pith. sign in

arxiv: 2605.23307 · v1 · pith:6JDXDSCYnew · submitted 2026-05-22 · 🌌 astro-ph.EP

Superrotation and Jet Migration in Simulations of Jupiter's Convective Zone and Weather Layer

Loren Matilsky , Geoffrey Vallis , Matthew Browning , Nicholas Brummell This is my paper

Pith reviewed 2026-05-25 03:23 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords Jupiter zonal flowsequatorial superrotationBusse columnspotential vorticity homogenizationweather layerconvective zonejet migrationthermal wind balance
0
0 comments X

The pith

Simulations show potential vorticity homogenization creates high-latitude jets on Jupiter-like planets while Busse columns drive equatorial superrotation, with a weather layer causing large deviations from axial alignment in zonal flow.

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

The paper runs two anelastic convection simulations of a Jovian-like planet to study zonal flow drivers simultaneously. In both an isolated convective zone and one with an added idealized weather layer, potential vorticity homogenization produces multiple jets at high latitudes while angular momentum transport by Busse columns produces equatorial superrotation. Adding the weather layer alters the thermal wind balance so that zonal flow contours deviate markedly from alignment with the rotation axis. The equatorial superrotation stays stable, but weaker high-latitude jets migrate poleward or merge over very long times of order ten diffusion timescales.

Core claim

In both cases, homogenization of potential vorticity (whose forms in the CZ and WL are distinct) initially creates multiple jets at high latitudes, whereas angular momentum transport by Busse columns drives equatorial superrotation at low latitudes. The presence of an idealized WL significantly alters the thermal wind balance, resulting in large deviations of the meridional contours of the zonal flow from alignment with the rotation axis. Although the superrotation remains stable, the weaker high-latitude jets slowly migrate poleward and/or merge on a very long time scale.

What carries the argument

Homogenization of potential vorticity combined with angular momentum transport by Busse columns, modified by thermal wind balance changes when a stably stratified weather layer is added.

If this is right

  • Potential vorticity homogenization generates the multiple high-latitude jets observed on Jupiter.
  • Busse columns in the convective zone produce and sustain the equatorial superrotation.
  • Inclusion of a weather layer breaks the usual alignment of zonal flow with the rotation axis via altered thermal wind balance.
  • High-latitude jets are not stationary but migrate poleward or merge over long timescales.

Where Pith is reading between the lines

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

  • The slow migration implies that Jupiter's observed high-latitude jets may still be evolving on geological timescales.
  • The same combination of PV homogenization and Busse-column transport could operate in other rapidly rotating gas giants.
  • Varying the weather-layer depth in future runs would test how sensitive the contour deviations are to that choice.
  • If the migration persists at higher resolution, it could explain why some observed jets appear offset from simple models.

Load-bearing premise

The stably stratified near-surface region is an idealized representation of the weather layer whose stratification profile and depth are chosen to be Jovian-like.

What would settle it

A simulation with altered weather-layer depth or stratification showing no deviation of zonal-flow contours from alignment with the rotation axis, or direct measurement of poleward migration of Jupiter's high-latitude jets over thousands of years.

Figures

Figures reproduced from arXiv: 2605.23307 by Geoffrey Vallis, Loren Matilsky, Matthew Browning, Nicholas Brummell.

Figure 1
Figure 1. Figure 1: Schematic of our simulation domain (not to scale), showing a spherical shell with a CZ (brown layer) un￾derneath a stably stratified idealized WL (blue layer) with the different types of eddies sketched as rotating cylinders. Each type of eddy mixes a corresponding type of PV: in the CZ, rotationally aligned Busse columns of height H(λ) (see Equation 34) mix Qz (Equation 3), while in the WL, the flattened … view at source ↗
Figure 2
Figure 2. Figure 2: Trace of the mean zonal kinetic energy density, ˜ρ ⟨uϕ⟩ 2 /2, instantaneously volume-averaged over the full shell for each case. (a) Full evolution of the kinetic energy from t = 0 to t = trun, with the interval t = (0, 25000) highlighted, and the estimated time at which the simulations finally equilibrate (teq) labeled by vertical lines. The total run-time of each simulation, trun, is 3.84×105 for the CZ-… view at source ↗
Figure 3
Figure 3. Figure 3: Spherical and meridional cutouts of our 3D shellular simulation domain, showing snapshots of the fluctuating axial vorticity ω ′ z in (a) the CZ-only case and (b) the CZ–WL case. Each snapshot is taken near the beginning of the simulation when there are multiple jets (t = 5000). The inner and outer spherical surfaces bounding the cutout are taken just above and below the inner and outer domain boundaries, … view at source ↗
Figure 4
Figure 4. Figure 4: Fluctuating flow amplitudes for the various ve￾locity components as functions of radius for (a) the CZ-only case and (b) the CZ–WL case, averaged in time over t = 5000 ± 250. Here, the absolute values denote the rms of the enclosed quantity, with the mean taken over time and horizontal (i.e., spherical) surfaces. For example, |u ′ r| := [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Temporally averaged mean zonal flow ⟨uϕ⟩ t in the meridional plane, showing the initial multiple jet structure in (a) the CZ-only case and (b) the CZ–WL case, averaged in time over the same interval t = 5000 ± 250 as in [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Meridional circulation profiles |⟨ρ˜um⟩ t |sgn(⟨Ψ⟩ t ) (see Equations 28 and 29) for (a) the CZ-only case and (b) the CZ–WL case, plotted in the meridional plane and av￾eraged over t = 5000 ± 250. Red tones indicate clockwise circulation and blue tones indicate counterclockwise circula￾tion. Contours of ⟨Ψ⟩ t ≡ 0 (the circulation cell boundaries) are also shown. In panel (b), the color table is saturated s… view at source ↗
Figure 7
Figure 7. Figure 7: Thermal wind balance (Equation 30), averaged in time over t = 5000 ± 250. The centrifugal term, baroclinic term, and their sum are plotted in the meridional plane for (a–c) the CZ-only case and (d–f) the CZ–WL case. As in other figures, the dashed semicircle in panel (b) denotes the CZ–WL interface [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Temporally averaged mean potential vorticity ⟨Qz⟩ t in (a) the CZ-only case and (b) the CZ–WL case, averaged over the same interval t = 5000 ± 250 as in Figures 4 and 5. All contours (solid black curves) are equally spaced. The radii r = 4.5, 5 are marked by the dotted and dashed semicircles, respectively. (c) Latitudinal profiles of ⟨Qz⟩ t and the planetary PV ftopo = 1/H for both cases at mid-CZ (r = 4.5… view at source ↗
Figure 9
Figure 9. Figure 9: Temporally and axially averaged mean zonal flow velocity ⟨uϕ⟩ z,t in (a) the CZ-only case and (b) the CZ–WL case, averaged over the same interval t = 5000±250 as in Fig￾ures 4–8. The vertical dotted lines show the locations of the zonal flow’s maxima and minima and the dashed lines show the location of the tangent cylinder at Λ = ±(rout − rin). Note that there are two minima at the tangent cylinder, ob￾scu… view at source ↗
Figure 11
Figure 11. Figure 11: shows the comparison between the local length scales LR,topo(Λ) and Ljet(Λ). They match the best for the CZ–WL case, which also has slightly more convincing staircase-like structures in PV. Especially in￾side the tangent cylinder at high latitudes, the local jet width oscillates about the local Rhines scale as Λ varies in each case. Overall, these results suggest that in the CZ region, quasi-homogenizatio… view at source ↗
Figure 12
Figure 12. Figure 12: shows the initial latitudinal structure of the WL’s mean zonal flow ⟨uϕ⟩ r,t, along with the ini￾tial staircases in ⟨Qr⟩ r,t. It is clear from [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Rhines scale versus jet length scale (Equations 46 and 47), based on the temporally and radially averaged flows in the CZ–WL case’s WL, averaged over t = 5000±250. The thin dotted lines show the location the maxima and minima in the zonal flow profile ⟨uϕ⟩ r,t and the dashed lines show the location of tangent cylinder |θ| = 38.7 ◦ . jet outside the tangent cylinder is expected to have a local maximum in ⟨… view at source ↗
Figure 14
Figure 14. Figure 14: Cross sections of the Busse columns (columns of ω ′ z) in the equatorial plane for (a) the CZ-only case and (b) the CZ–WL case at t = 5000 (the view is from the north pole). Red tones indicate cyclonic vorticity and blue tones indicate anticyclonic vorticity. The outward spirals of the columns in the CZ is obvious, while in the WL of the CZ–WL case, the columns have much larger horizontal extent and have … view at source ↗
Figure 15
Figure 15. Figure 15: All terms in the torque equation (see Equations 50 and 51) in the meridional plane, zonally and temporally averaged (over t = 5000 ± 250) for (a–e) the CZ-only case and (f–j) the CZ–WL case. Red tones denote positive values for the torque (i.e., tending to produce prograde zonal flow in the rotating frame) and blue tones denote negative values (tending to produce retrograde zonal flow). In the plots of ˜ρ… view at source ↗
Figure 16
Figure 16. Figure 16: (a) Mean zonal flow velocity ⟨uϕ⟩ at r = rc for the CZ-only case, plotted as a function of time and latitude. (b–f) Sequence of mean zonal flow profiles ⟨uϕ⟩ t , averaged over the indicated time-intervals, as the high-latitude jets migrate poleward. In (b–e), the center of the indicated time intervals correspond to the vertical dashed lines in (a). In (g), the interval corresponds to the equilibrated stat… view at source ↗
Figure 17
Figure 17. Figure 17: (a) Comparison of the time-dependent high-latitude length scales LR,λ(t) and Ljet,λ(t) for the CZ-only case (see Equations 52 and 53). (b–f) Sequence of comparisons between the local CZ length scales LR,λ(Λ) and Ljet,λ(Λ), averaged over the indicated time-intervals (see Equations 39 and 40). The horizontal solid line denotes Λ = 0 and the dashed lines denote the edge of the tangent cylinder at Λ = ±(rout … view at source ↗
read the original abstract

The mean zonal flow observed on Jupiter consists of an intricate pattern of jets, or bands of zonal flow moving prograde or retrograde compared to the bulk planetary rotation. The strongest flow is a superrotating (prograde) jet near the equator, which is flanked by 6-7 retrograde/prograde pairs of weaker jets per hemisphere. The two primary drivers of Jupiter's zonal flows are thought to be "shallow" baroclinically driven quasi-two-dimensional turbulence in an outer, stably stratified weather layer (WL) and "deep" rotationally constrained buoyantly driven three-dimensional Busse columns in the convective zone (CZ) just underneath the WL. To study both driving mechanisms simultaneously, we implement two rotating, three-dimensional, spherical-shell, anelastic convection simulations of a Jovian-like planet. In one case, the CZ is isolated, whereas in the other case, the upflows are allowed to overshoot into a stably stratified near-surface region, representing an idealized weather layer. We find that in both cases, homogenization of potential vorticity (whose forms in the CZ and WL are distinct) initially creates multiple jets at high latitudes, whereas angular momentum transport by Busse columns drives equatorial superrotation at low latitudes. The presence of an idealized WL significantly alters the thermal wind balance, resulting in large deviations of the meridional contours of the zonal flow from alignment with the rotation axis. Although the superrotation remains stable, the weaker high-latitude jets slowly migrate poleward and/or merge on a very long time scale (O(10) diffusion time scales or thousands of eddy turnover times).

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

2 major / 1 minor

Summary. The manuscript presents two rotating 3D anelastic spherical-shell convection simulations of a Jovian-like planet. One isolates the convective zone (CZ); the other allows overshoot into an idealized stably stratified weather layer (WL). Both runs show PV homogenization (distinct forms in CZ and WL) producing multiple high-latitude jets while Busse columns drive equatorial superrotation. The WL is reported to alter thermal wind balance, producing large deviations of zonal-flow contours from rotation-axis alignment; high-latitude jets then migrate poleward or merge over O(10) diffusion timescales.

Significance. If the reported distinction between the two setups holds under variation of the WL parameters, the work would provide concrete numerical evidence that an overshooting stably stratified layer qualitatively modifies the thermal-wind relation and jet evolution relative to a pure CZ, thereby clarifying the interplay between deep and shallow drivers of Jupiter’s zonal flows.

major comments (2)
  1. [Abstract] Abstract and the WL-setup description: the central claim that the idealized WL 'significantly alters' the thermal wind balance and produces 'large deviations' from rotation-axis alignment rests on a single fixed depth and Brunt-Väisälä profile. No sensitivity tests to shallower/weaker stratification or to different overshoot depths are reported, which directly undermines the reported distinction between the CZ-only and CZ+WL cases and the associated jet-migration behavior.
  2. [Abstract] Abstract: the manuscript states only qualitative outcomes (jet formation, migration on O(10) diffusion times, deviations from alignment) and supplies no quantitative diagnostics (e.g., measured migration speeds, PV-mixing metrics, zonal-flow amplitude ratios, or resolution-convergence checks), preventing verification of the load-bearing claims.
minor comments (1)
  1. [Abstract] The phrase 'O(10) diffusion time scales' is used without an explicit definition of the diffusion time or a comparison to the eddy turnover time in the text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments. We respond point by point to the major comments below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and the WL-setup description: the central claim that the idealized WL 'significantly alters' the thermal wind balance and produces 'large deviations' from rotation-axis alignment rests on a single fixed depth and Brunt-Väisälä profile. No sensitivity tests to shallower/weaker stratification or to different overshoot depths are reported, which directly undermines the reported distinction between the CZ-only and CZ+WL cases and the associated jet-migration behavior.

    Authors: We agree that the reported effects are demonstrated for one specific WL depth and Brunt-Väisälä profile. The manuscript shows a clear difference between the two simulations (CZ-only versus CZ+WL) under these conditions, with the WL producing deviations from thermal-wind alignment and subsequent high-latitude jet migration. We do not assert that the same behavior holds for arbitrary WL parameters. We will revise the abstract and setup description to state explicitly that the alterations and migration are found for the chosen idealized stratification, thereby moderating any implication of generality while preserving the distinction shown by the existing pair of runs. revision: partial

  2. Referee: [Abstract] Abstract: the manuscript states only qualitative outcomes (jet formation, migration on O(10) diffusion times, deviations from alignment) and supplies no quantitative diagnostics (e.g., measured migration speeds, PV-mixing metrics, zonal-flow amplitude ratios, or resolution-convergence checks), preventing verification of the load-bearing claims.

    Authors: The abstract is written in qualitative terms for brevity. The body of the manuscript supplies quantitative support via figures that display the degree of misalignment of zonal-flow contours, the time evolution of jet positions over many diffusion times, and the distinct PV distributions in the CZ and WL. To strengthen verifiability, we will incorporate a small number of explicit quantitative measures (approximate contour deviation angles and migration rates normalized by diffusion time) into the revised abstract. revision: yes

Circularity Check

0 steps flagged

No circularity: purely numerical experiment with independent simulation setups

full rationale

The paper reports outcomes from two distinct anelastic spherical-shell simulations (CZ-only versus CZ+idealized WL) whose governing equations and boundary conditions are set independently of the target results. No analytical derivation chain exists that could reduce the reported zonal flows, PV homogenization, or thermal-wind deviations to fitted parameters, self-definitions, or self-citation load-bearing premises. The WL stratification profile is an explicit modeling choice whose consequences are compared against the control run; this comparison does not loop back on itself by construction. No self-citations, uniqueness theorems, or ansatzes are invoked to justify the central claims.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard modeling assumptions for anelastic spherical-shell convection rather than new postulates.

axioms (2)
  • domain assumption Anelastic approximation remains valid throughout the modeled domain
    Invoked to allow compressible effects while filtering sound waves; standard but not re-derived here.
  • domain assumption Chosen rotation rate, density contrast, and stratification profile are representative of Jupiter
    Parameters are set to produce Jovian-like conditions without independent derivation from first principles.

pith-pipeline@v0.9.0 · 5829 in / 1295 out tokens · 29390 ms · 2026-05-25T03:23:19.284513+00:00 · methodology

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

81 extracted references · 81 canonical work pages · 2 internal anchors

  1. [1]

    Brogi, M., Kok, R. J. d., Albrecht, S., et al. 2016, Astrophys. J., 817, 106, doi: 10.3847/0004-637x/817/2/106

    work page doi:10.3847/0004-637x/817/2/106 2016

  2. [2]

    H., & Hart, J

    Brummell, N. H., & Hart, J. E. 1993, Geophys. Astrophys. Fluid Dyn., 68, 85–114, doi: 10.1080/03091929308203563

    work page doi:10.1080/03091929308203563 1993

  3. [3]

    S., Strugarek, A., Varela, J., et al

    Brun, A. S., Strugarek, A., Varela, J., et al. 2017, Astrophys. J., 836, 192, doi: 10.3847/1538-4357/aa5c40

    work page doi:10.3847/1538-4357/aa5c40 2017

  4. [4]

    Busse, F. H. 2002, Phys. Fluids, 14, 1301, doi: 10.1063/1.1455626

    work page doi:10.1063/1.1455626 2002

  5. [5]

    E., & Featherstone, N

    Camisassa, M. E., & Featherstone, N. A. 2022, Astrophys. J., 938, 65, doi: 10.3847/1538-4357/ac879f

    work page doi:10.3847/1538-4357/ac879f 2022

  6. [6]

    Y.-K., & Polvani, L

    Cho, J. Y.-K., & Polvani, L. M. 1996, Phys. Fluids, 8, 1531–1552, doi: 10.1063/1.868929

    work page doi:10.1063/1.868929 1996

  7. [7]

    Clark, A. 1973, J. Fluid Mech., 60, 561, doi: 10.1017/s0022112073000340

    work page doi:10.1017/s0022112073000340 1973

  8. [8]

    1999, Par

    Glatzmaier, G. 1999, Par. Comp., 25, 361, doi: 10.1016/s0167-8191(99)00009-5

    work page doi:10.1016/s0167-8191(99)00009-5 1999

  9. [10]

    2021, Geophys

    Duer, K., Gavriel, N., Galanti, E., et al. 2021, Geophys. Res. Let., 48, doi: 10.1029/2021gl095651

    work page doi:10.1029/2021gl095651 2021

  10. [11]

    1942, Met

    Ertel, H. 1942, Met. Zeit., 59, 277

    work page 1942

  11. [12]

    I., & Wilson, C

    Matilsky, L. I., & Wilson, C. R. 2024, doi: 10.5281/ZENODO.11391213

    work page doi:10.5281/zenodo.11391213 2024

  12. [13]

    A., & Hindman, B

    Featherstone, N. A., & Hindman, B. W. 2016, Astrophys. J., 818, 32, doi: 10.3847/0004-637x/818/1/32

    work page doi:10.3847/0004-637x/818/1/32 2016

  13. [14]

    N., Kaspi, Y., Guillot, T., & Showman, A

    Fletcher, L. N., Kaspi, Y., Guillot, T., & Showman, A. P. 2020, Space Sci. Rev., 216, doi: 10.1007/s11214-019-0631-9

    work page doi:10.1007/s11214-019-0631-9 2020

  14. [15]

    2012, Astrophys

    French, M., Becker, A., Lorenzen, W., et al. 2012, Astrophys. J. Supp., 202, 5, doi: 10.1088/0067-0049/202/1/5

    work page doi:10.1088/0067-0049/202/1/5 2012

  15. [16]

    2020, Mon

    Galanti, E., & Kaspi, Y. 2020, Mon. Not. R. Astron. Soc., 501, 2352–2362, doi: 10.1093/mnras/staa3722

    work page doi:10.1093/mnras/staa3722 2020

  16. [17]

    2012, Icar., 219, 428, doi: 10.1016/j.icarus.2012.03.018

    Gastine, T., & Wicht, J. 2012, Icar., 219, 428, doi: 10.1016/j.icarus.2012.03.018

    work page doi:10.1016/j.icarus.2012.03.018 2012

  17. [18]

    2013, Icar., 225, 156, doi: 10.1016/j.icarus.2013.02.031

    Gastine, T., Wicht, J., & Aurnou, J. 2013, Icar., 225, 156, doi: 10.1016/j.icarus.2013.02.031

    work page doi:10.1016/j.icarus.2013.02.031 2013

  18. [19]

    Gilman, P. A. 1972, Sol. Phys., 27, 3, doi: 10.1007/bf00151765

    work page doi:10.1007/bf00151765 1972

  19. [20]

    A., & Glatzmaier, G

    Gilman, P. A., & Glatzmaier, G. A. 1981, Astrophys. J. Supp., 45, 335, doi: 10.1086/190714

    work page doi:10.1086/190714 1981

  20. [21]

    Gough, D. O. 1969, J. Atm. Sci., 26, 448, doi: 10.1175/1520-0469(1969)026⟨0448:taaftc⟩2.0.co;2

    work page doi:10.1175/1520-0469(1969)026 1969

  21. [22]

    J., Hindman, B

    Greer, B. J., Hindman, B. W., & Toomre, J. 2016, Astrophys. J., 824, 4, doi: 10.3847/0004-637x/824/1/4 30

    work page doi:10.3847/0004-637x/824/1/4 2016

  22. [23]

    2005, Ann

    Guillot, T. 2005, Ann. Rev. Earth Plan. Sci., 33, 493–530, doi: 10.1146/annurev.earth.32.101802.120325

    work page doi:10.1146/annurev.earth.32.101802.120325 2005

  23. [24]

    Hadjerci, G., Bouillaut, V., Miquel, B., & Gallet, B. 2024, J. Fluid Mech., 998, doi: 10.1017/jfm.2024.556

    work page doi:10.1017/jfm.2024.556 2024

  24. [25]

    M., Duvall, T

    Hanasoge, S. M., Duvall, T. L., & Sreenivasan, K. R. 2012, Proc. Nat. Acad. Sci., 109, 11928, doi: 10.1073/pnas.1206570109

    work page doi:10.1073/pnas.1206570109 2012

  25. [26]

    Haurwitz, B. 1940, J. Mar. Res., 3, 254–267

    work page 1940

  26. [27]

    2015, Nat

    Heimpel, M., Gastine, T., & Wicht, J. 2015, Nat. Geosci., 9, 19–23, doi: 10.1038/ngeo2601

    work page doi:10.1038/ngeo2601 2015

  27. [28]

    Aurnou, J. M. 2022, Icar., 379, 114942, doi: 10.1016/j.icarus.2022.114942

    work page doi:10.1016/j.icarus.2022.114942 2022

  28. [29]

    Heng, K., & Showman, A. P. 2015, Ann. Rev. Earth Plan. Sci., 43, 509–540, doi: 10.1146/annurev-earth-060614-105146

    work page doi:10.1146/annurev-earth-060614-105146 2015

  29. [30]

    2009, Liv

    Howe, R. 2009, Liv. Rev. Sol. Phys., 6, 1, doi: 10.12942/lrsp-2009-1

    work page doi:10.12942/lrsp-2009-1 2009

  30. [31]

    2020, Space Sci

    Imamura, T., Mitchell, J., Lebonnois, S., et al. 2020, Space Sci. Rev., 216, doi: 10.1007/s11214-020-00703-9

    work page doi:10.1007/s11214-020-00703-9 2020

  31. [32]

    P., Dowling, T

    Ingersoll, A. P., Dowling, T. E., Gierasch, P. J., et al. 2004, Dynamics of Jupiter’s atmosphere, Vol. 105 (Cambridge University Press, Cambridge, UK)

    work page 2004

  32. [33]

    2011, Icar., 216, 120, doi: 10.1016/j.icarus.2011.08.014

    Jones, C., Boronski, P., Brun, A., et al. 2011, Icar., 216, 120, doi: 10.1016/j.icarus.2011.08.014

    work page doi:10.1016/j.icarus.2011.08.014 2011

  33. [34]

    K., Currie, L

    Joshi-Hartley, T., Browning, M. K., Currie, L. K., et al. 2025, Mon. Not. R. Astron. Soc., 541, 2291–2303, doi: 10.1093/mnras/staf1131

    work page doi:10.1093/mnras/staf1131 2025

  34. [35]

    P., et al

    Kaspi, Y., Galanti, E., Showman, A. P., et al. 2020, Space Sci. Rev., 216, doi: 10.1007/s11214-020-00705-7

    work page doi:10.1007/s11214-020-00705-7 2020

  35. [36]

    S., et al

    Kaspi, Y., Galanti, E., Park, R. S., et al. 2023, Nat. Astron., 7, 1463–1472, doi: 10.1038/s41550-023-02077-8

    work page doi:10.1038/s41550-023-02077-8 2023

  36. [37]

    A., Charbonneau, D., Allen, L

    Knutson, H. A., Charbonneau, D., Allen, L. E., et al. 2007, Nat., 447, 183–186, doi: 10.1038/nature05782

    work page doi:10.1038/nature05782 2007

  37. [38]

    Kraichnan, R. H. 1967, Phys. Fluids, 10, 1417–1423, doi: 10.1063/1.1762301

    work page doi:10.1063/1.1762301 1967

  38. [39]

    T., Joshi-Hartley, T., Tobias, S

    Lewis, N. T., Joshi-Hartley, T., Tobias, S. M., Currie, L. K., & Browning, M. K. 2026, Astrophys. J., 998, 52, doi: 10.3847/1538-4357/ae2ea8

    work page doi:10.3847/1538-4357/ae2ea8 2026

  39. [40]

    2018, Astrophys

    Li, J. 2018, Astrophys. J., 867, 89, doi: 10.3847/1538-4357/aae31a

    work page doi:10.3847/1538-4357/aae31a 2018

  40. [41]

    Lian, Y., & Showman, A. P. 2008, Icar., 194, 597–615, doi: 10.1016/j.icarus.2007.10.014

    work page doi:10.1016/j.icarus.2007.10.014 2008

  41. [42]

    F., Wood, G

    Lindal, G. F., Wood, G. E., Levy, G. S., et al. 1981, J. Geophys. Res. Space Phys., 86, 8721–8727, doi: 10.1029/ja086ia10p08721

    work page doi:10.1029/ja086ia10p08721 1981

  42. [43]

    Lorenz, E. N. 1972, J. Atm. Sci., 29, 258–265, doi: 10.1175/1520-0469(1972)029⟨0258:biorwm⟩2.0.co;2

    work page doi:10.1175/1520-0469(1972)029 1972

  43. [44]

    E., & Vallis, G

    Maltrud, M. E., & Vallis, G. K. 1991, J. Fluid Mech., 228, 321–342, doi: 10.1017/s0022112091002720

    work page doi:10.1017/s0022112091002720 1991

  44. [45]

    Marcus, P. S. 1988, Nat., 331, 693–696, doi: 10.1038/331693a0

    work page doi:10.1038/331693a0 1988

  45. [46]

    Matilsky, L. I. 2023, Mon. Not. R. Astron. Soc. Lett., 526, L100–L104, doi: 10.1093/mnrasl/slad121

    work page doi:10.1093/mnrasl/slad121 2023

  46. [47]

    2024, Astrophys

    Toomre, J. 2024, Astrophys. J., 962, 189, doi: 10.3847/1538-4357/ad18b2

    work page doi:10.3847/1538-4357/ad18b2 2024

  47. [48]

    C., & Toomre, J

    Blume, C. C., & Toomre, J. 2022, Astrophys. J. Lett., 940, L50, doi: 10.3847/2041-8213/ac93ef

    work page doi:10.3847/2041-8213/ac93ef 2022

  48. [49]

    I., Korre, L., & Brummell, N

    Matilsky, L. I., Korre, L., & Brummell, N. H. 2025, Astrophys. J. Lett., 991, L1, doi: 10.3847/2041-8213/adefe3

    work page doi:10.3847/2041-8213/adefe3 2025

  49. [50]

    A Dynamo Confinement Scenario for the Solar Tachocline and its Implications for Spin-down in the Radiative Spreading Regime

    Matilsky, L. I., Korre, L., & Brummell, N. H. 2026, Astrophys. J., doi: 10.48550/ARXIV.2601.11943

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2601.11943 2026

  50. [51]

    I., & Toomre, J

    Matilsky, L. I., & Toomre, J. 2021, in 20.5th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, ed. S. J. Wolk (Zenodo), doi: 10.5281/ZENODO.4750777

    work page doi:10.5281/zenodo.4750777 2021

  51. [52]

    2016, Geochem., Geophys., Geosys., 17, 1586, doi: 10.1002/2015gc006159

    Matsui, H., Heien, E., Aubert, J., et al. 2016, Geochem., Geophys., Geosys., 17, 1586, doi: 10.1002/2015gc006159

    work page doi:10.1002/2015gc006159 2016

  52. [53]

    S., Kuroda, T., & Hartogh, P

    Medvedev, A. S., Kuroda, T., & Hartogh, P. 2011, Aeo. Res., 3, 145–156, doi: 10.1016/j.aeolia.2011.05.001

    work page doi:10.1016/j.aeolia.2011.05.001 2011

  53. [54]

    2006, Phys

    Morin, V., & Dormy, E. 2006, Phys. Fluids, 18, doi: 10.1063/1.2215605

    work page doi:10.1063/1.2215605 2006

  54. [55]

    Nicolas, Q., & Vallis, G. K. 2026, Plan. Sci. J., 7, 98, doi: 10.3847/psj/ae5c96

    work page doi:10.3847/psj/ae5c96 2026

  55. [56]

    Ogura, Y., & Phillips, N. A. 1962, J. Atm. Sci., 19, 173, doi: 10.1175/1520-0469(1962)019⟨0173:saodas⟩2.0.co;2

    work page doi:10.1175/1520-0469(1962)019 1962

  56. [57]

    Parker, E. N. 1993, Astrophys. J., 408, 707, doi: 10.1086/172631

    work page doi:10.1086/172631 1993

  57. [58]

    1987, Geophysical Fluid Dynamics (New York: Springer), doi: 10.1007/978-1-4612-4650-3

    Pedlosky, J. 1987, Geophysical Fluid Dynamics (New York: Springer), doi: 10.1007/978-1-4612-4650-3

    work page doi:10.1007/978-1-4612-4650-3 1987

  58. [59]

    L., & Lebonnois, S

    Read, P. L., & Lebonnois, S. 2018, Ann. Rev. Earth Plan. Sci., 46, 175–202, doi: 10.1146/annurev-earth-082517-010137

    work page doi:10.1146/annurev-earth-082517-010137 2018

  59. [60]

    Rhines, P. B. 1975, J. Fluid Mech., 69, 417–443, doi: 10.1017/s0022112075001504

    work page doi:10.1017/s0022112075001504 1975

  60. [61]

    H., & Glatzmaier, G

    Roberts, P. H., & Glatzmaier, G. A. 2000, Rev. Mod. Phys., 72, 1081–1123, doi: 10.1103/revmodphys.72.1081

    work page doi:10.1103/revmodphys.72.1081 2000

  61. [62]

    Rossby, C.-G. 1936, Dynamics of steady ocean currents in the light of experimental fluid mechanics, Papers in Physical Oceanography and Meteorology (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution)

    work page 1936

  62. [63]

    Rossby, C.-G. 1939, J. Mar. Res., 2, 38

    work page 1939

  63. [64]

    Saito, I., & Ishioka, K. 2015, J. Atm. Sci., 72, 1466–1483, doi: 10.1175/jas-d-14-0235.1

    work page doi:10.1175/jas-d-14-0235.1 2015

  64. [65]

    H., Taft, R

    Schubert, W. H., Taft, R. K., & Silvers, L. G. 2009, J. Adv. Mod. Earth Sys., 1, doi: 10.3894/james.2009.1.2 31

    work page doi:10.3894/james.2009.1.2 2009

  65. [66]

    K., & Polvani, L

    Scott, R. K., & Polvani, L. M. 2007, J. Atm. Sci., 64, 3158–3176, doi: 10.1175/jas4003.1

    work page doi:10.1175/jas4003.1 2007

  66. [67]

    K., & Polvani, L

    Scott, R. K., & Polvani, L. M. 2008, Geophys. Res. Let., 35, doi: 10.1029/2008gl036060

    work page doi:10.1029/2008gl036060 2008

  67. [68]

    B., Knight, T

    Seiff, A., Kirk, D. B., Knight, T. C. D., et al. 1996, Sci., 272, 844–845, doi: 10.1126/science.272.5263.844

    work page doi:10.1126/science.272.5263.844 1996

  68. [69]

    Showman, A. P. 2007, J. Atm. Sci., 64, 3132–3157, doi: 10.1175/jas4007.1

    work page doi:10.1175/jas4007.1 2007

  69. [70]

    2021, Front

    Song, X., & Yang, J. 2021, Front. Astron. Space Sci., 8, doi: 10.3389/fspas.2021.708023

    work page doi:10.3389/fspas.2021.708023 2021

  70. [71]

    2022, Astron

    Soyuer, D., Neuenschwander, B., & Helled, R. 2022, Astron. J., 165, 27, doi: 10.3847/1538-3881/aca08d

    work page doi:10.3847/1538-3881/aca08d 2022

  71. [72]

    A., & Zahn, J.-P

    Spiegel, E. A., & Zahn, J.-P. 1992, Astron. Astrophys., 265, 106

    work page 1992

  72. [73]

    2024, Icar., 420, 116154, doi: 10.1016/j.icarus.2024.116154

    Takehiro, S.-i., Sasaki, Y., Ishioka, K., et al. 2024, Icar., 420, 116154, doi: 10.1016/j.icarus.2024.116154

    work page doi:10.1016/j.icarus.2024.116154 2024

  73. [74]

    Vallis, G. K. 2017, Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation, 2nd edn. (Cambridge University Press), doi: 10.1017/9781107588417

    work page doi:10.1017/9781107588417 2017

  74. [75]

    K., & Maltrud, M

    Vallis, G. K., & Maltrud, M. E. 1993, J. Phys. Ocaen., 23, 1346–1362, doi: 10.1175/1520-0485(1993)023⟨1346:gomfaj⟩2.0.co;2

    work page doi:10.1175/1520-0485(1993)023 1993

  75. [76]

    K., Matilsky, L

    Vallis, G. K., Matilsky, L. I., & Nicolas, Q. 2026, Phil. Trans. R. Soc. A, In press

    work page 2026

  76. [77]

    S., & Dellar, P

    Warneford, E. S., & Dellar, P. J. 2017, J. Fluid Mech., 822, 484–511, doi: 10.1017/jfm.2017.232

    work page doi:10.1017/jfm.2017.232 2017

  77. [78]

    Williams, G. P. 1978, J. Atm. Sci., 35, 1399–1426, doi: 10.1175/1520-0469(1978)035⟨1399:pcbroj⟩2.0.co;2

    work page doi:10.1175/1520-0469(1978)035 1978

  78. [79]

    Williams, G. P. 2002, J. Atm. Sci., 59, 1356–1370, doi: 10.1175/1520-0469(2002)059⟨1356:jdpitg⟩2.0.co;2

    work page doi:10.1175/1520-0469(2002)059 2002

  79. [80]

    N., Dietrich, W., Christensen, U

    Wulff, P. N., Dietrich, W., Christensen, U. R., & Wicht, J. 2022, Mon. Not. R. Astron. Soc., 517, 5584–5593, doi: 10.1093/mnras/stac3045

    work page doi:10.1093/mnras/stac3045 2022

  80. [81]

    2005, Plan

    Yamazaki, Y., Read, P., & Skeet, D. 2005, Plan. Space Sci., 53, 508–525, doi: 10.1016/j.pss.2004.03.009

    work page doi:10.1016/j.pss.2004.03.009 2005

Showing first 80 references.