Titlebook: Stretch, Twist, Fold: The Fast Dynamo; Stephen Childress,Andrew D. Gilbert Book 1995 Springer-Verlag Berlin Heidelberg 1995 Chaotic Dynbam

Prologue

Book 1995d literature, including in recent years a number of review articles and books dedicated to the dynamo theories of these fields. Against this background of work, some explanation of the scope and purpose of the present monograph, and of the presentation and organization of the material, is therefore

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0940-7677 and varied literature, including in recent years a number of review articles and books dedicated to the dynamo theories of these fields. Against this background of work, some explanation of the scope and purpose of the present monograph, and of the presentation and organization of the material, is

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Fast Dynamos in Mapses of fast dynamo action that have been examined. For three-dimensional steady flows there is some support for fast dynamo action, but there are still perplexing gaps in our understanding of magnetic structure and its measurement. The flux conjecture seems to work for the Kolmogorov flow but has not been verified for the ABC 111 flow of §2.6.

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Nearly Integrable Flows understand the geometry of slow and fast mechanisms. At the same time, any such study faces a basic obstacle, namely that one expects that then the fast dynamo growth rate will be ., with mean flux a small component of the total field, and therefore possibly difficult to evaluate either numerically or analytically.

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Random Fast Dynamosre the growth rate .(.) can be defined for . > 0 by, for example, the growth of magnetic energy or linear functionals: . Here <·> is an ensemble average. This definition is the most tractable mathematically; we return to discuss it in §11.5, but here we simply remark that it is not the only definition, and perhaps not the best definition.

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Dynamicsbout the fields that are ultimately excited in a dynamical model: the structure of the magnetic field must be determined by the coupled system of field and flow, and in particular the feedback of the Lorentz force.

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Dynamos and Non-dynamosan be used to exclude classes of flows from consideration and to help determine possible fast dynamo mechanisms. Finally in §4.3 we discuss a result of Moffatt & Proctor (1985) concerning the non-existence of smooth eigenfunctions when . = 0.

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