Chaotic/turbulent cross-helical MHD dynamo: from laboratory to the Sun

TL;DR

Cross-helicity plays a central role in MHD dynamos across scales, from laboratory von Karman flows to the Sun. The authors develop a Kolmogorov-like, cross-helicity inertial-range phenomenology and show how local symmetry breaking yields distributed chaos, predicting stretched-exponential spectra with a half-exponent. Laboratory experiments, DNS, and solar data converge on a cross-helicity–dominated dynamo mechanism that produces deterministic chaos for weak-cycle, equatorially concentrated fields and distributed chaos with dual regimes for strong activity, linked by the 11-year cycle. The work provides a unified framework connecting small-scale MHD turbulence, laboratory dynamos, and solar-cycle variability through cross-helicity dynamics, with potential implications for interpreting solar activity and stellar dynamos.

Abstract

Using the results of laboratory experiments and direct numerical simulations, as well as observations of the full-disc solar magnetic field and sunspot number dynamics, it is demonstrated that cross-helicity can dominate the frequency power spectra of the magnetic field generated by a magnetohydrodynamic (MHD) dynamo in chaotic/turbulent swirling flows. The theoretical consideration is based on a Kolmogorov-like phenomenology within the framework of the distributed chaos concept. It is shown that the solar full-disc magnetic field for the last two solar cycles with weak magnetic activity exhibits deterministic chaotic behavior concentrated around the equator. There is also observational indication that for the past periods of strong solar magnetic activity, there are two regimes of the smooth chaotic (but non-deterministic) cross-helical dynamo (high frequency and low frequency) separated by the 11-year phenomenon.

Figures (9)

• Figure 1: Power spectrum of the $x(t)$ variable for the Lorenz system Eq. (4) in a chaotic state. The inset shows the corresponding phase portrait of the system.
• Figure 2: Schematic representation of the setup's arrangement for experiments involving the von Kámán flow.
• Figure 3: Power spectrum (black curve) of the axial magnetic field component fluctuations measured in the bulk of the von Kármán flow in liquid sodium at $R_m \sim 50$ (MHD dynamo regime). The gray curve corresponds to the analogous power spectrum computed in a direct numerical simulation -- an analogue of the von Kármán flow.
• Figure 4: Power spectrum of the full disk solar magnetic field (the daily data for the period 2003--2017yy were taken from the site sol).
• Figure 5: Power spectrum of the full disk solar magnetic field (the daily data for the period 1975--2003yy were taken from the site mf).