Laminar instability of pressure-driven dynamos in multiple helical pipes

Abstract

Dynamo action is considered in a network of intertwined, helical pipes of rectangular cross-section. The flow in each pipe is driven solely by a pressure gradient and it is assumed that both the velocity and magnetic fields remain helically symmetric as the system evolves. The exact laminar solution is followed into the nonlinear regime. In a previous study, it was found that two such pipes produced a satisfactory dynamo. However, purely hydrodynamic instabilities were found to lead to flow configurations which did not support even a kinematic dynamo. The dynamo therefore only functioned at magnetic Prandtl numbers greater than unity. In this paper, it is shown that a multi-pipe configuration drives the dynamo at a significantly lower Prandtl number. A different flow instability is observed, which is found not to inhibit magnetic field generation. A model of the flow instability is considered by analysing the Dean equations for a low-aspect-ratio rectangle. The resultant quasi-one-dimensional flow gives rise to two linked stability equations of Orr–Sommerfeld type. The inflection point in the cross-pipe secondary flow is found to drive the new instability, with the downpipe primary flow having little influence.

Keywords:

• Helical symmetry
• Laminar dynamo
• Hydrodynamic instability