eCite Digital Repository

Nonlinear equilibration of a dynamo in a smooth helical flow


Bassom, AP and Gilbert, AD, Nonlinear equilibration of a dynamo in a smooth helical flow, Journal of Fluid Mechanics, 343 pp. 375-406. ISSN 0022-1120 (1997) [Refereed Article]

Copyright Statement

Copyright 1997 Cambridge University Press

DOI: doi:10.1017/S0022112097005880


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.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:108026
Year Published:1997
Web of Science® Times Cited:17
Deposited By:Mathematics and Physics
Deposited On:2016-04-04
Last Modified:2016-07-08

Repository Staff Only: item control page