Non-linear dynamo waves in magnetized shear flows: a candidate mechanism for the solar cycle
Abstract
Large-scale magnetic reversals in planets, stars, and accretion disks require a non-linear theory coupling the magnetic field to its sustaining flow. We derive exact non-linear solutions to incompressible magnetohydrodynamics in background rotational shear, with large-scale velocity and magnetic fields linear in position (affine form). They reveal a cyclic feedback between meridional circulation, shear, magnetic tension, induction, and the Coriolis force. The steady-circulation reversal orbit, or dynamo wave, periodically reverses all magnetic components and supports slower modulations. In the solar near-surface shear layer (NSSL), moderate shear permits stable 11-year reversals with poleward speeds of 8-12 m/s and poloidal and toroidal amplitudes of 4-11 G and 2.2-3.8 kG near 1 Mm depth, in reasonable agreement with regional observations. At stronger shear, an 88-year reversal exhibits a 203-207-year modulation, reproducing the Gleissberg and Suess-de Vries activity timescales but requiring weaker poloidal fields. Such reversals, however, remain observationally unestablished. At tachocline density, an 11-year reversal and the inferred return flow require toroidal fields of hundreds of kilogauss over a broad shear range, exceeding large-scale-field reconstructions but partly permitted by seismic upper limits. This favors a shallow NSSL origin for a local cycle, while leaving open the issue of a global dynamo. Toroidal dominance prolongs the cycle because shear acting on a weak poloidal field changes only a small fraction of the stronger toroidal field per rotation. Balancing the weak magnetic torque against advection and the Coriolis force also requires slow circulation, which gradually turns the poloidal field and reverses toroidal induction. Efficient poloidal regeneration would shorten this delay. A long solar cycle therefore favors a primarily shear-driven dynamo.
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BibTeX
@misc{banik2026nonlinear,
title = {{Non-linear dynamo waves in magnetized shear flows: a candidate mechanism for the solar cycle}},
author = {Uddipan Banik},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30367},
eprint = {2609.30367},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30367},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-linear dynamo waves in magnetized shear flows: a candidate mechanism for the solar cycle
AU - Uddipan Banik
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30367
UR - https://arxiv.org/abs/2609.30367
AB - Large-scale magnetic reversals in planets, stars, and accretion disks require a non-linear theory coupling the magnetic field to its sustaining flow. We derive exact non-linear solutions to incompressible magnetohydrodynamics in background rotational shear, with large-scale velocity and magnetic fields linear in position (affine form). They reveal a cyclic feedback between meridional circulation, shear, magnetic tension, induction, and the Coriolis force. The steady-circulation reversal orbit, or dynamo wave, periodically reverses all magnetic components and supports slower modulations. In the solar near-surface shear layer (NSSL), moderate shear permits stable 11-year reversals with poleward speeds of 8-12 m/s and poloidal and toroidal amplitudes of 4-11 G and 2.2-3.8 kG near 1 Mm depth, in reasonable agreement with regional observations. At stronger shear, an 88-year reversal exhibits a 203-207-year modulation, reproducing the Gleissberg and Suess-de Vries activity timescales but requiring weaker poloidal fields. Such reversals, however, remain observationally unestablished. At tachocline density, an 11-year reversal and the inferred return flow require toroidal fields of hundreds of kilogauss over a broad shear range, exceeding large-scale-field reconstructions but partly permitted by seismic upper limits. This favors a shallow NSSL origin for a local cycle, while leaving open the issue of a global dynamo. Toroidal dominance prolongs the cycle because shear acting on a weak poloidal field changes only a small fraction of the stronger toroidal field per rotation. Balancing the weak magnetic torque against advection and the Coriolis force also requires slow circulation, which gradually turns the poloidal field and reverses toroidal induction. Efficient poloidal regeneration would shorten this delay. A long solar cycle therefore favors a primarily shear-driven dynamo.
ER -