Kinematic dynamo in random flow

The growth of a magnetic field in a given random flow of a well-conducting liquid is considered. The known Lagrange solution for the transport of a frozen-in magnetic field is utilized. Magnetic diffusion is taken into account by averaging the result of this transport over a set of random trajectories. This permits a derivation of the equations for the mean magnetic field and its moments, as well as an investigation of the true (random) magnetic field. The field and its moments increase exponentially in the limit of large magnetic Reynolds numbers, and the field distribution becomes intermittent. The analysis is devoted mainly to streams that are restored after a definite time interval, but stationary flows with stochastic properties are also discussed.

PACS: 47.65.−d, 47.27.Jv, 47.10.A− (all)
DOI: 10.1070/PU1985v028n04ABEH003869
URL: https://ufn.ru/en/articles/1985/4/b/
Citation: Molchanov S A, Ruzmaikin A A, Sokolov D D "Kinematic dynamo in random flow" Sov. Phys. Usp. 28 307–327 (1985)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Молчанов С А, Рузмайкин А А, Соколов Д Д «Кинематическое динамо в случайном потоке» УФН 145 593–628 (1985); DOI: 10.3367/UFNr.0145.198504b.0593

Cited by (91) Similar articles (20) ↓

S.I. Vainshtein, Ya.B. Zel’dovich “Origin of Magnetic Fields in Astrophysics (Turbulent ’Dynamo’ Mechanisms)” Sov. Phys. Usp. 15 159–172 (1972)
Ya.B. Zel’dovich, S.A. Molchanov et al “Intermittency in random media” Sov. Phys. Usp. 30 353–369 (1987)
Ya.B. Zeldovich, A.A. Ruzmaikin “The hydromagnetic dynamo as the source of planetary, solar, and galactic magnetism” Sov. Phys. Usp. 30 494–506 (1987)
O.G. Bakunin “Reconstruction of streamline topology, and percolation models of turbulent transport” Phys. Usp. 56 243–260 (2013)
G.M. Zaslavskii, B.V. Chirikov “Stochastic instability of non-linear oscillations” Sov. Phys. Usp. 14 549–568 (1972)
V.I. Klyatskin “Integral characteristics: a key to understanding structure formation in stochastic dynamic systems” Phys. Usp. 54 441–464 (2011)
L.M. Zelenyi, A.I. Neishtadt et al “Quasiadiabatic dynamics of charged particles in a space plasma” Phys. Usp. 56 347–394 (2013)
A.B. Severnyi “Magnetic fields of the Sun and stars” Sov. Phys. Usp. 9 1–30 (1966)
A.Z. Dolginov “Origin of the magnetic fields of the earth and celestial bodies” Sov. Phys. Usp. 30 475–493 (1987)
A.S. Monin “On the nature of turbulence” Sov. Phys. Usp. 21 429–442 (1978)
A.S. Monin “Turbulence and microstructure in the ocean” Sov. Phys. Usp. 16 121–131 (1973)
F.V. Dolzhanskii, V.A. Krymov, D.Yu. Manin “Stability and vortex structures of quasi-two-dimensional shear flows” Sov. Phys. Usp. 33 (7) 495–520 (1990)
K.V. Koshel, S.V. Prants “Chaotic advection in the ocean” Phys. Usp. 49 1151–1178 (2006)
A.A. Vedenov, E.P. Velikhov, R.Z. Sagdeev “STABILITY OF PLASMA” Sov. Phys. Usp. 4 332–369 (1961)
V.V. Zhuravlev “Analytical models of relativistic accretion disks” Phys. Usp. 58 527–555 (2015)
A.S. Monin “Hydrodynamic instability” Sov. Phys. Usp. 29 843–868 (1986)
A.S. Mikhailov, I.V. Uporov “Critical phenomena in media with breeding, decay, and diffusion” Sov. Phys. Usp. 27 695–714 (1984)
G.M. Zaslavskii, R.Z. Sagdeev et al “Minimal chaos, stochastic webs, and structures of quasicrystal symmetry” Sov. Phys. Usp. 31 887–915 (1988)
A.A. Chernyshov, K.V. Karelsky, A.S. Petrosyan “Subgrid-scale modeling for the study of compressible magnetohydrodynamic turbulence in space plasmas” Phys. Usp. 57 421–452 (2014)
A.P. Zhilinskii, L.D. Tsendin “Collisional diffusion of a partially-ionized plasma in a magnetic field” Sov. Phys. Usp. 23 331–355 (1980)

The list is formed automatically.