Abstract
Abstract
Highlights
An informal introduction is provided to a range of topics in fluid dynamics having a topological character
Magnetic relaxation is a means by which magnetostatic equilibria of arbitrarily prescribed field topology may be determined
The method of magnetic relaxation to magnetostatic equilibria can be extended to the problem of determining steady solutions of the full magnetohydrodynamic equations in an ideal fluid (ν = η = 0), having prescribed magnetic field topology and prescribed interlinkage of vorticity and magnetic fields
Summary
I welcome this opportunity to write a Perspectives article for JFM, and I thank the Editors for their invitation to do so. One dictionary definition of ‘perspective’ is ‘a particular attitude towards or way of regarding something; a point of view’ This gives me freedom to express my personal opinions throughout the article, and to adopt a more informal style than is perhaps usual for JFM. I propose to provide a necessarily superficial survey of a range of topics, all of which have some topological aspect, in which I have been personally involved at some stage over the last 60 years Some of these topics involve flow at low Reynolds numbers, where viscous effects dominate; and some at high Reynolds numbers where viscous effects are negligible nearly everywhere. Topological properties are relevant in both fast- and slow-dynamo theory (§ 6) and in the theory of magnetic relaxation (§ 8) which raises issues of stability (§ 9) This leads naturally to questions concerning the existence and structure of knotted flux tubes, and of field discontinuities that are inevitably encountered (§ 10). I gladly dedicate this Perspective to George Batchelor, in memoriam
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