Pith. sign in

REVIEW 3 major objections 5 minor 90 references

From Geostrophic to Magnetically-Damped Turbulence in Liquid Metal Rotating Magnetoconvection

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read Direct velocity measurements of magnetostrophic liquid-metal convection show a sharp regime switch near N_ℓ ≈ 3, from geostrophic-turbulence scaling to a magnetically damped law — and Earth's core likely sits in the damped regime.

desk verdict First direct velocity measurements in liquid-metal RMC show a believable N_l ~ 3 damping transition; the core extrapolation leans on a shaky scale assumption. read the letter →

arxiv 2509.03689 v1 pith:CUK6Z75M submitted 2025-09-03 physics.flu-dyn

Tao Liu , Yufan Xu , Jewel A. Abbate , Jonathan S. Cheng , Jonathan M. Aurnou This is my paper
classification physics.flu-dyn PACS 47.65.-d91.25.Cw
keywords rotatingmagnetoconvectionliquidgalliummagnetostrophicbalancemagneticdampinglocalinteractionparameterdiffusivity-freescalinggeostrophicturbulenceEarth'scoreconvection
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

This paper reports the first direct velocity measurements of magnetostrophic convection — rotating convection in which Coriolis and Lorentz forces both reach leading order — made in liquid gallium with a strong axial magnetic field (Elsasser number Λ = 1) at moderate rotation rates (Ekman numbers 10^-4 to 10^-5). The authors find that once the local interaction parameter N_ℓ, the ratio of magnetic to inertial forces on the convective eddy scale, exceeds about 3, measured flow speeds fall below the geostrophic-turbulence (diffusivity-free) prediction and follow instead Re ≈ 2 N_ℓ^-1/2 Re_df; below that threshold the same measurements match the diffusivity-free rotating convection scaling. The magnetic slowdown comes with enhanced heat transfer, which the authors attribute to more coherent, vertically aligned flow. Extrapolating the damped scaling, they predict convection in Earth's core operates in the magnetically damped regime at Rayleigh numbers between 10^24 and 10^26.

What carries the argument

The load-bearing object is the local interaction parameter, N_ℓ = σB^2ℓ/(ρU) — the ratio of quasi-static Lorentz force to fluid inertia evaluated on the convective eddy scale, built from the measured peak vertical velocity. Its input-only counterpart, the convective interaction parameter N_c ≈ Λ/Ro_c, tracks N_ℓ almost linearly (N_ℓ ≈ 1.11 N_c^1.14) away from onset, so the laboratory regime boundary can be projected onto planetary parameters without velocity data. The comparison baseline is the diffusivity-free rotating-convection Reynolds number Re_df = C_J^2/5 Ro_c Re_ff, built from the established diffusivity-free heat-transfer constant; the empirical collapse Re/Re_df ≈ 2 N_ℓ^-1/2 define

What would settle it

A decisive test: run rotating magnetoconvection at Ekman numbers below 10^-5 (or a DNS at such parameters) with Λ ≈ 1 and measure both the RMS velocity and the convective eddy scale directly in the N_ℓ ≥ 3 regime. If the eddy scale deviates from ℓ ≈ Ro_c H, or if Re/Re_df departs from the fitted 2 N_ℓ^-1/2 curve, the input-only scaling (23) — and with it the core Rayleigh-number estimate near 5×10^25 — would need revision.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is a regime boundary: rotating magnetoconvection in a quasi-static, low-Prandtl liquid metal crosses from geostrophic turbulence into a magnetically damped state at local interaction parameter N_ℓ ≈ 3 (fit values N_ℓ ≈ 4.0, N_c ≈ 3.1). Above the threshold, root-mean-square vertical velocities fall below the diffusivity-free rotating convection scaling Re_df and collapse onto Re_MD ≈ 2 N_ℓ^-1/2 Re_df — velocities decay roughly as the inverse square root of magnetic forcing. Purely in input parameters this is Re_MD = 4C_J^4/5 (Ra Ek / Pr)^3/2 Ek^1/2 / Λ, with 4C_J^4/5 ≈ 0.3. Applied to Earth's core (Ek = 10^-15, Pr = 0.1, Λ = 0.1–10), it predicts convect

Load-bearing premise

The core prediction assumes the convective eddies keep the size predicted by rotating-convection theory (a fraction of the layer depth set by the convective Rossby number, ℓ ≈ Ro_c H) even in the magnetically damped regime — exactly where that geostrophic scale estimate is least secure.

Editorial extensions

If this is right

  • Rotating magnetoconvection velocities follow the diffusivity-free geostrophic scaling when N_ℓ ≲ 3 and drop below it as Re ≈ 2 N_ℓ^-1/2 Re_df when N_ℓ ≳ 3.
  • In the damped regime convective velocities fall while heat transfer rises: the same axially aligned, more coherent flow both transports heat better and moves more slowly.
  • Earth's core convection is predicted to lie in the magnetically damped regime, with Rayleigh number between 10^24 and 10^26 (center ≈ 5×10^25) and convective Rossby number ≈ 2×10^-2.
  • The input-only form Re_MD = 4C_J^4/5 (Ra Ek / Pr)^3/2 Ek^1/2 / Λ lets core convective speeds be estimated from externally estimable parameters alone, without direct velocity measurements.
  • Dynamo simulations at Ek ≳ 10^-5 (weak-field regime) should track the diffusivity-free rotating convection scaling, while strong-field models at Ek ≲ 10^-5 should show larger-scale, magnetically damped convective velocities.

Reading between the lines

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

  • The N_ℓ ≈ 3 threshold transfers as a regime test: any rotating magnetized convective system — other planetary cores, subsurface oceans — with local interaction parameter above about 3 should be parameterized by magnetic damping rather than geostrophic turbulence.
  • Whether the N_ℓ^-1/2 damping law survives at core-like magnetic Reynolds numbers, beyond the quasi-static limit this experiment operates in, is the open question that would firm up the geophysical extrapolation.
  • A testable signature of the mechanism: in the damped regime the flow should become more anisotropic (preferentially axially coherent), measurable with multi-axis velocity diagnostics in future liquid-metal experiments.
  • Because the input-only scaling (23) inherits the geostrophic scale assumption ℓ ≈ Ro_c H, a simulation that measures the true eddy scale in the damped regime would show whether the predicted core Rayleigh number shifts.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper presents rotating magnetoconvection (RMC) experiments in liquid gallium at Ek = 10^-4-10^-5 and Elsasser number Lambda = 1, together with Lambda = 0 rotating-convection controls. Vertical velocities are measured with a single UDV chord and heat fluxes with thermistors. The central claim is that RMC velocities follow the geostrophic-turbulent CIA and diffusivity-free scalings when the local interaction parameter N_l is below about 3, and are magnetically damped, falling below those scalings as Re ~ 2 Re_df N_l^{-1/2}, when N_l is above about 3; this damping coexists with enhanced heat transfer attributed to axially coherent structures. The empirical fit is then recast into an 'input-only' scaling, Eq. (23), using the geostrophic scale l ~ Roc H, and extrapolated to Earth's core to predict convection-scale flow in the magnetically damped regime at Ra ~ 10^24-10^26.

Significance. If established, this would be the first direct velocity measurement of magnetostrophic liquid-metal convection and a valuable experimental anchor for rotating magnetoconvection scaling laws. The damping is visible in the raw data, the comparison against pre-existing CIA/DF scalings is appropriate, and the appendix data tables support reproducibility. The heat-transfer enhancement concurrent with velocity suppression is an interesting, falsifiable observation. The paper's main limitations are two load-bearing gaps: the length scale used to evaluate N_l is not stated, and the core extrapolation assumes the geostrophic scale l ~ Roc H holds in the damped regime, which is precisely where the paper's own data show larger, slower structures. In addition, Eq. (23) is described as input-only although its constants are calibrated on the same velocity data. With these points fixed or carefully qualified, the central result is likely to be a significant contribution.

major comments (3)
  1. [Sec. 5, Eq. (22)] The derivation of the input-only scaling (23) substitutes l = Roc H into Eq. (7). This scale relation is introduced in Sec. 2.1 before Eq. (8) under the explicit assumption that the flow is in or near the geostrophic-turbulence regime. It is then applied in Eq. (22) to the N_l >= 3 magnetically damped regime, whose defining property is Lorentz dominance. The paper's own Hovmoller data in Fig. 5(d) show larger, slower, axially coherent structures in the damped cases, so the geostrophic scale is least secure exactly where the prediction is made. This is not a cosmetic issue: with alpha = -1/2, Eq. (22) gives Re_MD ~ c^2 Re_df^2 / [Ch (l/H)], so a scale differing from Roc H changes Re_MD multiplicatively and shifts the Rayleigh-number range obtained from the intersection in Fig. 11(b). Please either justify l ~ Roc H in the damped regime with a scale measurement or a separate estimate, or p
  2. [Sec. 3.1 and Sec. 4.2.1, Eq. (7)] The local interaction parameter N_l is central to the regime transition and to the fits in Figs. 7-10, but the length scale l entering Eq. (7) is never defined. Sec. 3.1 states only that uz,max is used for U; the data tables list Re_z but not N_l or l. Without this information the reported threshold N_l ~ 3 and the fit Re_MD = c Re_df N_l^alpha cannot be reproduced or independently checked. The sentence after Fig. 8 that N_l 'makes no assumptions on flow velocities or scales' is also misleading: an operational choice of l, or a measured correlation length, is required. Please define l explicitly, state its value for each case (or table it), and if it is not measured, state the assumption.
  3. [Sec. 5, Eq. (23)] Eq. (23) is presented as a predictive formulation depending solely on externally estimable parameters, but the constants c ~ 2 and alpha ~ -1/2 in Eq. (19) are obtained by fitting the same RMC velocity data. Eq. (23) is therefore an algebraic rearrangement of an empirical fit, not an independent ab initio prediction. This does not make the damping observation circular, because the normalization Re_df and the threshold comparison use pre-existing scalings, but it should be stated transparently wherever 'input-only' or 'without direct velocity measurements' appears. The core Ra values inherit both the fit uncertainty and the scale assumption of the previous comment.
minor comments (5)
  1. [Abstract and Sec. 5] The abstract gives Ra in the range 10^24-10^26, while Sec. 5 and Fig. 11 state the overlap extends to 5 x 10^26. Please unify the quoted range.
  2. [Sec. 3.1 and Fig. 7 caption] Typographical errors: 'Elssaser number' should be 'Elsasser number' in Sec. 3.1; 'superficiality' in the Fig. 7 caption should be 'supercriticality'.
  3. [Sec. 5, Eq. (21)] Eq. (21) is called a unified prediction, but the piecewise form uses N_l, which depends on the measured velocity and scale. Clarify that Eq. (23) is the input-only form and state when each expression is intended to be used.
  4. [Sec. 3.1 and Sec. 4.2] The velocity measurement is axial-only and along a single chord at 2R/3, but Re_z is compared with scaling laws written for the total Reynolds number Re. A sentence justifying the substitution and noting the possible bias for anisotropic structures would help the reader judge the quantitative agreement.
  5. [Appendix tables] Several RMC entries list no Re_z value. Please state whether those velocities were too small to measure, and explicitly indicate which cases were included in the fits shown in Figs. 7-10.

Circularity Check

1 steps flagged · score 6.0 of 10

The measured magnetic damping is not circular, but the 'input-only' core prediction (Eq. 23) is an algebraic rearrangement of the same fitted relation and inherits its fitted constants.

  1. fitted input called prediction [Sec. 5, Eqs. (19)-(23), Figs. 10-11b]
    "The best fit to (19) is shown as the black dotted line in Figure 10, with corresponding best fit parameter values of c = 1.72 ± 0.14 ≈ 2 and α = −0.46 ± 0.05 ≈ −1/2. ... ReM D = cRed f(σB^2 ℓ/ρU)^α = cRed f(σB^2(RocH)/ρU)^α = c(C^{2/5}_J RocRef f)(ChRo c/ReM D)^α ... Recasting (22) using our best-fit empirical values, c ≈ 2 and α ≈ −1/2, then yields: ReM D = 4C^{4/5}_J (RaEk/Pr)^{3/2} Ek^{1/2}/Λ ... Expression (23) captures the Nℓ ≳ 3 dependence of the magnetically damped Reynolds number solely using input parameters."

    Equation (23) is not a new input-only derivation: it is obtained by substituting the definition of Nℓ into the empirical fit (19), replacing the velocity in Nℓ with ReM D itself via ChRoc/ReM D, and then inserting the same fitted constants c≈2 and α≈−1/2. The algebra simply inverts the measured ReM D vs Nℓ relation into a formula in Ra, Ek, Pr, Λ. Thus the 'prediction' for Earth's core in Fig. 11b is the laboratory fit evaluated at core parameters; it is statistically forced by the fit and contains no independent information beyond that fit. Calling Eq. (23) 'solely using input parameters' obscures that the prefactor 4C^{4/5}_J ≈ 0.3 encodes c² from the fit to the very velocity data that the formula is then used to predict.

full rationale

The core experimental finding — suppression of RMC velocities below geostrophic RC scalings for Nℓ ≳ 3 — is genuine empirical evidence: the data are compared against pre-existing, parameter-free CIA (Eq. 11) and DF (Eq. 13) scalings, and the damping itself is not an artifact of the comparison. The circularity is confined to the packaging of this fit as an input-only predictive law. Eq. (19) fits c and α to the Re/Re_df vs Nℓ data; Eq. (22) then rewrites Nℓ using ℓ=RocH and U=ReM D, which is an identity; combining this with the same fitted constants yields Eq. (23). Therefore Eq. (23) is a rearranged fit, not a first-principles prediction, and the headline core Ra ≈ 10^24–10^26 is the intersection of that rearranged fit with an assumed core Re range. The additional geostrophic-scale assumption ℓ=RocH is applied inside the damped regime where the paper's own Hovmöller data show larger-scale coherent structures; this is an extrapolation risk and a correctness concern, not itself a circular step. Self-citations to Horn and Aurnou (2022, 2025) and Aurnou et al. (2020) provide mode thresholds, DNS comparisons, and scale estimates, but they are not the load-bearing source of the damping result. Hence the score is 6: one central 'prediction' reduces by construction to the fitted empirical relation.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central experiment is self-contained, but the predictive layer pulls in several external scale assumptions (quasi-static Lorentz force, geostrophic length scale, diffusivity-free heat transport) and fits two constants (c and alpha) to the same data it then uses to predict core flow. No invented entities are introduced. The Earth-core numbers also inherit all parameter estimates from geophysical references.

free parameters (3)
  • c (prefactor in Re_MD scaling) = 1.72 +/- 0.14, rounded to ~2
    Best-fit prefactor in Eq (19)-(20) for N_l >= 3 RMC data after excluding one Ek=1e-4 outlier and magnetostrophic-stable cases. Enters the core Re and Ra predictions through Eq (23).
  • alpha (exponent in Re_MD scaling) = -0.46 +/- 0.05, rounded to ~-1/2
    Best-fit exponent on N_l in Eq (19). The -1/2 form is empirical, not derived from a governing equation, and controls the final Re ~ Lambda^{-1} dependence.
  • Transition interaction parameter N_l (and N_c) = N_l ~ 4.0, N_c ~ 3.1, reported as N_l ~ 3
    Estimated from the intersection of separate power-law fits for fRa < 8 and fRa >= 8 in Fig 7. This threshold is load-bearing for the regime classification and for where magnetic damping begins.
assumptions (6)
  • domain assumption Quasi-static Lorentz force density f_L ~ sigma U B^2 applies to the liquid gallium experiments (small magnetic Reynolds number).
    Used throughout Sec 2.1 and in Eq (22) to construct N_l and N_c. The authors state this applies, citing Horn and Aurnou (2025). Not independently verified in this paper.
  • domain assumption Convection is in or near the geostrophic turbulence regime, so characteristic scales are ell ~ Roc H and U ~ U_Omega.
    Explicitly assumed in Sec 2.1 before Eq (8); used to define N_c and later to convert the empirical Re_MD law into the input-only expression Eq (23) and the Earth-core predictions. Least secure in the magnetically damped regime that the paper targets.
  • domain assumption Julien et al. (2012a) diffusivity-free heat transport scaling Nu-1 = C_J Ra^{3/2} Ek^2 Pr^{-1/2} with C_J ~ 1/25 describes rotating convection in the experimental regime.
    Used to define Re_df in Eq (13) and as the normalization in Figs 9 and 10. This external scaling is adopted without re-derivation.
  • domain assumption UDV measurements of uz along a single chord at 2R/3 are representative of the convective velocity scale used in Re and N_l.
    Used in Eqs (15)-(18) to compute Re_z and uz,max for N_l. The paper provides no spatial or temporal convergence test for this single-chord proxy.
  • domain assumption Earth core parameter estimates: Ek = 10^-15, Pr = 0.1, Ra in [10^23, 10^29], Lambda in [0.1, 10], taken from prior geophysical estimates.
    Used for Fig 11 extrapolations. The authors acknowledge some of these estimates are uncertain, especially the link between large-scale core flow inversions and small-scale convective flow.
  • domain assumption Linear-theory critical Rayleigh numbers from Horn and Aurnou (2022) classify supercriticality and active modes in the experiments.
    Used to set fRa, to color data points, and to exclude magnetostrophic-stable cases from the N_l >= 3 fit.

how reviews work

0 comments
Cite this review

Pith. "Pith review of From Geostrophic to Magnetically-Damped Turbulence in Liquid Metal Rotating Magnetoconvection." pith.science (2026). https://pith.science/paper/CUK6Z75M

@misc{pith2026250903689,
  author       = {Pith},
  title        = {Pith review of: From Geostrophic to Magnetically-Damped Turbulence in Liquid Metal Rotating Magnetoconvection},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CUK6Z75M}},
  note         = {Machine review of arXiv:2509.03689}
}
abstract

Understanding planetary core convection dynamics requires the study of convective flows in which the Coriolis and Lorentz forces attain a leading-order, so-called magnetostrophic balance. Experimental investigations of rotating magnetoconvection (RMC) in the magnetostrophic regime are therefore essential to broadly characterize the properties of local-scale planetary core flow. Towards this end, we present here the first thermovelocimetric measurements of magnetostrophic, liquid metal convection, which are made using liquid gallium as the working fluid, at moderate rotation rates (Ekman numbers $10^{-4} \leq Ek\leq 10^{-5}$) and in the presence of dynamically strong magnetic fields (Elsasser number $\Lambda=1$). Complementary rotating convection (RC) experiments are performed at the same rotation rates to serve as reference cases. Our RMC velocity measurements adequately follow a geostrophic turbulent scaling for cases in which local-scale convective inertial forces exceed the Lorentz forces in the fluid bulk. In cases where Lorentz forces exceed local-scale inertia ($N_\ell \gtrsim 3$), the root-mean-square RMC velocities are magnetically damped, yielding values below the geostrophic turbulent RC scaling prediction. An enhancement in heat transfer is observed, which we attribute to the increased coherence of vertically aligned magnetostrophic convective flow. Extrapolating these laboratory results, we predict that convection-scale flows in Earth's core occur in the magnetically damped $N_\ell \gtrsim 3$ regime with Rayleigh number values between $10^{24}$ and $10^{26}$.

Figures

Figures reproduced from arXiv: 2509.03689 by the authors.

Figure 1
Figure 1. (a) Illustration of earth interior with a cylindrical container in outer core rep [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. (a) A photograph of the RoMag set-up with aspect ratio Γ = 2 [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. (a) Experimental (Ek, Ra/Racrit,min) parameter space, where Ramin is the minimum of all the critical Ra values. Hollow RC symbols are offset in Ek for visibility. Gold edge color indicates cases in geostrophic regime, magenta edge color marks cases where the magnetostrophic mode is not active. Liquid gallium critical Ra predictions from Horn and Aurnou (2022) for (b) Ek = 10−4 and (c) Ek = 10−5 . Hollow (filled) cir… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Validation cases for side-wall thermistor measurements of oscillatory and wall [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: Hovm¨oller diagrams of vertical velocities obtained from the vertical UDV probe. [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: (a) Convective heat flux relative to conduction heat flux [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]
Figure 7
Figure 7. Figure 7: Vertical Reynolds number normalized by the CIA scaling prediction, [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]
Figure 8
Figure 8. Figure 8: Local interaction parameter Nℓ vesus convective interaction parameter Nc for RMC data, gold edge color indicates cases in geostrophic regime, magenta edge color marks cases where the magnetostrophic mode is not active, cyan dashed line is the best of the data with Nℓ ≥…
Figure 9
Figure 9. Figure 9: (a) Convective heat flux relative to conduction heat flux Nu−1 as a function of the diffusivity free prediction CJRo2 cP ef f ; (b) vertical Reynolds number Rez as a function of diffusivity free prediction C 2/5 J RocRef f ; (c) vertical Reynolds number Rez, normalized…
Figure 10
Figure 10. Figure 10: Reynolds number normalized by the diffusion-free RC scaling prediction, [PITH_FULL_IMAGE:figures/full_fig_p024_10.png]
Figure 11
Figure 11. Figure 11: (a) Convective interaction parameter Nc via (8) and (b) magnetically damped Reynolds number ReMD based on the predictions from (23) as a function Rayleigh number Ra, using Earth’s outer core parameters: Ek = 10−15 , P r = 0.1. Blue and red solid lines represent Λ = 0.…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

90 extracted references · 72 canonical work pages

  1. [1]

    Jewel A. Abbate. Laboratory-Theoretical Investigations of Rotating Convection in Planetary Interiors. PhD thesis, 2024

    2024

  2. [2]

    Abbate and Jonathan M

    Jewel A. Abbate and Jonathan M. Aurnou. Rotating convective turbulence in moderate to high prandtl number fluids. Geophysical & Astrophysical Fluid Dynamics, 117 0 (6): 0 397--436, 2023. doi:10.1080/03091929.2023.2280874

    work page arXiv 2023

  3. [3]

    Shadowgraph measurements of rotating convective planetary core-style flows

    Jewel A Abbate and Jonathan M Aurnou. Shadowgraph measurements of rotating convective planetary core-style flows. Journal of Geophysical Research: Planets, 129 0 (9): 0 e2024JE008471, 2024

    2024

  4. [4]

    Abbate, Yufan Xu, Tobias Vogt, Susanne Horn, Keith Julien, and Jonathan M

    Jewel A. Abbate, Yufan Xu, Tobias Vogt, Susanne Horn, Keith Julien, and Jonathan M. Aurnou. Diffusivity-free turbulence in tabletop rotating rayleigh-b\'enard convection experiments. 2024

    2024

  5. [5]

    A systematic experimental study of rapidly rotating spherical convection in water and liquid gallium

    Julien Aubert, Daniel Brito, Henri-Claude Nataf, Philippe Cardin, and Jean-Paul Masson. A systematic experimental study of rapidly rotating spherical convection in water and liquid gallium. Physics of the Earth and Planetary Interiors, 128 0 (1): 0 51--74, 2001. ISSN 0031-9201. doi:https://doi.org/10.1016/S0031-9201(01)00277-1. Dynamics and Magnetic Field...

    work page doi:10.1016/s0031-9201(01)00277-1 2001

  6. [6]

    Onset of plane layer magnetoconvection at low ekman number

    K \'e lig Aujogue, Alban Poth \'e rat, and Binod Sreenivasan. Onset of plane layer magnetoconvection at low ekman number. Physics of Fluids, 27 0 (10), 2015

    2015

  7. [7]

    Experiments on convection in earth’s core tangent cylinder

    Jonathan Aurnou, Steven Andreadis, Lixin Zhu, and Peter Olson. Experiments on convection in earth’s core tangent cylinder. Earth and Planetary Science Letters, 212 0 (1): 0 119--134, 2003. ISSN 0012-821X. doi:https://doi.org/10.1016/S0012-821X(03)00237-1

    work page doi:10.1016/s0012-821x(03)00237-1 2003

  8. [8]

    Aurnou and Eric M

    Jonathan M. Aurnou and Eric M. King. The cross-over to magnetostrophic convection in planetary dynamo systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473 0 (2199): 0 20160731, 2017

    2017

Show all 90 references
  1. [9]

    Aurnou, Michael A

    Jonathan M. Aurnou, Michael A. Calkins, Jonathan S. Cheng, Keith Julien, Eric M. King, David Nieves, Krista M. Soderlund, and Stephan Stellmach. Rotating convective turbulence in earth and planetary cores. Physics of the Earth and Planetary Interiors, 246: 0 52--71, 2015

    2015

  2. [10]

    Rotating thermal convection in liquid gallium: multi-modal flow, absent steady columns

    Jonathan M Aurnou, Vincent Bertin, Alexander M Grannan, Susanne Horn, and Tobias Vogt. Rotating thermal convection in liquid gallium: multi-modal flow, absent steady columns. Journal of Fluid Mechanics, 846: 0 846--876, 2018

    2018

  3. [11]

    Aurnou, Susanne Horn, and Keith Julien

    Jonathan M. Aurnou, Susanne Horn, and Keith Julien. Connections between nonrotating, slowly rotating, and rapidly rotating turbulent convection transport scalings. Phys. Rev. Res., 2: 0 043115, Oct 2020. doi:10.1103/PhysRevResearch.2.043115

    2020 doi

  4. [12]

    Theory and simulations of rotating convection

    Adrian J Barker, Adam M Dempsey, and Yoram Lithwick. Theory and simulations of rotating convection. The Astrophysical Journal, 791 0 (1): 0 13, 2014

    2014

  5. [13]

    Experimental observation of the geostrophic turbulence regime of rapidly rotating convection

    Vincent Bouillaut, Benjamin Miquel, Keith Julien, Sébastien Aumaître, and Basile Gallet. Experimental observation of the geostrophic turbulence regime of rapidly rotating convection. Proceedings of the National Academy of Sciences, 118 0 (44): 0 e2105015118, 2021. doi:10.1073/...

    2021 doi

  6. [14]

    Ultrasonic doppler velocimetry in liquid gallium

    Daniel Brito, Henri-Claude Nataf, Philippe Cardin, Julien Aubert, and Jean-Paul Masson. Ultrasonic doppler velocimetry in liquid gallium. Experiments in fluids, 31 0 (6): 0 653--663, 2001

    2001

  7. [15]

    Turbulent viscosity measurements relevant to planetary core-mantle dynamics

    Daniel Brito, Jonathan Aurnou, and Philippe Cardin. Turbulent viscosity measurements relevant to planetary core-mantle dynamics. Physics of the Earth and Planetary Interiors, 141 0 (1): 0 3--8, 2004

    2004

  8. [16]

    A multiscale dynamo model driven by quasi-geostrophic convection

    Michael A Calkins, Keith Julien, Steven M Tobias, and Jonathan M Aurnou. A multiscale dynamo model driven by quasi-geostrophic convection. Journal of Fluid Mechanics, 780: 0 143--166, 2015

    2015

  9. [17]

    Solar-like to antisolar differential rotation: a geometric interpretation

    Maria E Camisassa and Nicholas A Featherstone. Solar-like to antisolar differential rotation: a geometric interpretation. The Astrophysical Journal, 938 0 (1): 0 65, 2022

    2022

  10. [18]

    Chaotic thermal convection in a rapidly rotating spherical shell: consequences for flow in the outer core

    Philippe Cardin and Peter Olson. Chaotic thermal convection in a rapidly rotating spherical shell: consequences for flow in the outer core. Physics of the Earth and Planetary Interiors, 82 0 (3): 0 235--259, 1994. ISSN 0031-9201. doi:https://doi.org/10.1016/0031-9201(94)90075-2

    1994 doi

  11. [19]

    Hydrodynamic and Hydromagnetic Stability

    Subrahmanyan Chandrasekhar. Hydrodynamic and Hydromagnetic Stability. Clarendon Press, 1961

    1961

  12. [20]

    : Elbert

    Subrahmanyan Chandrasekhar and Donna D. : Elbert. The instability of a layer of fluid heated below and subject to coriolis forces. ii. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 231 0 (1185): 0 198--210, 1955. doi:10.1098/rspa.1955.0166

    1955

  13. [21]

    Strong coupling of flow structure and heat transport in liquid metal thermal convection

    Xin-Yuan Chen, Yi-Chao Xie, Juan-Cheng Yang, and Ming-Jiu Ni. Strong coupling of flow structure and heat transport in liquid metal thermal convection. Journal of Fluid Mechanics, 975: 0 A21, 2023

    2023

  14. [22]

    A heuristic framework for next-generation models of geostrophic convective turbulence

    Jonathan S Cheng, Jonathan M Aurnou, Keith Julien, and Rudie PJ Kunnen. A heuristic framework for next-generation models of geostrophic convective turbulence. Geophysical & Astrophysical Fluid Dynamics, 112 0 (4): 0 277--300, 2018

    2018

  15. [23]

    Cheng, Ibrahim Mohammad, Bitong Wang, Declan F

    Jonathan S. Cheng, Ibrahim Mohammad, Bitong Wang, Declan F. Keogh, Jarod M. Forer, and Douglas H. Kelley. Oscillations of the large-scale circulation in experimental liquid metal convection at aspect ratios 1.4–3. Journal of Fluid Mechanics, 949: 0 A42, 2022. doi:10.1017/jfm.2022.778

    2022 doi

  16. [24]

    Kai Leong Chong, Yantao Yang, Shi-Di Huang, Jin-Qiang Zhong, Richard JAM Stevens, Roberto Verzicco, Detlef Lohse, and Ke-Qing Xia. Confined rayleigh-b \'e nard, rotating rayleigh-b \'e nard, and double diffusive convection: A unifying view on turbulent transport enhancement th...

    2017

  17. [25]

    Strong-field spherical dynamos

    Emmanuel Dormy. Strong-field spherical dynamos. Journal of Fluid Mechanics, 789: 0 500--513, 2016

    2016

  18. [26]

    Rapidly rotating magnetohydrodynamics and the geodynamo

    Emmanuel Dormy. Rapidly rotating magnetohydrodynamics and the geodynamo. Annual Review of Fluid Mechanics, 57, 2025

    2025

  19. [27]

    Eltayeb and Subrahmanyan Chandrasekhar

    Ibrahim A. Eltayeb and Subrahmanyan Chandrasekhar. Hydromagnetic convection in a rapidly rotating fluid layer. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 326 0 (1565): 0 229--254, 1972. doi:10.1098/rspa.1972.0007

    1972

  20. [28]

    Finlay and Hagay Amit

    Christopher C. Finlay and Hagay Amit. On flow magnitude and field-flow alignment at earth's core surface. Geophysical Journal International, 186 0 (1): 0 175--192, 07 2011. ISSN 0956-540X. doi:10.1111/j.1365-246X.2011.05032.x

    2011 arXiv

  21. [29]

    Thomas Gastine, Johannes Wicht, and Jonathan M. Aurnou. Zonal flow regimes in rotating anelastic spherical shells: An application to giant planets. Icarus, 225 0 (1): 0 156--172, 2013 a

    2013

  22. [30]

    From solar-like to antisolar differential rotation in cool stars

    Thomas Gastine, Rakesh K Yadav, Julien Morin, Ansgar Reiners, and Johannes Wicht. From solar-like to antisolar differential rotation in cool stars. Monthly Notices of the Royal Astronomical Society: Letters, 438 0 (1): 0 L76--L80, 2013 b

    2013

  23. [31]

    Fast torsional waves and strong magnetic field within the earth’s core

    Nicolas Gillet, Dominique Jault, Elisabeth Canet, and Alexandre Fournier. Fast torsional waves and strong magnetic field within the earth’s core. Nature, 465 0 (7294): 0 74--77, 2010. ISSN 1476-4687. doi:10.1038/nature09010

    2010 doi

  24. [32]

    H. F. Goldstein, E. Knobloch, I. Mercader, and M. Net. Convection in a rotating cylinder. part 2. linear theory for low prandtl numbers. Journal of Fluid Mechanics, 262: 0 293–324, 1994. doi:10.1017/S0022112094000510

    1994 doi

  25. [33]

    Internally heated convection and Rayleigh-B \'e nard convection

    David Goluskin. Internally heated convection and Rayleigh-B \'e nard convection . Springer, 2016

    2016

  26. [34]

    Grannan, Jonathan S

    Alexander M. Grannan, Jonathan S. Cheng, Ashna Aggarwal, Emily K. Hawkins, Yufan Xu, Susanne Horn, Jose Sánchez-Álvarez, and Jonathan M. Aurnou. Experimental pub crawl from rayleigh–bénard to magnetostrophic convection. Journal of Fluid Mechanics, 939: 0 R1, 2022. doi:10.1017/...

    2022 doi

  27. [35]

    Greenspan

    Harvey P. Greenspan. Theory of Rotating Fluids. Cambridge University Press, 1969

    1969

  28. [36]

    The rayleigh number for convection in the earth’s core

    David Gubbins. The rayleigh number for convection in the earth’s core. Physics of the Earth and Planetary Interiors, 128 0 (1): 0 3--12, 2001. ISSN 0031-9201. doi:https://doi.org/10.1016/S0031-9201(01)00273-4. Dynamics and Magnetic Fields of the Earth's and Planetary Interiors

    2001 doi

  29. [37]

    Turbulent convective length scale in planetary cores

    Céline Guervilly, Philippe Cardin, and Nathanaël Schaeffer. Turbulent convective length scale in planetary cores. Nature, 570: 0 368--371, 2019. doi:10.1038/s41586-019-1301-5

    2019 doi

  30. [38]

    Rapidly rotating radiatively driven convection: experimental and numerical validation of the ‘geostrophic turbulence’ scaling predictions

    Gabriel Hadjerci, Vincent Bouillaut, Benjamin Miquel, and Basile Gallet. Rapidly rotating radiatively driven convection: experimental and numerical validation of the ‘geostrophic turbulence’ scaling predictions. Journal of Fluid Mechanics, 998: 0 A9, 2024. doi:10.1017/jfm.2024.556

    2024 doi

  31. [39]

    Hawkins, Jonathan S

    Emily K. Hawkins, Jonathan S. Cheng, Jewel A. Abbate, Timothy Pilegard, Stephan Stellmach, Keith Julien, and Jonathan M. Aurnou. Laboratory models of planetary core-style convective turbulence. Fluids, 8 0 (4), 2023. ISSN 2311-5521. doi:10.3390/fluids8040106

    2023 doi

  32. [40]

    Herrmann and Friedrich Hermann Busse

    J. Herrmann and Friedrich Hermann Busse. Asymptotic theory of wall-attached convection in a rotating fluid layer. Journal of Fluid Mechanics, 255: 0 183–194, 1993. doi:10.1017/S0022112093002447

    1993 doi

  33. [41]

    Evidence for turbulent magnetic diffusion in earth's core

    D Holdenried-Chernoff and B\_A Buffett. Evidence for turbulent magnetic diffusion in earth's core. Geochemistry, Geophysics, Geosystems, 23 0 (12): 0 e2022GC010672, 2022

    2022

  34. [42]

    Large-scale flow in the core

    Richard Holme. Large-scale flow in the core. In Gerald Schubert, editor, Treatise on Geophysics, 2nd edition, volume 8, pages 107--130. Elsevier, 2015

    2015

  35. [43]

    Susanne Horn and Jonathan M. Aurnou. The elbert range of magnetostrophic convection. i. linear theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 478 0 (2264): 0 20220313, 2022. doi:10.1098/rspa.2022.0313

    2022

  36. [44]

    Susanne Horn and Jonathan M. Aurnou. The elbert range of magnetostrophic convection. ii. comparing linear theory to nonlinear low-<i>rm</i> simulations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 481 0 (2310): 0 20240016, 2025. doi:10....

    2025

  37. [45]

    Susanne Horn and Peter J. Schmid. Prograde, retrograde, and oscillatory modes in rotating rayleigh–bénard convection. Journal of Fluid Mechanics, 831: 0 182–211, 2017. doi:10.1017/jfm.2017.631

    2017 doi

  38. [46]

    Unravelling the large-scale circulation modes in turbulent rayleigh-b \'e nard convection (a)

    Susanne Horn, Peter J Schmid, and Jonathan M Aurnou. Unravelling the large-scale circulation modes in turbulent rayleigh-b \'e nard convection (a). Europhysics Letters, 136 0 (1): 0 14003, 2022

    2022

  39. [47]

    Confinement-induced heat-transport enhancement in turbulent thermal convection

    Shi-Di Huang, Matthias Kaczorowski, Rui Ni, and Ke-Qing Xia. Confinement-induced heat-transport enhancement in turbulent thermal convection. Phys. Rev. Lett., 111: 0 104501, Sep 2013

    2013

  40. [48]

    Motion in the interiors and atmospheres of jupiter and saturn: Scale analysis, anelastic equations, barotropic stability criterion

    Andrew P Ingersoll and David Pollard. Motion in the interiors and atmospheres of jupiter and saturn: Scale analysis, anelastic equations, barotropic stability criterion. Icarus, 52 0 (1): 0 62--80, 1982

    1982

  41. [49]

    Chris A. Jones. Planetary magnetic fields and fluid dynamos. Annual Review of Fluid Mechanics, 43: 0 583--614, 2011. ISSN 1545-4479. doi:https://doi.org/10.1146/annurev-fluid-122109-160727

    2011 doi

  42. [50]

    Strongly nonlinear convection cells in a rapidly rotating fluid layer: the tilted f-plane

    Keith Julien and Edgar Knobloch. Strongly nonlinear convection cells in a rapidly rotating fluid layer: the tilted f-plane. Journal of Fluid Mechanics, 360: 0 141–178, 1998. doi:10.1017/S0022112097008446

    1998 doi

  43. [51]

    Reduced equations for rotationally constrained convection

    Keith Julien, Edgar Knobloch, and Joseph Werne. Reduced equations for rotationally constrained convection. In Turbulence and Shear Flows, I. Begell House, 1999

    1999

  44. [52]

    Rubio, and Geoffrey M

    Keith Julien, Edgar Knobloch, Antonio M. Rubio, and Geoffrey M. Vasil. Heat transport in low-rossby-number rayleigh-b\'enard convection. Phys. Rev. Lett., 109: 0 254503, Dec 2012 a . doi:10.1103/PhysRevLett.109.254503

    2012 doi

  45. [53]

    Statistical and physical balances in low rossby number rayleigh--b \'e nard convection

    Keith Julien, Antonio M Rubio, Ian Grooms, and Edgar Knobloch. Statistical and physical balances in low rossby number rayleigh--b \'e nard convection. Geophysical & Astrophysical Fluid Dynamics, 106 0 (4-5): 0 392--428, 2012 b

    2012

  46. [54]

    King and Jonathan M

    Eric M. King and Jonathan M. Aurnou. Magnetostrophic balance as the optimal state for turbulent magnetoconvection. Proceedings of the National Academy of Sciences, 112 0 (4): 0 990--994, 2015. doi:10.1073/pnas.1417741112

    2015 doi

  47. [55]

    King and Bruce A

    Eric M. King and Bruce A. Buffett. Flow speeds and length scales in geodynamo models: The role of viscosity . Earth and Planetary Science Letters, 371: 0 156--162, June 2013. doi:https://doi.org/10.1016/j.epsl.2013.04.001

    2013 doi

  48. [56]

    Heat transfer by rapidly rotating rayleigh--b \'e nard convection

    Eric M King, Stephan Stellmach, and Jonathan M Aurnou. Heat transfer by rapidly rotating rayleigh--b \'e nard convection. Journal of Fluid Mechanics, 691: 0 568--582, 2012

    2012

  49. [57]

    Rudie P. J. Kunnen. The geostrophic regime of rapidly rotating turbulent convection. Journal of Turbulence, 22 0 (4-5): 0 267--296, 2021. doi:10.1080/14685248.2021.1876877

    2021

  50. [58]

    Radiative heating achieves the ultimate regime of thermal convection

    Simon Lepot, Sébastien Aumaître, and Basile Gallet. Radiative heating achieves the ultimate regime of thermal convection. Proceedings of the National Academy of Sciences, 115 0 (36): 0 8937--8941, 2018. doi:10.1073/pnas.1806823115

    2018 doi

  51. [59]

    X. Liao, K. Zhang, and Y. Chang. On boundary-layer convection in a rotating fluid layer. Journal of Fluid Mechanics, 549: 0 375–384, 2006. doi:10.1017/S0022112005008189

    2006 doi

  52. [60]

    An accelerating high-latitude jet in earth’s core

    Philip W Livermore, Rainer Hollerbach, and Christopher C Finlay. An accelerating high-latitude jet in earth’s core. Nature Geoscience, 10 0 (1): 0 62--68, 2017

    2017

  53. [61]

    Differential rotation in magnetized and non-magnetized stars

    Jun Mabuchi, Youhei Masada, and Akira Kageyama. Differential rotation in magnetized and non-magnetized stars. The Astrophysical Journal, 806 0 (1): 0 10, 2015

    2015

  54. [62]

    Niiler and Frederic E

    Pearn P. Niiler and Frederic E. Bisshopp. On the influence of coriolis force on onset of thermal convection. Journal of Fluid Mechanics, 22 0 (4): 0 753–761, 1965. doi:10.1017/S002211206500112X

    1965 doi

  55. [63]

    Experimental evidence of inertial waves in a precessing spheroidal cavity

    J \'e r \^o me Noir, Daniel Brito, Keith Aldridge, and Philippe Cardin. Experimental evidence of inertial waves in a precessing spheroidal cavity. Geophysical Research Letters, 28 0 (19): 0 3785--3788, 2001

    2001

  56. [64]

    Small scale quasigeostrophic convective turbulence at large rayleigh number

    Tobias G Oliver, Adrienne S Jacobi, Keith Julien, and Michael A Calkins. Small scale quasigeostrophic convective turbulence at large rayleigh number. Physical Review Fluids, 8 0 (9): 0 093502, 2023

    2023

  57. [65]

    On the motion of solids in a liquid possessing vorticity

    Joseph Proudman and Horace Lamb. On the motion of solids in a liquid possessing vorticity. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 92 0 (642): 0 408--424, 1916. doi:10.1098/rspa.1916.0026

    1916

  58. [66]

    On the genesis of the earth's magnetism

    Paul H Roberts and Eric M King. On the genesis of the earth's magnetism. Reports on Progress in Physics, 76 0 (9): 0 096801, sep 2013. doi:10.1088/0034-4885/76/9/096801

    2013 doi

  59. [67]

    Linear magnetoconvection in rotating fluid spheres permeated by a uniform axial magnetic field

    Ataru Sakuraba. Linear magnetoconvection in rotating fluid spheres permeated by a uniform axial magnetic field. Geophysical & Astrophysical Fluid Dynamics, 96 0 (4): 0 291--318, 2002

    2002

  60. [68]

    Turbulent geodynamo simulations: a leap towards earth’s core

    Nathana \"e l Schaeffer, Dominique Jault, H-C Nataf, and Alexandre Fournier. Turbulent geodynamo simulations: a leap towards earth’s core. Geophysical Journal International, 211 0 (1): 0 1--29, 2017

    2017

  61. [69]

    The competition between lorentz and coriolis forces in planetary dynamos

    Krista M Soderlund, Andrey Sheyko, Eric M King, and Jonathan M Aurnou. The competition between lorentz and coriolis forces in planetary dynamos. Progress in Earth and Planetary Science, 2 0 (1): 0 24, 2015

    2015

  62. [70]

    Magnetohydrodynamic control of differential rotation and dynamo transitions: rise of the local magnetic rossby number

    Krista M Soderlund, Paula Wulff, Petri J Käpylä, and Jonathan M Aurnou. Magnetohydrodynamic control of differential rotation and dynamo transitions: rise of the local magnetic rossby number. Monthly Notices of the Royal Astronomical Society, 541 0 (2): 0 1816--1830, 07 2025. I...

    2025 doi

  63. [71]

    Convection in stars: I

    Edward A Spiegel. Convection in stars: I. basic boussinesq convection. Annual Review of Astronomy and Astrophysics, vol. 9, p. 323, 9: 0 323, 1971

    1971

  64. [72]

    Turbulent thermal convection in the presence of rotation and a magnetic field: a heuristic theory

    David J Stevenson. Turbulent thermal convection in the presence of rotation and a magnetic field: a heuristic theory. Geophysical & Astrophysical Fluid Dynamics, 12 0 (1): 0 139--169, 1979

    1979

  65. [73]

    Velocity profile measurement by ultrasonic doppler method

    Yasushi Takeda. Velocity profile measurement by ultrasonic doppler method. Experimental Thermal and Fluid Science, 10 0 (4): 0 444--453, 1995. ISSN 0894-1777. doi:https://doi.org/10.1016/0894-1777(94)00124-Q. Experimental methods in Thermal and Fluid Science

    1995 doi

  66. [74]

    Motion of solids in fluids when the flow is not irrotational

    Geoffrey Ingram Taylor and Horace Lamb. Motion of solids in fluids when the flow is not irrotational. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 93 0 (648): 0 99--113, 1917. doi:10.1098/rspa.1917.0007

    1917

  67. [75]

    Scaling of strong-field spherical dynamos

    Robert J Teed and Emmanuel Dormy. Scaling of strong-field spherical dynamos. arXiv preprint arXiv:2508.05639, 2025

    2025 arXiv

  68. [76]

    Bridging the rossby number gap in rapidly rotating thermal convection

    Adrian van Kan, Keith Julien, Benjamin Miquel, and Edgar Knobloch. Bridging the rossby number gap in rapidly rotating thermal convection. Journal of Fluid Mechanics, 1010: 0 A42, 2025

    2025

  69. [77]

    Vasil, Keaton J

    Geoffrey M. Vasil, Keaton J. Burns, Daniel Lecoanet, Jeffrey S. Oishi, Benjamin P. Brown, and Keith Julien. Rapidly rotating wall‑mode convection. arXiv preprint arXiv:2409.20541, 2024. doi:10.48550/arXiv.2409.20541

    2024 doi arXiv

  70. [78]

    Grannan, and Jonathan M

    Tobias Vogt, Susanne Horn, Alexander M. Grannan, and Jonathan M. Aurnou. Jump rope vortex in liquid metal convection. Proceedings of the National Academy of Sciences, 115 0 (50): 0 12674--12679, 2018. doi:10.1073/pnas.1812260115

    2018 doi

  71. [79]

    Tobias Vogt, Susanne Horn, and Jonathan M. Aurnou. Oscillatory thermal–inertial flows in liquid metal rotating convection. Journal of Fluid Mechanics, 911: 0 A5, 2021 a . doi:10.1017/jfm.2020.976

    2021 doi

  72. [80]

    Free-fall velocities and heat transport enhancement in liquid metal magneto-convection

    Tobias Vogt, Juan-Cheng Yang, Felix Schindler, and Sven Eckert. Free-fall velocities and heat transport enhancement in liquid metal magneto-convection. Journal of Fluid Mechanics, 915: 0 A68, 2021 b

    2021

  73. [81]

    Heat transport by turbulent rotating rayleigh--b \'e nard convection and its dependence on the aspect ratio

    Stephan Weiss and Guenter Ahlers. Heat transport by turbulent rotating rayleigh--b \'e nard convection and its dependence on the aspect ratio. Journal of fluid mechanics, 684: 0 407--426, 2011

    2011

  74. [82]

    Tuning heat transport via coherent structure manipulation: recent advances in thermal turbulence

    Ke-Qing Xia, Shi-Di Huang, Yi-Chao Xie, and Lu Zhang. Tuning heat transport via coherent structure manipulation: recent advances in thermal turbulence. National Science Review, 10 0 (6): 0 nwad012, 2023

    2023

  75. [83]

    Thermovelocimetric characterization of liquid metal convection in a rotating slender cylinder

    Yufan Xu, Jewel Abbate, Cy David, Tobias Vogt, and Jonathan Aurnou. Thermovelocimetric characterization of liquid metal convection in a rotating slender cylinder. International Journal of Heat and Mass Transfer, 252: 0 127325, 2025

    2025

  76. [84]

    Effect of shear and magnetic field on the heat-transfer efficiency of convection in rotating spherical shells

    Rakesh K Yadav, Thomas Gastine, Ulrich R Christensen, Lucia DV Duarte, and Ansgar Reiners. Effect of shear and magnetic field on the heat-transfer efficiency of convection in rotating spherical shells. Geophysical Journal International, 204 0 (2): 0 1120--1133, 2016 a

    2016

  77. [85]

    Yadav, Thomas Gastine, Ulrich R

    Rakesh K. Yadav, Thomas Gastine, Ulrich R. Christensen, Scott J. Wolk, and Katja Poppenhaeger. Approaching a realistic force balance in geodynamo simulations. Proceedings of the National Academy of Sciences, 113 0 (43): 0 12065--12070, 2016 b . doi:10.1073/pnas.1608998113

    2016 doi

  78. [86]

    Calkins, Stefano Maffei, Keith Julien, Steven M

    Ming Yan, Michael A. Calkins, Stefano Maffei, Keith Julien, Steven M. Tobias, and Philippe Marti. Heat transfer and flow regimes in quasi-static magnetoconvection with a vertical magnetic field. Journal of Fluid Mechanics, 877: 0 1186–1206, 2019. doi:10.1017/jfm.2019.615

    2019 doi

  79. [87]

    The onset of convection in rotating circular cylinders with experimental boundary conditions

    Keke Zhang and Xinhao Liao. The onset of convection in rotating circular cylinders with experimental boundary conditions. Journal of Fluid Mechanics, 622: 0 63–73, 2009. doi:10.1017/S002211200800517X

    2009 doi

  80. [88]

    Rotating rayleigh-bénard convection: Küppers-lortz transition

    Fang Zhong, Robert Ecke, and Victor Steinberg. Rotating rayleigh-bénard convection: Küppers-lortz transition. Physica D: Nonlinear Phenomena, 51 0 (1): 0 596--607, 1991. ISSN 0167-2789. doi:https://doi.org/10.1016/0167-2789(91)90266-C

    1991 doi

  81. [89]

    Combined measurement of velocity and temperature in liquid metal convection

    Till Zürner, Felix Schindler, Tobias Vogt, Sven Eckert, and Jörg Schumacher. Combined measurement of velocity and temperature in liquid metal convection. Journal of Fluid Mechanics, 876: 0 1108–1128, 2019. doi:10.1017/jfm.2019.556

    2019 doi

  82. [90]

    Appendix landscape 4pt 0.9 table [H] center 0 tabular cccccccccccccc & Ek 10^ 4 & Ra 10^ -6 & Ra _o^ & Ra _o^ cyl & Ra _w^ & Ra _ mac ^ & Ra _ s ^ & Pr & P(W) & T & Nu & Re_ z,rms & Ro_c \\[3pt] 0 & 1 & 0.335 & 10.55 & 3.39 & 1.40 & - & 0.18 & 0.0275 & 20 & 1.33 & 1.44 & 265 &...

    1933

Pith tools

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