Abstract
The dynamics of a statistically homogeneous isotropic magnetic field generated by an incompressible turbulent plasma flow with a large, yet finite magnetic Prandtl number is discussed. It has been found that, on scales smaller than the Kolmogorov viscosity scale, the nonlinear feedback of a magnetic field to the fluid dynamics decreases exponentially, despite the fast exponential growth of the magnetic field. It is shown that the anisotropy of diffusion in a cosmic plasma leads to an additional decrease in the feedback. It is demonstrated that the feedback degeneracy leads to an energy paradox, which is resolved at a later stage of the development of initial disturbances when the spatial scale of magnetic fluctuations approaches the Kolmogorov scale. The possibility of the nonlinearity degeneracy in more complex systems is discussed: a similar phenomenon can occur in hydrodynamic turbulence, which makes it possible to find a key to the theoretical analysis of the latter.
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Notes
Note that, at Prm = 1, the initial dynamics of the magnetic field coincides with the initial dynamics of acoustic turbulence [3].
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Translated by E. Bondareva
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Zybin, K.P., Il’yn, A.S., Kopyev, A.V. et al. The Degeneracy of Nonlinearity in a Turbulent System. Dokl. Phys. 67, 278–281 (2022). https://doi.org/10.1134/S1028335822090166
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DOI: https://doi.org/10.1134/S1028335822090166