Inverse cascades and time-dependent dynamos in MHD flows
type: Item
instance of: scholarly article
title: Inverse cascades and time-dependent dynamos in MHD flows
zbMATH Open document ID: 0722.58050
DOI: 10.1016/0167-2789(91)90039-C
author: D. Kharzeev
published in: Physica D
publication date: 1991-01-01T00:00:00Z
review text: This paper addresses the effects of two different kinds of instabilities on magnetohydrodynamical (MHD) flows. The alpha effect occurs in a three- dimensional small-scale fluid flow which is helical or otherwise lacks parity invariance) when it acts on a large-scale magnetic field and generates an electromotive force which is a function of the field itself. The alpha effect may lead to dynamo action, which is the growth of a large-scale magnetic field. An analogous transport effect occurs in ordinary hydrodynamics; when a large-scale velocity field is superimposed on a small-scale flow lacking Galilean invariance, the mean Reynolds stress can be a function of the large-scale flow. This is called the anisotropic kinetic alpha (AKA) effect, and it may lead to the growth of the large-scale flow when the original three-dimensional small-scale flow is anisotropic and lacks parity invariance. The authors examine the phenomenon known as ``inverse cascade'' whereby energy is transferred from the linearly most unstable modes to successively larger scales, and the mean fields eventually saturate in a state whose dominant mode is that of the system. The authors relate metastable states (states dominated by larger and larger scales) to the existence of a steady cellular solution. Such cellular solutions are unstable, and there is eventually transition to a cellular solution on a larger scale. This suggests the existence of heteroclinic connections going from any steady solution to a steady solution on a larger scale. This picture is supported by the analysis of a simple solvable model.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 76E25
Mathematics Subject Classification ID: 76W05
zbMATH DE Number: 4190786
zbMATH Keywords: nonlinear alpha effect
zbMATH Keywords: dynamo instability
zbMATH Keywords: anisotropic kinetic alpha effect
zbMATH Keywords: magnetohydrodynamic instabilities
Wikidata QID: Q57927240
MaRDI profile type: Publication
cites work: Helicity is unnecessary for alpha effect dynamos, but it helps
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cites work: The α-chain-termination mutants and their relation to the α-thalassaemias
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full work available at URL: 0167-2789(91)90039-c
OpenAlex ID: W1984471711
description: scientific article; zbMATH DE number 4190786