NONLINEAR MAGNETOCONVECTION AND THE GEOSTROPHIC FLOW - SUBCRITICAL SOLUTIONS

Authors
Citation
Mr. Walker, NONLINEAR MAGNETOCONVECTION AND THE GEOSTROPHIC FLOW - SUBCRITICAL SOLUTIONS, Studia geophysica et geodaetica, 42(3), 1998, pp. 272-279
Citations number
18
Categorie Soggetti
Geochemitry & Geophysics
ISSN journal
00393169
Volume
42
Issue
3
Year of publication
1998
Pages
272 - 279
Database
ISI
SICI code
0039-3169(1998)42:3<272:NMATGF>2.0.ZU;2-I
Abstract
The magnetoconvection problem under the magnetostrophic approximation is investigated as the nonlinear regime is entered. The model consists of a fluid filled sphere, internally heated, and rapidly rotating in the presence of a prescribed, axisymmetric, toroidal magnetic field. F or simplicity only a dipole parity and a single azimuthal wavenumber ( m = 2) is considered here. The leading order nonlinearity at small amp litude is the geostrophic flow U-g which is introduced to the previous ly linear model (Walker and Barenghi, 1997a, b). Walker and Barenghi ( 1997c) considered parameter space above critical and found that U-g ac ts as an equilibration mechanism for moderately supercritical solution s. However, for solutions well above critical a Taylor state is approa ched and the system can no longer equilibrate. More importantly though , in the context of this paper, is that subcritical solutions were fou nd. Here subcritical solutions are considered in more detail. A was fo und that, at (Ra) over tilde = (Ra) over tilde(c), R-m is strongly dep endent on Lambda. ((Ra) over tilde(c) is the critical value of the mod ified Rayleigh number (Ra) over tilde, Rm is a measure of the maximum amplitude of the generated geostrophic flow while Lambda, the Elsasser number, defines the strength of the prescribed toroidal field.) Rm at (Ra) over tilde = (Ra) over tilde(c) proves to be the key measure in determining how far into the subcritical regime the system can advance .