably generalizes beyond the Sun: any magnetized stellar atmosphere with strong swirls and inclined fields should show vortex-guided magnetoacoustic heating, not solely Alfvénic channeling.
  • Because the observed kink mode evolves into a helical mode with height, vortex bending may be the physical mechanism connecting misaligned photospheric and chromospheric structures; a direct test would measure the phase relationship between vortex-center displacement and chromospheric emission.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript combines SST/CRISP Hα and Ca II 8542 Å observations of quiet-Sun swirls, a Bifrost coronal-hole simulation (ch024031_by200bz005), and synthetic rotating-Gaussian vortex models to argue that solar vortices are vertically coherent MHD waveguides. It computes Shannon entropy, mutual information, and Jensen–Shannon divergence to connect photospheric bright points to chromospheric swirls; applies Spectral Proper Orthogonal Decomposition (SPOD) to intensity, velocity, Poynting flux, temperature/FWHM maps; and independently tracks vortex centers/radii with A-MorphIS to infer Kink/Helical and Sausage mode frequencies. The paper's central claims are (i) first direct evidence that vortices carry magnetoacoustic modes through multiple layers, and (ii) compressive (magnetoacoustic) wave flux dominates below ~1 Mm and offsets chromospheric radiative losses, challenging Alfvén-dominated vortex energetics.

Significance. If established, the waveguide result would be a substantial advance: it would move vortex studies from morphological swirl detection and indirect connectivity to explicit multi-height wave-mode identification, and it would challenge the standard torsional-Alfvén picture for lower-atmosphere vortex energetics. The study has genuine strengths: the mode identification is cross-checked by two independent methods (SPOD and A-MorphIS/FFT); the morphological frequencies (2.5–6.7 mHz) are consistent with prior vortex oscillation measurements; the analysis includes ten simulated and ten observed vortices rather than a single event; and the authors openly disclose the Bifrost lower-boundary limitation. However, the quantitative energy-balance conclusion is not equally robust: its principal input, W_p, is acknowledged to be inflated by the reflective lower boundary, and the synthetic SPOD validation is circular in its construction. These caveats are disclosed, but they are not consistently carried into the abstract and Discussion. With revisions that calibrate or temper the flux claim and quantify mode-classification confidence, the paper could be suitable for publication.

major comments (4)
  1. [Wave energy transport / Supplementary Wave energy flux analysis] The abstract's quantitative conclusion that magnetoacoustic waves 'efficiently transfer energy, offset losses from radiation, and dominate energy transport in the lower chromosphere' rests on the magnitude of W_p computed with Eqs. (22)–(24). The Supplementary text states that the Bifrost lower boundary is a pressure node that reflects acoustic waves, excites a limited set of p-modes with larger amplitudes than in the real Sun, 'could artificially enhance the compressive wave energy flux (W_p)', and 'complicates direct interpretation of W_p >> W_m below 1 Mm as a purely physical result.' Yet the Results and Discussion quote W_pz ≈ 10^4 W m^-2 at 0.6 Mm and ≈200 W m^-2 at 2 Mm and present them as meeting/exceeding chromospheric heating requirements, without propagating the caveat into the headline. This is load-bearing for the energy-balance claim. I ask the authors to calibrate W_p again
  2. [Supplementary Synthetic data / Results MHD wave analysis] The synthetic SPOD calibration is constructed by imposing exactly the two modes that are then 'recovered' (Kink at 7 mHz and Sausage at 9 mHz in the rotating Gaussian model). This validates the numerical pipeline but does not establish that the same SPOD classification has a low false-positive rate on real vortices, where the true modal content is unknown. The authors explicitly caution that frequencies must be estimated or validated by complementary methods, and the A-MorphIS/FFT analysis does supply independent frequency estimates consistent with published ranges (2.5–6.7 mHz). What is missing is a quantitative measure of classification confidence for the real-data spatial modes: no null cases (rotation plus noise without waves), no template-matching scores, no inter-rater or algorithmic consistency metric. Because the paper's central claim is 'first direct evidence' of magnetoacoustic
  3. [Results: Wave energy transport] The quoted energetics for vortex N1 are internally inconsistent: at 2 Mm the paper reports total wave energy S ≈ 4.29×10^26 erg with W_m ≈ 1.32×10^26 erg and W_p ≈ 1.28×10^25 erg. Since Eqs. (22)–(24) define the total as the sum of the compressive and magnetic components (or at least do not define any additional term), the components sum to 1.45×10^26 erg, a factor ~3 below the stated total. Either define what S includes or correct the value. Separately, the population range 10^24–10^28 erg is obtained by 'assuming similar fluxes but variable size and duration' from a single simulated vortex; no scaling law or uncertainty is given, so the extension to 10 observed swirls is not yet quantitatively supported. This matters for the 'nanoflare regime' comparison.
  4. [Abstract / Discussion] The phrase 'clear wave-heating signatures' overstates what the evidence shows. The temperature SPOD modes for N1 and FWHM modes for S1 demonstrate oscillatory thermal perturbations correlated with Sausage/Kink modes; they are wave signatures, not a demonstrated net heating contribution. A net heating claim would require a quantitative energy budget linking the wave flux to radiative loss and excess emission in the same vortex. This is especially relevant given the boundary-affected W_p issue, because the only quantitative link to radiative losses is that boundary-dependent flux. Please either provide such a budget or temper the wording to 'temperature perturbations consistent with wave propagation'.
minor comments (5)
  1. [Results: Vortex photosphere - chromosphere connectivity] The sentence 'Our initial goal was to assess how well the simulated vortices from the Bifrost model compare to the structural properties of the observed vortices' appears twice verbatim in consecutive paragraphs.
  2. [Figure 5 caption] 'vorted' should be 'vortex' in 'the individual behaviour of each vorted'.
  3. [Figure 22 caption] 'a interval' should be 'an interval'.
  4. [Figure 10 caption] The phrase 'panels (j) and (h)' appears to be a typo for 'panels (e) and (j)' referring to the two PSD panels.
  5. [References] Reference [47] (Gupta et al., J. Optics, with TBD metadata) appears unrelated to the excitation of overtones in Gaussian waveguides; please verify or replace with a directly relevant source.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: synthetic SPOD validation is a recovery test, real-data mode frequencies come from independent morphological analysis, and the Bifrost boundary limitation is a disclosed simulation-fidelity caveat, not a circular reduction.

full rationale

The paper's derivation chain is: Bifrost simulation -> synthetic Hα spectra via non-LTE radiative transfer (SunnyNet/Muspel) -> A-MorphIS vortex identification -> SPOD decomposition of S_z, v_z, temperature, v_LOS, FWHM -> wave energy flux decomposition W_p, W_m -> comparison with chromospheric radiative-loss estimates. The synthetic vortex models (M-I/M-II) are used as a controlled recovery test: Kink and Sausage waveforms are imposed with frequencies 7/9 mHz and SPOD is shown to recover the correct families. This is a validation experiment, not a fit: the imposed frequencies are not used as free parameters in the observational or simulation analysis, and the real-data mode frequencies are instead derived from independent A-MorphIS time series of the vortex center displacement (f_D) and radius (f_R, Table S2). The classification of SPOD spatial patterns as Kink/Helical or Sausage is qualitative pattern matching, but the quantitative frequency support is external to the synthetic construction. The Bifrost lower-boundary pressure-node effect is explicitly disclosed by the authors as a possible artificial enhancement of W_p below 1 Mm; this is a correctness/fidelity caveat, not a circular step, because W_p is computed from the simulation fields and compared with external estimates (e.g., Rajaguru et al. 2019, Withbroe & Noyes 1977), not defined in terms of the conclusion. Self-citations (A-MorphIS, temperature-gradient proxy, WaLSAtools, prior vortex-tube papers) are methodological or background; none is an unverified uniqueness theorem or the sole justification for the central waveguide/heating claim. No equation is defined in terms of its target, and no fitted parameter is renamed as a prediction. Therefore the paper does not reduce to its inputs by construction.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The ledger is dominated by hand-chosen analysis choices, not new physics: synthetic calibration inputs, per-vortex SPOD windows, the 3.4 arcsec mask, and the 0.3 arcsec filter. No new physical entities are invented (empty invented_entities). The domain assumptions are standard for this kind of study, but the Bifrost lower-boundary assumption is the one that directly bears on the quantitative claim that compressive flux alone can balance radiative losses, and it is flagged by the authors themselves.

free parameters (5)
  • Synthetic SPOD calibration inputs (imposed frequencies, amplitudes, random walk) = Sausage 9 mHz, Kink 7 mHz; A_walk = 0.03 px/s; scale 0.0764; noise U(0, 0.2)
    Chosen by hand to mimic SST/CRISP cadence and observed swirl dynamics. Used to certify SPOD mode identification; the validation itself shows kink frequency errors of -44.65% (model I) and +24.28% (model II).
  • Per-vortex SPOD analysis windows = S1 photosphere 10:21-10:24 UT, chromosphere 10:21-10:28 UT; N1 3800-4300 s; temp +100 s
    Chosen post hoc to capture 'well-established' vortex rotation; the paper states any photospheric window displays both modes, so the selection is not shown to be neutral.
  • Vortex isolation mask radius (simulation) = circular mask, approximately 3.4 arcsec
    Hand-selected to enclose the tilted, kinking vortex; the energy flux profiles in Fig. 5 depend on this mask.
  • Spatial low-pass filter cutoff for N1 H-alpha = Gaussian, 0.3 arcsec
    Applied to force the SPOD linear-superposition assumption by smoothing features smaller than 0.3 arcsec; changes the resulting modes.
  • Observational population energy scaling = 10^24 to 10^28 erg across vortex population
    Extrapolated 'assuming similar fluxes but variable size and duration' from the single detailed vortex N1 estimate; not validated against per-vortex measurements.
assumptions (6)
  • domain assumption Bifrost lower boundary is a pressure node; the limited set of excited p-modes has larger amplitudes than in the real Sun
    The authors' own caveat: 'could artificially enhance the compressive wave energy flux (W_p), particularly for global-scale modes' and 'complicates direct interpretation of W_p >> W_m below 1 Mm as a purely physical result' (Supplementary, Wave energy flux analysis). The energy-dominance claim rests on W_p magnitudes.
  • standard math SPOD assumes linear superposition of modes
    The authors Gaussian-filter N1 H-alpha data 'to ensure consistency with the assumptions of the method' (MHD wave analysis). Nonlinearity would distort the identified modes.
  • domain assumption H-alpha core FWHM is a proxy for chromospheric temperature
    Used for the S1 thermal-perturbation SPOD analysis, citing Leenaarts et al. (ref 31); the wave-heating signature claim rests on this proxy.
  • domain assumption SunnyNet faithfully approximates non-LTE hydrogen populations
    Synthetic H-alpha spectra for the Bifrost run use SunnyNet instead of full Multi3D non-LTE transfer; biases propagate into the simulated vortex intensities used for entropy and mode analysis.
  • domain assumption MI and JSD of intensity time series quantify physical photosphere-chromosphere coupling
    Z-scored, binned intensities measure statistical dependency; high MI and low JSD in region A are interpreted as dynamic and structural linkage between layers.
  • domain assumption Bifrost run ch024031_by200bz005 (coronal hole) represents the observed quiet-Sun conditions
    Observed swirl S1 is quiet-Sun disk center while the simulation is an open-field coronal-hole run; the paper compares them directly for entropy, connectivity, and modes.

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Cite this review

Pith. "Pith review of Solar Vortices as Conduits for Magnetoacoustic Waves: Multi-Layer Coupling and Their Role in Atmospheric Heating." pith.science (2026). https://pith.science/paper/4GSXTIU5

@misc{pith2026250902895,
  author       = {Pith},
  title        = {Pith review of: Solar Vortices as Conduits for Magnetoacoustic Waves: Multi-Layer Coupling and Their Role in Atmospheric Heating},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4GSXTIU5}},
  note         = {Machine review of arXiv:2509.02895}
}
read the original abstract

The Sun's atmosphere hosts swirling plasma structures, known as solar vortices, which have long been thought to channel wave energy into higher layers. Until now, no direct observations have confirmed their role in the heating of the atmosphere. Here, we present the first direct evidence that solar vortices act as structured waveguides, carrying magnetoacoustic modes (waves that behave like sound waves but travel through magnetized plasma) that leave clear wave-heating signatures. By mapping vortex regions at multiple heights and analysing the waves they contain, we show that magnetoacoustic waves efficiently transfer energy, offset losses from radiation, and dominate energy transport in the lower chromosphere. These results challenge the long-standing assumption that vortices primarily support twisting disturbances traveling along magnetic field lines (Alfven waves), revealing instead that magnetoacoustic modes play the leading role in the lower atmosphere. This redefines the role of vortices in magnetized plasmas and has broader implications for wave-plasma interactions in regions of strong magnetic fields.

Figures

Figures reproduced from arXiv: 2509.02895 by the authors.

Figure 1
Figure 1. Photosphere – chromosphere coupling analysis using Shannon entropy and Jensen–Shannon [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Detected wave modes. Left panel: Spatial distribution of dominant wave modes in a solar tornado [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Detection of Helical (top row) and Sausage (bottom row) modes in vortex region of observational [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (43 more)
Figure 4
Figure 4. Figure 4: SPOD analysis of plasma variables and observables. The first column shows the variable average [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Height profile of the ratio between the net components of magnetic and pressure energy fluxes [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Selected swirls for analysis in the Bifrost simulation. The main image shows the H [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: Here, the synthetic H𝛼 wing is overlaid with the Line Integration Convolution (LIC) (42) of the magnetic (left panel) and velocity fields (right panel) computed at 100 km above the solar surface. Darker LIC lines indicate vectors tangent to the field along the plane. V…
Figure 8
Figure 8. Figure 8: Synthetic vortex as waveguide modelled by a rotating Gaussian distribution. Panels (a) and (b) show [PITH_FULL_IMAGE:figures/full_fig_p028_8.png]
Figure 9
Figure 9. Figure 9: Snapshots of the 10 analysed swirl events in H [PITH_FULL_IMAGE:figures/full_fig_p030_9.png]
Figure 10
Figure 10. Figure 10: Selected spatial modes of SPOD computed during the interval 10:21 UT to 10:28 UT within [PITH_FULL_IMAGE:figures/full_fig_p032_10.png]
Figure 11
Figure 11. Figure 11: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p033_11.png]
Figure 12
Figure 12. Figure 12: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p033_12.png]
Figure 13
Figure 13. Figure 13: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p034_13.png]
Figure 14
Figure 14. Figure 14: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p034_14.png]
Figure 15
Figure 15. Figure 15: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p035_15.png]
Figure 16
Figure 16. Figure 16: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p035_16.png]
Figure 17
Figure 17. Figure 17: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p036_17.png]
Figure 18
Figure 18. Figure 18: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p036_18.png]
Figure 19
Figure 19. Figure 19: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p037_19.png]
Figure 20
Figure 20. Figure 20: Selected spatial modes of SPOD computed during an interval of 400 seconds within the lifetime [PITH_FULL_IMAGE:figures/full_fig_p037_20.png]
Figure 21
Figure 21. Figure 21: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p038_21.png]
Figure 22
Figure 22. Figure 22: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p038_22.png]
Figure 23
Figure 23. Figure 23: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p039_23.png]
Figure 24
Figure 24. Figure 24: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p039_24.png]
Figure 25
Figure 25. Figure 25: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p040_25.png]
Figure 26
Figure 26. Figure 26: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p040_26.png]
Figure 27
Figure 27. Figure 27: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p041_27.png]
Figure 28
Figure 28. Figure 28: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p041_28.png]
Figure 29
Figure 29. Figure 29: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p042_29.png]
Figure 30
Figure 30. Figure 30: Detection of Helical (left panel) and Sausage (right panel) modes in the synthetic H [PITH_FULL_IMAGE:figures/full_fig_p043_30.png]
Figure 31
Figure 31. Figure 31: Detected Helical Kink- and Sausage-like modes in swirl S1 in H [PITH_FULL_IMAGE:figures/full_fig_p044_31.png]
Figure 32
Figure 32. Figure 32: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p045_32.png]
Figure 33
Figure 33. Figure 33: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p045_33.png]
Figure 34
Figure 34. Figure 34: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p046_34.png]
Figure 35
Figure 35. Figure 35: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p046_35.png]
Figure 36
Figure 36. Figure 36: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p047_36.png]
Figure 37
Figure 37. Figure 37: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p048_37.png]
Figure 38
Figure 38. Figure 38: Ratio of the magnitude of magnetic to pressure wave energy fluxes as a function of height. The [PITH_FULL_IMAGE:figures/full_fig_p050_38.png]
Figure 39
Figure 39. Figure 39: The vertical component of the magnetic wave energy flux. [PITH_FULL_IMAGE:figures/full_fig_p050_39.png]
Figure 40
Figure 40. Figure 40: The vertical component of the pressure wave energy flux. [PITH_FULL_IMAGE:figures/full_fig_p051_40.png]
Figure 41
Figure 41. Figure 41: Magnitude of pressure wave energy flux profiles. [PITH_FULL_IMAGE:figures/full_fig_p051_41.png]
Figure 42
Figure 42. Figure 42: Magnitude of magnetic wave energy flux, height-dependent profiles. [PITH_FULL_IMAGE:figures/full_fig_p052_42.png]
Figure 43
Figure 43. Figure 43: Vertical wave energy flux. 𝑊𝑧 = 𝑊 𝑝𝑧 + 𝑊𝑚𝑧 plotted as a function of height using the same line colour coding as [PITH_FULL_IMAGE:figures/full_fig_p052_43.png]
Figure 44
Figure 44. Figure 44: Magnitude of wave energy flux. |W| plotted as a function of height using the same line colour coding as [PITH_FULL_IMAGE:figures/full_fig_p053_44.png]
Figure 45
Figure 45. Figure 45: Ratio of energy fluxes in a vortex and a region without vortical motion a function of height. [PITH_FULL_IMAGE:figures/full_fig_p053_45.png]
Figure 46
Figure 46. Figure 46: SPOD of magnetic field components at H𝛼 line center formation height of vortex N1. The black circles indicate the vortex region (same as Fig.4, main text, top row) and the red arrows indicate the direction of the horizontal components of the dominant SPOD magnetic fie…

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Reviewed August 5, 2026 · model on record in the stance chip above.