On the spin-up of an electrically conducting fluid Part 2. Hydromagnetic spin-up between infinite flat insulating plates
- 17 August 1970
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 43 (4), 785-799
- https://doi.org/10.1017/s0022112070002744
Abstract
The linear spin-up of a homogeneous electrically conducting fluid confined between infinite flat insulating plates is analyzed for the case in which a uniform magnetic field is applied normal to the boundaries. As in part 1 (Benton & Loper 1969), complete hydromagnetic interaction is embraced even within linearized equations. Approximate inversion of the exact Laplace transform solution reveals the presence of several flow structures: two thin Ekman–Hartmann boundary layers (one on each plate), which are quasi-steady on the time scale of spin-up, two thicker continuously growing magnetic diffusion regions, and an essentially inviscid, current-free core, which may or may not be present on the spin-up time scale, depending upon the growth rate of the magnetic diffusion regions. When a current-free core exists, it is found to spin-up at the same rate as the fluid within magnetic diffusion regions, although different physical mechanisms are at play. As a result, a single hydromagnetic spin-up time is derived, independently of the thickness of magnetic diffusion regions; this time is shorter than in the non-magnetic problem.Keywords
This publication has 3 references indexed in Scilit:
- On the spin-up of an electrically conducting fluid Part 1. The unsteady hydromagnetic Ekman-Hartmann boundary-layer problemJournal of Fluid Mechanics, 1969
- Influence of an Axial Magnetic Field on the Steady Linear Ekman Boundary LayerPhysics of Fluids, 1968
- On a time-dependent motion of a rotating fluidJournal of Fluid Mechanics, 1963