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research
Stochastic Analysis of Subcritical Amplification of Magnetic Energy in a Turbulent Dynamo
Authors
Baggett
Baggett
+38Â more
Beck
Blackman
Brandenburg
Cattaneo
Farrel
Farrell
Farrell
Farrell
Fedotov
Fedotov
Fuchs
Gardiner
Gebhardt
Gog
Grossmann
Gruzinov
Horsthemke
Hoyng
Hoyng
Hoyng
Irina Bashkirtseva
Kraichnan
Krause
Lev Ryashko
Moffatt
Moss
Platt
Rogachevskii
Ruzmaikin
Ryashko
Schmid
Sergei Fedotov
Silant'ev
Tobias
Trefethen
Vishniac
Widrow
Zeldovich
Publication date
1 January 2004
Publisher
'Elsevier BV'
Doi
Cite
View
on
arXiv
Abstract
We present and analyze a simplified stochastic
α
Ω
−
\alpha \Omega -
α
Ω
−
dynamo model which is designed to assess the influence of additive and multiplicative noises, non-normality of dynamo equation, and nonlinearity of the
α
−
\alpha -
α
−
% effect and turbulent diffusivity, on the generation of a large-scale magnetic field in the subcritical case. Our model incorporates random fluctuations in the
α
−
\alpha -
α
−
parameter and additive noise arising from the small-scale fluctuations of magnetic and turbulent velocity fields. We show that the noise effects along with non-normality can lead to the stochastic amplification of the magnetic field even in the subcritical case. The criteria for the stochastic instability during the early kinematic stage are established and the critical value for the intensity of multiplicative noise due to
α
−
\alpha -
α
−
fluctuations is found. We obtain numerical solutions of non-linear stochastic differential equations and find the series of phase transitions induced by random fluctuations in the
α
−
\alpha -
α
−
parameter.Comment: 21pages,7 figure
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The University of Manchester - Institutional Repository
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Institutional repository of Ural Federal University named after the first President of Russia B.N.Yeltsin
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Last time updated on 17/05/2022