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Helicity effect on turbulent passive and active scalar diffusivities

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Kinetic helicity increases the turbulent diffusivity of passive and active scalars, opposite to its effect on turbulent magnetic diffusivity.

desk verdict Solid new test-field measurements showing a ~10-15% helicity enhancement of turbulent scalar diffusivity, but the printed theory in Eq. (16) has a sign error that makes the claimed agreement impossible. read the letter →

arxiv 2501.08879 v3 pith:P6FTY6DC submitted 2025-01-15 physics.flu-dyn astro-ph.SRphysics.plasm-ph

Axel Brandenburg , Petri J. Käpylä , Igor Rogachevskii , Nobumitsu Yokoi This is my paper · ORCID
classification physics.flu-dynastro-ph.SRphysics.plasm-ph MSC 76F2576F0576W05 PACS 47.27.-i47.65.-d
keywords kinetichelicityturbulentdiffusionpassivescalardiffusivitythermaltest-fieldmethodmean-fieldmagnetohydrodynamicsturbulencecorrelationtime
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

Turbulent flows are usually assigned an effective diffusivity that mixes scalars, heat, and magnetic fields far faster than molecular diffusion. This paper argues that kinetic helicity—the net swirl or handedness of the turbulence—changes that effective diffusivity in opposite directions for magnetic fields and for passive scalars (contaminants that do not affect the flow): it suppresses the turbulent magnetic diffusivity $\eta_t$ but enhances the turbulent passive scalar diffusivity $\kappa_t$ and the thermal diffusivity $\chi_t$. The evidence comes from direct numerical simulations using the test-field method, where the enhancement appears once the Reynolds number exceeds about 10 and reaches roughly 10–15 percent. The authors attribute the effect to a helicity-dependent growth of the turbulent correlation time, approximately $\tau_c/\tau_0 = 1 + 0.5\epsilon_f^4$, and note that the usual second-order correlation approximation, which drops nonlinear fluctuation terms, cannot produce such a correction. If correct, the result matters because astrophysical estimates of mixing in helical flows would need separate helicity corrections for field and scalar transport.

What carries the argument

The central mechanism is the dependence of the turbulent correlation time $\tau_c$ on kinetic helicity $H_K = \langle \mathbf{u}\cdot\boldsymbol{\omega}\rangle$. The paper measures $\tau_c$ two ways—through the time integral of the velocity autocorrelation and through the energy-to-dissipation ratio $E_K/\epsilon_K$—and finds growth with the fractional helicity $\epsilon_f = H_K/(k_f u_{\rm rms}^2)$, fitted as $\tau_c/\tau_0 \approx 1+0.5\epsilon_f^4$. Combined with the theoretical transport coefficients, $\eta_t(H_K) = \eta_{t0}(\tau_c/\tau_0)(1 - \tau_c^2 H_K^2/(3\langle u^2\rangle))$ and $\kappa_t(H_K) = \kappa_{t0}(\tau_c/\tau_0)(1 - \tau_c^2 H_K^2/(6\langle u^2\rangle))$, the increased correlation time overcompensates the negative helical correction for scalars but not for magnetic fields. The numerical workhorse is the test-field method, which solves auxiliary equations for fluctuations induced by imposed large-scale sinusoidal test fields and extracts $\eta_t$, $\kappa_t$, and $\chi_t$ from the resulting mean fluxes.

What would settle it

A matched pair of simulations with identical forcing spectra and Mach number, differing only by the addition of helicity in the forcing, would settle the attribution: if $\kappa_t$ and $\tau_c$ do not increase, the claim fails.

Watch

Extended reading notes

Core claim

Working with forced homogeneous turbulence and sinusoidal test fields, the paper establishes that the turbulent scalar diffusivity $\kappa_t$ is larger when the flow carries kinetic helicity than when it does not, while under the same conditions the turbulent magnetic diffusivity $\eta_t$ is smaller. Tables 1 and 2 show the $\kappa_t$ and $\chi_t$ enhancement for $Re \gtrsim 10$, with the effect absent at the smallest Reynolds number. The proposed mechanism is a lengthening of the velocity correlation time by helicity: measured both from the velocity autocorrelation integral and from the kinetic-energy-to-dissipation ratio, $\tau_c$ rises with the fractional helicity $\epsilon_f$, consistent with $\tau_c/\tau_0 \approx 1 + 0.5\epsilon_f^4$. Inserting this into the companion theory's expressions for $\eta_t(H_K)$ and $\kappa_t(H_K)$ yields suppression for the magnetic diffusivity and enhancement for the scalar diffusivity, matching the simulations. The paper also notes that simulations where helicity is produced self-consistently by rotating stratified turbulence do not show the scalar enhancement, which it ascribes to rotational suppression of turbulent transport.

Load-bearing premise

The central attribution assumes the helical and nonhelical runs differ only in the injected kinetic helicity, so the measured increases in $\kappa_t$, $\chi_t$, and $\tau_c$ come from helicity rather than from the slightly different Mach numbers or unchanged forcing statistics.

Editorial extensions

If this is right

  • Mean-field models of stellar convection and other helical flows should use a larger turbulent scalar and thermal diffusivity than nonhelical calibrations predict at the same Reynolds number.
  • Astrophysical estimates of turbulent magnetic diffusivity that ignore helicity will be systematically too high, while estimates of chemical or thermal mixing will be systematically too low.
  • Closure schemes for turbulent transport must include a helicity-dependent correlation time; approaches that omit it predict the wrong sign for the scalar correction.
  • The growth of $\tau_c$ with helicity implies that helicity alters the effective eddy turnover time, which may also affect transport coefficients such as turbulent viscosity.
  • The weak dependence of the scalar enhancement on forcing wavenumber suggests the effect persists across a range of turbulent scales.

Reading between the lines

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

  • The Appendix A discrepancy suggests a decisive test: force stratified rotating turbulence with and without explicit helical injection; if the scalar enhancement appears only with forced helicity, the conclusion applies to externally helical flows and not to helicity generated self-consistently by rotation and stratification.
  • A direct measurement of $\tau_c$ at higher Reynolds numbers would clarify whether the $\epsilon_f^4$ growth and the resulting diffusivity enhancement saturate; if they saturate, the quantitative predictions would need revision.
  • If the correlation-time mechanism is correct, helicity should also measurably change turbulent viscosity, since it shares the same $\tau_c$ prefactor; this could be checked with existing Reynolds-stress measurements.
  • The opposite signs of the magnetic and scalar corrections offer a possible diagnostic: in a helical astrophysical flow, comparing the mixing of a chemical tracer with the evolution of a magnetic field could constrain the local fractional helicity.
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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 / 4 minor

Summary. The paper reports direct numerical simulations of isothermal and nonisothermal turbulence in which the turbulent passive scalar diffusivity κt and the active scalar (thermal) diffusivity χt are measured with the test-field method for helical and nonhelical forcing. The central numerical claim is that kinetic helicity enhances κt and χt by about 10–15% for Reynolds numbers above about 10, opposite to the well-known suppression of the turbulent magnetic diffusivity ηt. The paper additionally reports that the turbulent correlation time τc increases with fractional helicity, and presents this as the key theoretical interpretation, citing a companion theory paper. A comparison with rotating stratified turbulence in Appendix A shows no such enhancement, which the authors attribute to rotational suppression without a quantitative test.

Significance. If the numerical result stands, it identifies a new and potentially important transport effect: helicity affects scalar diffusion in the opposite sense from magnetic diffusion. The test-field simulations are direct measurements, not derived from the theory, so the core numerical finding is not circular. The paper also offers a falsifiable prediction (the correlation-time increase) and provides data tables with error bars. However, the theoretical comparison, which is a central part of the paper's interpretation, contains apparent sign and normalization errors that, as printed, contradict the reported numerical enhancements.

major comments (4)
  1. [§3.3, Eq. (16)] Equation (16), κt(HK)=κt0 (τc/τ0)(1 − τc² HK²/(6⟨u²⟩)), contains a negative helicity correction. Combining it with Eq. (17), τc/τ0≈1+0.5 εf⁴, yields κt/κt0 = t(1 − t² εf²/6) with t=1+0.5 εf⁴. For the fully helical runs (εf≈0.93, as in Fig. 5), this evaluates to ≈1.00, and the maximum over all εf is only ≈1.02 near εf≈0.8. This is mathematically incapable of producing the 10–16% enhancements reported in Tables 1 and 2 (e.g., κhel/κnhel=1.14 at Re=120; χhel/χnhel=1.12 at Re=152). As written, the printed formula predicts a slight reduction for small εf and a negligible increase at most. The theoretical interpretation therefore cannot explain the central numerical result; either Eq. (16) has a sign typo or the curves in Fig. 7 do not come from Eqs. (15)–(17).
  2. [§3.3, text before Fig. 7] The text states that "the turbulent diffusion coefficient for the scalar field is increased by the kinetic helicity," but the figure is described as plotting κt(0)−κt. With Eq. (16) having a minus sign, κt(0)−κt is positive when κt is reduced, so a positive curve in Fig. 7 would indicate suppression, not enhancement. The textual claim and the plotted quantity are therefore inconsistent. This is not a cosmetic issue—it prevents the reader from knowing whether the figure actually supports the stated conclusion.
  3. [§3.3, Eq. (17) vs. Fig. 6] The empirical fit τc/τ0 ≈ 1 + 0.5 εf⁴ appears to be inconsistent with the data shown in Figure 6. In that figure, the normalized correlation time τc urms kf (= τc/τ0, since τ0=(urms kf)⁻¹) is approximately 2.5 at εf=0 and rises to about 7.5 at εf≈0.93 for the correlation-based estimate, with the dissipation-based estimate showing a similar offset. A fit of the form τc/τ0 ≈ 2.5 + 5 εf⁴ (with considerable scatter) would describe the data, not 1 + 0.5 εf⁴. The offset of roughly 2.5 is missing from Eq. (17). Since Eq. (17) is presented as the basis for the theoretical comparison, its mismatch with the displayed data is a load-bearing error.
  4. [§3.3, reliability warning] The paper explicitly states that the theoretical results for εf ≳ 0.8 "may not be reliable" and plots those parts with dotted lines. However, the fully helical runs in Tables 1 and 2 correspond precisely to that regime (εf≈0.93), and Figure 7 presumably compares the numerical data at these high εf values with the theory. Any apparent agreement in Fig. 7 therefore occurs in the regime where the authors themselves doubt the theory, which undermines the claimed validation. The authors should either provide a quantitative criterion for reliability or restrict the comparison to εf values where the theory is trusted.
minor comments (4)
  1. [Fig. 5] The y-axis label in Figure 5 is the full defining formula for τc(t), not the normalized quantity actually plotted; this makes it impossible to read the figure without guessing the normalization. Please replace it with a clear label such as τc(t)/τ0 or τc(t) urms kf.
  2. [Table 1] Several entries list errors as ±0.00 (e.g., ηnhel for Runs C and D, and αhel for Run c in Table 3). Such values are unrealistic; either give an upper bound (e.g., <0.005) or quote more significant digits.
  3. [§3.1 and Fig. 5] The text says the correlation time "is more than double" as εf increases from zero to one (near Fig. 5), but the normalized values in Fig. 6 show a factor of about three between εf=0 and εf≈0.93 (from ≈2.5 to ≈7.5). Please reconcile the wording with the data; also note that Eq. (17) gives a factor of only 1.37, which is inconsistent with both.
  4. [Appendix A] The comparison with rotating stratified turbulence is only qualitative; the claim that rotational suppression is the dominant effect is not tested quantitatively. A simple scaling estimate (e.g., comparing Co and Gr with εf) would strengthen the argument.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the central enhancement claims are direct simulation outputs; the Section 3.3 interpretation is post-hoc and Eq. (16) as printed cannot reproduce the enhancement, a correctness issue rather than circularity.

full rationale

The paper's main claims (κt and χt enhanced by helicity, Tables 1–2; τc increase, Figs. 5–6) are measured quantities from test-field runs and enthalpy-flux correlations, not derived from the theory or from fitted parameters. The theoretical section 3.3 imports Eqs. (15)–(16) from the accompanying same-author paper and combines them with Eq. (17), an empirical fit to the same simulations, so the 'theoretical' curves are partly post-hoc. However, this is not a circular reduction of the central result: the measured diffusivities do not depend on Eq. (17), and, as printed, Eq. (16) with τc/τ0 = 1 + 0.5 εf^4 gives at most ≈1.02 for κt/κt0, so it cannot even produce the 10–16% enhancements in Tables 1–2. The discrepancy with rotating stratified turbulence (Appendix A) is acknowledged as a limitation and attributed to rotational suppression without quantitative test; that is a correctness/generality concern, not a circularity. The self-citation to Rogachevskii et al. (2025) supplies the theoretical framework but is not the sole support for the paper's empirical findings, so it is not load-bearing circularity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central measurement is directly simulated, but the interpretation imports a companion theory and an empirical fit from the same runs. No new physical entities are introduced.

free parameters (2)
  • Coefficient in empirical correlation-time relation (Eq. 17) = 0.5
    Fitted to correlation-time data at Re=13 in Figure 6; used as input to the theoretical curves in Figure 7.
  • Power-law exponent in empirical correlation-time relation (Eq. 17) = 4
    Chosen as epsilon_f^4 to match the dotted lines in Figure 6; not derived from theory.
assumptions (5)
  • domain assumption The turbulent scalar and electromotive fluxes can be parameterized with local transport coefficients alpha, eta, and kappa (Eqs. 10 and 11).
    Central to the test-field extraction of kappa_t and eta_t; invoked in Section 2.4.
  • domain assumption Turbulence is homogeneous in the xy plane and transport coefficients are well defined at test-field wavenumber k_T = k_1 with scale separation k_f/k_1 = 5.1.
    Justifies z-averaging and single-scale measurement; scale dependence is only briefly checked in Section 3.4.
  • domain assumption The companion path-integral formulas for eta_t(H_K) and kappa_t(H_K), Eqs. (15) and (16) from Rogachevskii et al. (2025), are correct.
    Used in Section 3.3 to interpret the numerical results; not derived in this paper and authored in part by the same research group.
  • domain assumption Compressibility affects only the nonhelical contribution to turbulent diffusion, so small Mach number differences between helical and nonhelical runs can be ignored.
    Stated in Section 3.1 with a citation to Rogachevskii et al. (2018).
  • ad hoc to paper The correlation time increase with helicity is governed by Eq. (17), tau_c/tau_0 approximately 1 + 0.5 epsilon_f^4.
    Empirical fit to the same simulations; used as the basis for the theoretical curves in Figure 7.

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Pith. "Pith review of Helicity effect on turbulent passive and active scalar diffusivities." pith.science (2026). https://pith.science/paper/P6FTY6DC

@misc{pith2026250108879,
  author       = {Pith},
  title        = {Pith review of: Helicity effect on turbulent passive and active scalar diffusivities},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P6FTY6DC}},
  note         = {Machine review of arXiv:2501.08879}
}
abstract

Turbulent flows are known to produce enhanced effective magnetic and passive scalar diffusivities, which can fairly accurately be determined with numerical methods. It is now known that, if the flow is also helical, the effective magnetic diffusivity is reduced relative to the nonhelical value. Neither the usual second-order correlation approximation nor the various $\tau$ approaches have been able to capture this. Here we show that the helicity effect on the turbulent passive scalar diffusivity works in the opposite sense and leads to an enhancement. We have also demonstrated that the correlation time of the turbulent velocity field increases with the kinetic helicity. This is a key point in the theoretical interpretation of the obtained numerical results. Simulations in which helicity is being produced self-consistently by stratified rotating turbulence resulted in a turbulent passive scalar diffusivity that was found to be decreasing with increasing rotation rate.

Figures

Figures reproduced from arXiv: 2501.08879 by the authors.

Figure 1
Figure 1. Time series of κt (upper panel) and ηt (lower panel) for Runs A without helicity (solid black line) and with helicity (dashed red line) with Re = 2.4. The thick black and red horizontal lines denote the time-averaged values [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Similar to [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 5
Figure 5. Correlation time of turbulence computed from time integrals of velocity autocorrelation from runs with Re = 13 and different relative helicity ǫf = hu · ωi/kfu 2 rms. The result is shown in [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Dependence of χt for nonhelical (black symbols, solid line) and fully helical turbulence (red symbols, dashed line) as a function of Reynolds number Re = Pe/Pr with Pr = 1 in all cases. To make the error bars more visible, they have been exaggerated by a factor of 4. t…
Figure 6
Figure 6. Figure 6: Correlation time τc as function of ǫf from the late-time limit of Equation (13) (black symbols) and from Equation (14) (red symbols) normalized by the turnover time (urmskf) −1 for the same runs as in [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Dependencies of α (red solid line), ηt(0)−ηt (blue solid line) and κt(0) − κt (black solid line) on the fraction ǫf of the kinetic helicity for Re = 13. The theoretical depen￾dencies given by Equations (15)–(17) are shown by dashed and dotted blue and black curves. The…
Figure 9
Figure 9. Figure 9: Dependence of the fractional helicity, ǫf, and comparison of the values of α and the turbulent magnetic and passive scalar diffusivities with the earlier work of Brandenburg et al. (2012), in which kinetic helicity is being produced by the interaction with rotation and…

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Cited by 2 Pith papers

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Reference graph

Works this paper leans on

29 extracted references · 10 canonical work pages · cited by 2 Pith papers

  1. [1]

    2005, AN, 326, 787, doi: 10.1002/asna.200510414

    Brandenburg, A. 2005, AN, 326, 787, doi: 10.1002/asna.200510414

    doi:10.1002/asna.200510414 2005

  2. [2]

    H., & Kemel, K

    Brandenburg, A., R¨ adler, K. H., & Kemel, K. 2012, A&A, 539, A35, doi: 10.1051/0004-6361/201117871

    work page doi:10.1051/0004-6361/201117871 2012

  3. [3]

    2008, A&A, 482, 739, doi: 10.1051/0004-6361:200809365

    Brandenburg, A., R¨ adler, K.-H., & Schrinner, M. 2008, A&A, 482, 739, doi: 10.1051/0004-6361:200809365

    doi:10.1051/0004-6361:200809365 2008

  4. [4]

    2017, AN, 338, 790, doi: 10.1002/asna.201713384

    Brandenburg, A., Schober, J., & Rogachevskii, I. 2017, AN, 338, 790, doi: 10.1002/asna.201713384

    doi:10.1002/asna.201713384 2017

  5. [5]

    2002, GApFD, 96, 319, doi: 10.1080/03091920290032974

    Brandenburg, A., & Sokoloff, D. 2002, GApFD, 96, 319, doi: 10.1080/03091920290032974

    doi:10.1080/03091920290032974 2002

  6. [6]

    Brandenburg, A., Svedin, A., & Vasil, G. M. 2009, MNRAS, 395, 1599, doi: 10.1111/j.1365-2966.2009.14646.x

    arXiv 2009

  7. [7]

    G., Hnatich, M., Jurˇ ciˇ sinov´ a, E., et al

    Chkhetiani, O. G., Hnatich, M., Jurˇ ciˇ sinov´ a, E., et al. 2006, PhRvE, 74, 036310, doi: 10.1103/PhysRevE.74.036310 de Avillez, M. A., & Mac Low, M.-M. 2002, ApJ, 581, 1047, doi: 10.1086/344256

    doi:10.1103/physreve.74.036310 2006

  8. [8]

    2013, MNRAS, 432, 1651, doi: 10.1093/mnras/stt590

    Devlen, E., Brandenburg, A., & Mitra, D. 2013, MNRAS, 432, 1651, doi: 10.1093/mnras/stt590

    doi:10.1093/mnras/stt590 2013

Show all 29 references
  1. [9]

    Z., & Silant’ev, N

    Dolginov, A. Z., & Silant’ev, N. A. 1987, Zh. Eksp. Teor. Fiz., 93, 159

    1987

  2. [10]

    1997, Phys

    Elperin, T., Kleeorin, N., & Rogachevskii, I. 1997, Phys. Rev. E, 55, 2713, doi: 10.1103/PhysRevE.55.2713

    1997 doi

  3. [11]

    Furutsu, K. 1963, J. Res. Natl Bureau Standards – D. Radio Propagation, 67D, 303–323

    1963

  4. [12]

    2012, PhFl, 24, 075106

    Brandenburg, A. 2012, PhFl, 24, 075106

    2012

  5. [13]

    2009, ApJ, 706, 712, doi: 10.1088/0004-637X/706/1/712

    Hubbard, A., & Brandenburg, A. 2009, ApJ, 706, 712, doi: 10.1088/0004-637X/706/1/712

    2009 doi

  6. [14]

    2014, A&A, 568, A112, doi: 10.1051/0004-6361/201423499 K¨ apyl¨ a, P

    Rogachevskii, I. 2014, A&A, 568, A112, doi: 10.1051/0004-6361/201423499 K¨ apyl¨ a, P. J., & Singh, N. K. 2022, JFM, 952, R1, doi: 10.1017/jfm.2022.906

    2014 doi

  7. [15]

    Kishore, G., & Singh, N. K. 2025, ArXiv:2502.02946

    2025 arXiv

  8. [16]

    J., Tavakol, R., & Brandenburg, A

    Mitra, D., K¨ apyl¨ a, P. J., Tavakol, R., & Brandenburg, A. 2009, A&A, 495, 1, doi: 10.1051/0004-6361:200810359

    2009 doi

  9. [17]

    Mizerski, K. A. 2023, PhRvE, 107, 055205, doi: 10.1103/PhysRevE.107.055205

    2023 doi

  10. [18]

    1988, GApFD, 43, 149, doi: 10.1080/03091928808213623

    Nicklaus, B., & Stix, M. 1988, GApFD, 43, 149, doi: 10.1080/03091928808213623

    1988 doi

  11. [19]

    Novikov, E. A. 1965, JETP, 20, 1290 Pencil Code Collaboration, Brandenburg, A., Johansen, A., et al. 2021, J. Open Source Softw., 6, 2807, doi: 10.21105/joss.02807 R¨ adler, K.-H., Brandenburg, A., Del Sordo, F., &

    1965 doi

  12. [20]

    2011, PhRvE, 84, 046321, doi: 10.1103/PhysRevE.84.046321 R¨ adler, K.-H., Kleeorin, N., & Rogachevskii, I

    Rheinhardt, M. 2011, PhRvE, 84, 046321, doi: 10.1103/PhysRevE.84.046321 R¨ adler, K.-H., Kleeorin, N., & Rogachevskii, I. 2003, GApFD, 97, 249, doi: 10.1080/0309192031000151212

    2011 doi

  13. [21]

    2012, AN, 333, 71, doi: 10.1002/asna.201111625

    Rheinhardt, M., & Brandenburg, A. 2012, AN, 333, 71, doi: 10.1002/asna.201111625

    2012 doi

  14. [22]

    Rogachevskii, I. 2021, Introduction to turbulent transpor t of particles, temperature and magnetic fields: analytical methods for physicists and engineers (Cambridge University Press), doi: 10.1063/5.0188732,2024

    2021 doi

  15. [23]

    2018, JPlPh, 84, 735840502, doi: 10.1017/S0022377818000983 11

    Rogachevskii, I., Kleeorin, N., & Brandenburg, A. 2018, JPlPh, 84, 735840502, doi: 10.1017/S0022377818000983 11

    2018 doi

  16. [24]

    2025, ApJ, in press; arXiv:2501.13807, doi: 10.48550/arXiv.2501.13807 R¨ udiger, G

    Rogachevskii, I., Kleeorin, N., & Brandenburg, A. 2025, ApJ, in press; arXiv:2501.13807, doi: 10.48550/arXiv.2501.13807 R¨ udiger, G. 1989, Differential rotation and stellar convection. Sun and the solar stars (Berlin: Akademie Verlag)

    2025 doi arXiv

  17. [25]

    2018 , ApJ, 858, 124, doi: 10.3847/1538-4357/aaba75

    Schober, J., Rogachevskii, I., Brandenburg, A., et al. 2018 , ApJ, 858, 124, doi: 10.3847/1538-4357/aaba75

    2018 doi

  18. [26]

    , & Christensen, U

    Schrinner, M., R¨ adler, K.-H., Schmitt, D., Rheinhardt, M. , & Christensen, U. 2005, AN, 326, 245, doi: 10.1002/asna.200410384

    2005 doi

  19. [27]

    , & Christensen, U

    Schrinner, M., R¨ adler, K.-H., Schmitt, D., Rheinhardt, M. , & Christensen, U. R. 2007, GApFD, 101, 81, doi: 10.1080/03091920701345707

    2007 doi

  20. [28]

    2008, MNRAS, 385, L15, doi: 10.1111/j.1745-3933.2008.00423.x

    Sur, S., Brandenburg, A., & Subramanian, K. 2008, MNRAS, 385, L15, doi: 10.1111/j.1745-3933.2008.00423.x

    2008

  21. [29]

    1990, PhRvA, 41, 5683, doi: 10.1103/PhysRevA.41.5683

    Zhou, Y. 1990, PhRvA, 41, 5683, doi: 10.1103/PhysRevA.41.5683

    1990 doi

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