Published online by Cambridge University Press: 29 March 2006
Finite amplitude, impulsively started spin-up and spin-down is analysed for axially symmetric flow of a viscous, incompressible, electrically conducting fluid confined between infinite, flat, parallel, insulating boundaries. A uniform axial magnetic field is present in the initial state, but is subsequently distorted by fluid motions. The method of matched asymptotic expansions reduces the problem to a first-order, ordinary, nonlinear, integro-differential equation for the transient development of the interior angular velocity on the time scale of spin- up, as driven by quasi-steady nonlinear Ekman-Hartmann boundary layers. This two-parameter equation is solved analytically in certain limits and numeric-ally in general. The solutions show that nonlinear non-magnetic spin-up and spin-down take longer than for linearized flow, spin-down occurring more rapidly in the early stages but requiring more time for completion than spin-up. A magnetic field promotes both spin-up and spin-down, but a weak field is relatively ineffective for spin-down yet very effective for spin-up. A strong magnetic field dominates nonlinear processes and gives identical spin-up and spin-down times, which coincide with that found from linear hydromagnetic theory.
To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.
To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.