Abstract
The generation of magnetic field in an electrically conducting fluid generally involves the complicated nonlinear interaction of flow turbulence, rotation and field. This dynamo process is of great importance in geophysics, planetary science and astrophysics, since magnetic fields are known to play a key role in the dynamics of these systems. This paper gives an introduction to dynamo theory for the fluid dynamicist. It proceeds by laying the groundwork, introducing the equations and techniques that are at the heart of dynamo theory, before presenting some simple dynamo solutions. The problems currently exercising dynamo theorists are then introduced, along with the attempts to make progress. The paper concludes with the argument that progress in dynamo theory will be made in the future by utilising and advancing some of the current breakthroughs in neutral fluid turbulence such as those in transition, self-sustaining processes, turbulence/mean-flow interaction, statistical and data-driven methods and maintenance and loss of balance.
Highlights
To a practitioner dynamo theory is a field with myriad subtleties; in a severe interpretation the Navier–Stokes equations and the whole of neutral fluid mechanics may be regarded as forming a useful invariant subspace of the dynamo problem, with – it has to be said – non-trivial dynamics
A natural question, is ‘What is the origin of this organisation and how does the mechanism leading to organised flows compete with that leading the production of small-scale fields?’ Can this competition be understood within a kinematic framework, or are nonlinear effects from the momentum equation required? Is it the case that the organisation arises as a consequence of turbulent interactions or despite them? These questions are discussed in § 5, where the concept of mean-field electrodynamics will be introduced and critiqued
Such theories are ubiquitous in fluid mechanics owing to the historical path of research in dynamo theory, the statistical theories in the two disciplines have tended to develop along different tracks
Summary
It is really just a matter of perspective. To the fluid dynamicist, dynamo theory may appear as a rather esoteric and niche branch of fluid mechanics – in dynamo theory much attention has focused on seeking solutions to the induction equation rather than those for the Navier–Stokes equations. To a practitioner dynamo theory is a field with myriad subtleties; in a severe interpretation the Navier–Stokes equations and the whole of neutral fluid mechanics may be regarded as forming a useful invariant subspace of the dynamo problem, with – it has to be said – non-trivial dynamics In this perspective, I shall attempt to present the important and interesting developments in dynamo theory from the point of view of a fluid dynamicist, pointing out common themes. I shall present the key results and features of dynamo theory, I shall not be exhaustive by any means This perspective is focused on those areas of dynamo theory that I believe are both accessible and of interest to fluid dynamicists, drawing analogies with other areas of fluids where necessary. By giving motivation for the study of dynamos – much of which arises from observations of cosmical magnetic fields, including those of planets, stars, galaxies and disks
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