Advected fields in maps. I: Magnetic flux growth in the stretch-fold-shear map
type: Item
instance of: scholarly article
title: Advected fields in maps. I: Magnetic flux growth in the stretch-fold-shear map
zbMATH Open document ID: 1059.76078
DOI: 10.1016/S0167-2789(02)00444-X
author: Andrew D. Gilbert
published in: Physica D
publication date: 2002-06-04T00:00:00Z
review text: The author investigates the role of the stretch-fold-shear (SFS) mechanism in producing fast dynamos with two-dimensional but not confined to a plane flows, for zero-magnetic diffusion. A combination of analytical and numerical techniques is used to establish growth rates with error bounds. It is shown that the SFS map is a perfect dynamo: for sufficiently large shear, the adjoint operator has smooth, growing eigenfunctions, and so smooth flux averages grow exponentially with time for zero diffusion.
reviewed by: Iuliana Oprea
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 37N10
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 85A30
zbMATH DE Number: 1749457
zbMATH Keywords: kinematic dynamo
zbMATH Keywords: hyperbolic map
Wikidata QID: Q57943679
MaRDI profile type: Publication
cites work: Recycling of strange sets: I. Cycle expansions
cites work: Construction of fast dynamos using unsteady flows and maps in three dimensions
cites work: Unsteady dynamo effects at large magnetic reynolds number
cites work: Q3995211
cites work: Q4273515
cites work: Stretch, Twist, Fold: The Fast Dynamo
cites work: The Magnetic Field of Sunspots
cites work: Chaotic flows and fast magnetic dynamos
cites work: Q4001616
cites work: Towards a realistic fast dynamo: models based on cat maps and pseudo-Anosov maps
cites work: Advected fields in maps: II. Dynamo action in the stretch–fold–shear map
cites work: Advected fields in maps—III. Passive scalar decay in baker's maps
cites work: Q3874765
cites work: Q4273537
cites work: Rigorous bounds on the fast dynamo growth rate involving topological entropy
cites work: Q5552090
cites work: Golden mean renormalization for the Harper equation: The strong coupling fixed point
cites work: The correlation spectrum for hyperbolic analytic maps
cites work: A fast kinematic dynamo in two-dimensional time-dependent flows
cites work: Hyperfunctions and harmonic analysis on symmetric spaces
cites work: On the role of stagnation points and periodic particle paths in a two-dimensional pulsed flow fast dynamo model
cites work: Wavelets and Dilation Equations: A Brief Introduction
cites work: Pseudospectra of Linear Operators
cites work: Magnetic field generation by the motion of a highly conducting fluid
cites work: Q3874718
cites work: Q3243818
description: scientific article; zbMATH DE number 1749457