Analysis of Global MHD Instability in the Tachocline Using a Shallow-water Model
Abstract
Results from studying 2D models indicate that tachocline differential rotation is hydrodynamically stable, but is magnetohydrodynamically unstable with a coexisting toroidal field (Gilman & Fox 1997, ApJ,484, 439). In a recent study, Dikpati & Gilman (2001, ApJ, Mar.20 issue) have shown, by including simplified 3D effects through use of a shallow-water model, that the overshoot part of the tachocline can be hydrodynamically unstable even without a toroidal field. Hydrodynamic shallow-water equations have an MHD analog (Gilman 2000, ApJ, 544, L79). We study here the linear MHD shallow-water instability of tachocline latitudinal differential rotation with a variety of coexisting toroidal field profiles. We show that both the radiative and overshoot parts of the tachocline become unstable in presence of almost all toroidal field profiles, from broad to narrow, with a wide range of field strengths, generalizing the 2D MHD instability, as well as the shallow-water HD instability. Instability occurs for a wide range of subadiabatic tachocline stratifications. Unstable MHD shallow-water modes possess kinetic helicity which, unlike the kinetic helicity of HD shallow-water modes, depends on field strength and latitude-location of the peak toroidal field. Therefore, the α -effect produced by global MHD shallow-water instability contains its own quenching, as well as time-dependence, if we identify the latitude of the peak magnetic field as a proxy for solar-cycle phase. We also demonstrate how the toroidal field band can be twisted in the tachocline due to the first order effect of the instability. Acknowledgements: This work is supported by NASA grants W-19752 and S-10145-X. National Center for Atmospheric Research is sponsored by National Science Foundation.
- Publication:
-
AGU Spring Meeting Abstracts
- Pub Date:
- May 2001
- Bibcode:
- 2001AGUSM..SP22A05G
- Keywords:
-
- 7522 Helioseismology;
- 7524 Magnetic fields