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- Title
Derivation of the Basic Magnetohydrodynamic Dynamo Equations Obtained by the Vector Potential Averaging in a Time Short-Correlated Turbulence.
- Authors
Allahverdiyev, R. R.; Yushkov, E. V.; Sokoloff, D. D.
- Abstract
The freezing of a magnetic field into a turbulent flow of a conducting fluid or plasma at high magnetic Reynolds numbers can lead to an exponential increase in magnetic energy due to the accumulated hydrodynamic energy. This process is described by the magnetohydrodynamic dynamo theory and can be conventionally divided into two regimes, in the first of which the average magnetic field increases along with the energy, while in the second, only the energy increases while the average magnetic field remains equal to zero. Both regimes are called a "mean-field dynamo" and a "turbulent dynamo" and are described by the Steenbeck-Krause-Rädler and Kazantsev equations, respectively. These equations are a direct consequence of averaging the magnetic induction equation over a random velocity field; the first moment is calculated in the first case, and the second moment is calculated in the second case. There are many methods of such averaging. However, in this paper, we derive both dynamo models using the method of multiplicative integrals based on the assumption that the random velocity field is short-correlated in time. The main result is that we demonstrate the convenience of averaging not the magnetic field itself, but the vector potential, whose use greatly simplifies the mathematical apparatus of the derivation and, as a result, becomes very promising for generalizing standard models in the case of inhomogeneous and nonisotropic turbulence.
- Subjects
ELECTRIC generators; TURBULENCE; TURBULENT flow; ELECTROMAGNETIC induction; RANDOM fields; MAGNETOHYDRODYNAMICS
- Publication
Geomagnetism & Aeronomy, 2023, Vol 63, Issue 7, p882
- ISSN
0016-7932
- Publication type
Article
- DOI
10.1134/S0016793223070034