HR: 0830h
AN: GP31D-0776    [PDF]
TI: Critical bifurcations among viscous boundary layers of the geodynamo
AU: * Love, J J
EM: jlove@usgs.gov
AF: USGS Geomagnetism Group, Box 25046 MS 966 DFC, Denver, CO 80225 United States
AU: Walker, M R
EM: matthew.walker@phpc.cam.ac.uk
AF: Department of Public Health and Primary Care, University Forvie Site, Robinson Way, University of Cambridge, Cambridge, CB2 2SR United Kingdom
AB: An analysis is made of a specific class of solutions to the non-linear mean-field equations of magnetohydrodynamics which approximate the dynamo in the Earth's core. These solutions, obtained after separation of variables, have all of their nonlinearity in one spatial dimension. The resulting enormous numerical economy with which the solutions can be constructed, as compared to more traditional two-dimensional and three-dimensional approaches, enables us to explicitly model the viscous boundary layers on the core side of the core-mantle boundary. In analyzing these solutions we concentrate specifically on the structure of the boundary layers for small Ekman number. Assuming a simple, but geophysically plausible, alpha structure, there is a bifurcation of solutions from the critical alpha number: one solution branch traces super-critical dynamo action, but which has a Hartmann-type force balance, the other, sub-critical branch has the more usually expected Ekman-type force balance. The subcritical branch eventually connects onto a different super-critical branch, but one with solutions having a complicated sandwich of nested Hartmann and Ekman boundary layers. The Ekman-number-dependent scalings of representative solutions on these various branches are explored. The implications for the discovery of these various solution types have significance to dynamo theory, since most simulations assume, a priori, that the boundary layer beneath the core-mantle boundary is of a simple Ekman structure. Yet our results indicate that those are only a subset of the possible solutions, other solutions can have a very different force-balance structure. We are reminded, once again, that boundary layers, albeit thin, can have a global-scale controlling influence on the nature of the Earth's magnetic field.
DE: 1510 Dynamo theories
DE: 3220 Nonlinear dynamics
SC: Geomagnetism and Paleomagnetism [GP]
MN: 2003 Fall Meeting