Published online by Cambridge University Press: 29 March 2006
The propagation of plane hydromagnetic waves in a fluid rotating with angular velocity ω and permeated by a magnetic field B = {Bx(z), By(z), 0} varying in both magnitude and direction with z is studied by techniques recently applied to the propagation of internal gravity waves in a shear flow (Bretherton 1966; Booker & Bretherton 1967). Particular attention is paid to a class of 'slow’ hydromagnetic waves of interest in connexion with the dynamics of the earth's liquid core. While, in general, rotation permits propagation across the lines of force, there is associated with each wave a ‘critical level’ z = zc, which acts as a valve by effectively permitting the wave to penetrate it from one side only. A slow hydromagnetic wave with frequency ω and wavenumber components k,l normal to the magnetic field gradient can only effectively penetrate its critical level if its propagation speed across field lines W is such that Wωz,(ωx,k+ ωy,l)ω < 0. The phenomenon of ‘critical-layer absorption’ evidently does not in general require the presence of a mean shear flow; a non-uniform magnetic field gives rise to similar effects provided that some other restoring mechanism (in this case the Coriolis force) is available to permit hydromagnetic waves to propagate across field lines.
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.