Kinematic dynamo action in a helical pipe

Abstract

Steady incompressible laminar flow of an electrically conducting fluid down a helically symmetric pipe is investigated with regard to possible dynamo action. Both the fluid motion and the magnetic field are assumed to be helically symmetric, with the same pitch. Such a velocity field can be represented by its down-pipe component, $v$, and a streamfunction $\Psi$ defining the secondary cross-pipe flow.

The helical geometry automatically links the cross-pipe and down-pipe field components and permits laminar dynamo action. It is found that the relatively weak secondary motion, which is always present in real pipe flows, has an inhibitory effect on the magnetic field growth and frequently suppresses dynamo action completely. In such a case for large magnetic Reynolds number ($R_m{\to}\infty$) the asymptotic structure of the neutral mode is analysed using a streamline integral approach.

Kinematic velocity fields, without the cross-pipe flow ($\Psi{=}0$), usually generate a dynamo even for perfectly conducting walls. For large $R_m$ the growing modes are shown to have a two-layer structure with rapid tangential variation.

For appropriate pipe geometry, steady pressure-driven pipe flow is found to drive a dynamo for moderate values (${\sim}1000$) of the magnetic Reynolds number.