Magnetic instabilities in rapidly rotating spherical geometries II. more realistic fields and resistive instabilities

Details Magnetic instabilities in rapidly rotating spherical geometries II. more realistic fields and resistive instabilities Magnetic instabilities in rapidly rotating spherical geometries II. more realistic fields and resistive instabilities

Nov 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991gapfd..60..275f&link_type=abstract

Geophysical and Astrophysical Fluid Dynamics, vol. 60, Issue 1, pp.275-294

Physics

Fluid Dynamics

13

Earth'S Core, Hydromagnetic Waves, Magnetic Instabilities (Ideal And Resistive), Spherical Geometry

Scientific paper

Magnetic instabilities play an important role in the understanding of the dynamics of the Earth's fluid core. In this paper we continue our study of the linear stability of an electrically conducting fluid in a rapidly rotating, rigid, electrically insulating spherical geometry in the presence of a toroidal basic state, comprising magnetic field BMBO(r, )1ø and flow UMUO(r, )1ø The magnetostrophic approximation is employed to numerically analyse the two classes of instability which are likely to be relevant to the Earth. These are the field gradient (or ideal) instability, which requires strong field gradients and strong fields, and the resistive instability, dependent on finite resistivity and the presence of a zero in the basic state BO(r,θ). Based on a local analysis and numerical results in a cylindrical geometry we have established the existence of the field gradient instability in a spherical geometry for very simple basic states in the first paper of this series. Here, we extend the calculations to more realistic basic states in order to obtain a comprehensive understanding of the field gradient mode. Having achieved this we turn our attention to the resistive instability. Its presence in a spherical model is confirmed by the numerical calculations for a variety of basic states. The purpose of these investigations is not just to find out which basic states can become unstable but also to provide a quantitative measure as to how strong the field must become before instability occurs. The strength of the magnetic field is measured by the Elsasser number; its critical value c describing the state of marginal stability. For the basic states which we have studied we find c 200-1000 for the field gradient mode, whereas for the resistive modes c 50-160. For the field gradient instability, c increases rapidly with the azimuthal wavenumber m whereas in the resistive case there is no such pronounced difference for modes corresponding to different values of m. The above values of c indicate that both types of instability, ideal and resistive, are of relevance to the parameter regime found inside the Earth. For the resistive mode, as is increased from c, we find a shortening lengthscale in the direction along the contour BO = 0. Such an effect was not observable in simpler (for example, cylindrical) models.

Affiliated with

Also associated with

No associations

Rating

Magnetic instabilities in rapidly rotating spherical geometries II. more realistic fields and resistive instabilities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Magnetic instabilities in rapidly rotating spherical geometries II. more realistic fields and resistive instabilities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Magnetic instabilities in rapidly rotating spherical geometries II. more realistic fields and resistive instabilities will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1717288