Journal ArticleDOI
Dynamo action associated with random inertial waves in a rotating conducting fluid
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TLDR
In this article, it was shown that a random superposition of inertial waves in a rotating conducting fluid can act as a dynamo, i.e. can systematically transfer energy to a magnetic field which has no source other than electric currents within the fluid.Abstract:
It is shown that a random superposition of inertial waves in a rotating conducting fluid can act as a dynamo, i.e. can systematically transfer energy to a magnetic field which has no source other than electric currents within the fluid. Dynamo action occurs provided the statistical properties of the velocity field lack reflexional symmetry, and this occurs when conditions are such that there is a net energy flux (positive or negative) in the direction of the rotation vector Ω.If the magnetic field grows from an infinitesimal level, then the mode of maximum growth rate dominates before the back-reaction associated with the Lorentz force becomes significant. This mode is first determined, and then the back-reaction associated with it alone is analysed. It is shown that the magnetic energy grows exponentially during the stage when the Lorentz forces are negligible, then reaches a maximum depending on the values of the parameters
\[
R_m = u_0 l/\lambda,\quad Q = \Omega l^2/\lambda,
\]
(u0 = initial r.m.s. velocity, l = length scale characteristic of the velocity field, λ = magnetic diffusivity) and ultimately decays as t−1 (equation (5.15)). This decay is coupled with a decay of the velocity field due to ohmic dissipation, and it occurs because there is no external source of energy for the fluid motion.read more
Citations
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Astrophysical magnetic fields and nonlinear dynamo theory
TL;DR: The current understanding of astrophysical magnetic fields is reviewed in this paper, focusing on their generation and maintenance by turbulence, where analytical and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamo, where some form of parity breaking is crucial.
Journal ArticleDOI
Strong MHD helical turbulence and the nonlinear dynamo effect
TL;DR: In this paper, a nonlinear theory is developed for three-dimensional, homogeneous, isotropic, incompressible MHD turbulence with helicity, i.e. not statistically invariant under plane reflexions.
Journal ArticleDOI
Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence
TL;DR: In this article, the authors investigated the consequences of the conservation of magnetic helicity for incompressible three-dimensional turbulent MHD flows and obtained absolute equilibrium spectra for inviscid infinitely conducting flows truncated at lower and upper wavenumbers kmin and kmax.
Journal ArticleDOI
Helicity in Laminar and Turbulent Flow
H. K. Moffatt,A. Tsinober +1 more
TL;DR: In this article, the authors define a helical flow u = U+1/2f~ x where U and f are constants and u is the helicity density of the flow.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Journal ArticleDOI
Berechnung der mittleren Lorentz-Feldstärke für ein elektrisch leitendes Medium in turbulenter, durch Coriolis-Kräfte beeinflußter Bewegung
TL;DR: In this article, the average crossproduct of velocity and magnetic field has a non-vanishing component parallel to the average magnetic field, which is the average of the products of two components of the velocity field.