An Anti-Perfect Dynamo Result

TL;DR

This paper proves that perfect dynamo action cannot occur if the flow vector is a coordinate basis vector, providing criteria and methods to identify such basis vectors using Lie derivatives.

Contribution

It introduces criteria for identifying coordinate basis vectors using Lie derivatives and demonstrates that perfect dynamo action is impossible under these conditions.

Findings

Flow vectors as coordinate basis vectors prevent perfect dynamo action

Criteria for basis vector property are expressed via Lie derivatives

Construction methods for basis vector sets are straightforward

Abstract

It is shown that if the flow vector is a coordinate basis vector, then perfect dynamo action is not possible, regardless of whether the steady flow is compressible. Criteria determining the basis vector property are found to be expressible in terms of Lie derivatives, and construction of basis vector sets is straightforward.