Journal of Fluid Mechanics

Nonlinear equilibration of a dynamo in a smooth helical flow

a1 Department of Mathematics, University of Exeter, North Park Road, Exeter, Devon, EX4 4QE, UK


We investigate the nonlinear equilibration of magnetic fields in a smooth helical flow at large Reynolds number Re and magnetic Reynolds number Rm with Re[dbl greater-than sign]Rm[dbl greater-than sign]1. We start with a smooth spiral Couette flow driven by boundary conditions. Such flows act as dynamos, that is are unstable to growing magnetic fields; here we disregard purely hydrodynamic instabilities such as Taylor–Couette modes. The dominant feedback from a magnetic field mode is only on the mean flow and this yields a simplified ‘mean-flow system’ consisting of one magnetic mode and the mean flow, which we solve numerically. We also obtain the asymptotic structure of the equilibrated fields for weakly and strongly nonlinear regimes. In particular the field tends to concentrate in a cylindrical shell where all stretching and differential rotation is suppressed by the Lorentz force, and the fluid is in solid-body motion. This shell is bounded by thin diffusive layers where the stretching that maintains the field against diffusive decay is dominant.

(Received August 7 1996)
(Revised January 8 1997)