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In magnetostrophic rotating magnetoconvection, a fluid layer heated from below and cooled from above is equidominantly influenced by the Lorentz and the Coriolis forces. Strong rotation and magnetism each act separately to suppress thermal convective instability. However, when they act in concert and are near in strength, convective onset occurs at less extreme Rayleigh numbers ( R a , thermal forcing) in the form of a stationary, large-scale, inertia-less, inviscid magnetostrophic mode. Estimates suggest that planetary interiors are in magnetostrophic balance, fostering the idea that magnetostrophic flow optimizes dynamo generation. However, it is unclear if such a mono-modal theory is realistic in turbulent geophysical settings. Donna Elbert first discovered that there is a range of Ekman ( E k , rotation) and Chandrasekhar ( C h , magnetism) numbers, in which stationary large-scale magnetostrophic and small-scale geostrophic modes coexist. We extend her work by differentiating five regimes of linear stationary rotating magnetoconvection and by deriving asymptotic solutions for the critical wavenumbers and Rayleigh numbers. Coexistence is permitted if E k < 16 / ( 27 π ) 2 and C h ≥ 27 π 2 . The most geophysically relevant regime, the Elbert range , is bounded by the Elsasser numbers 4 3 ( 4 4 π 2 E k ) 1 / 3 ≤ Λ ≤ 1 2 ( 3 4 π 2 E k ) − 1 / 3 . Laboratory and Earth’s core predictions both exhibit stationary, oscillatory, and wall-attached multi-modality within the Elbert range.
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This content will become publicly available on March 1, 2026
The Elbert range of magnetostrophic convection. II. Comparing linear theory to nonlinear low- Rm simulations
The magnetostrophic dynamo hypothesis has greatly influenced planetary dynamo research. Many magnetostrophic dynamo theories are founded upon the linear stability analysis by Chandrasekhar and Elbert, and by the canonical laboratory photographs taken by Nakagawa that show a significant enlargement of the convective flow scales in the magnetostrophic regime of liquid metal rotating magnetoconvection (RMC). We test whether these linear predictions are relevant for the nonlinear RMC system by exploring the five possible regimes using direct numerical simulations of RMC in the low magnetic Reynolds number quasi-static approximation. We map out the heat and momentum transport in these regimes, look at the flow structures and focus especially on the length scales. We have also included numerical counterparts of Nakagawa’s experiments and our results show an excellent agreement with three of these cases and linear theory. However, agreement with Nakagawa is not found in the magnetostrophic case: no enlargement of scales is observed, but still in good agreement with linear theory. Oscillatory bulk modes dominate all the RMC cases in which they exist, thus, suggesting that oscillatory convective flows may dominate all the other convective modes in planetary cores and may provide the motions that primarily generate planetary dynamo action.
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- Award ID(s):
- 2143939
- PAR ID:
- 10581130
- Publisher / Repository:
- Royal Society
- Date Published:
- Journal Name:
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 481
- Issue:
- 2310
- ISSN:
- 1364-5021
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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