Virtual states and exponential decay in small-scale dynamo
arXiv:2509.13206 · doi:10.1103/wfb9-n2zl
Abstract
We develop the Kazantsev theory of small-scale dynamo generation at small Prandtl numbers near the generation threshold and restore the concordance between the theory and numerical simulations: the theory predicted a power-law decay below the threshold, while simulations demonstrate exponential decay. We show that the exponential decay is temporary and owes its existence to the flattening of the velocity correlator at large scales. This effect corresponds to the existence of a long-living virtual level in the corresponding Schrodinger type equation. We also find the critical Reynolds number and the increment of growth/decay above and under the threshold; we express them in terms of the quantitative characteristic properties of the velocity correlator, which makes it possible to compare the results with the data of different simulations.
References in corpus (16)
- On magnetic field generation in Kolmogorov turbulence
- Current status of turbulent dynamo theory: From large-scale to small-scale dynamos
- Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers
- Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers
- Scaling exponents saturate in three-dimensional isotropic turbulence
- The Small-Scale Dynamo at Low Magnetic Prandtl Numbers
- Mean field models of flux transport dynamo and meridional circulation in the Sun and stars
- Small-scale dynamos: From idealized models to solar and stellar applications
- Magnetic dynamo action at low magnetic Prandtl numbers
- Dynamo effect in the Kraichnan magnetohydrodynamic turbulence
- Numerical evidence for a small-scale dynamo approaching solar magnetic Prandtl numbers
- Varying the forcing scale in low Prandtl number dynamos
- Growth rate of small-scale dynamo at low magnetic Prandtl numbers
- Non-Gaussian generalization of the Kazantsev-Kraichnan model
- Suppression of small-scale dynamo in time irreversible turbulence
- Evolution of localized magnetic field perturbations and the nature of turbulent dynamo