D. Loper $^(a), A. Chulliat $^(a) and H. Shimizu $^(b)
$^(a) Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, FL, USA $^(b) Earthquake Research Institute, university of Tokyo, Tokyo, Japan
A serious limitation of current numerical models of large-scale MHD flows and dynamos is the lack of a realistic parameterization of small -scale processes. This presentation will report on initial progress toward improved parameterizations, based on representations of flows, perturbation fields and electric currents generated by small-scale buoyant parcels. In the initial phase of research, the perturbations are driven by a single isolated parcel of Gaussian shape. The solution method consists of taking the 3-D Fourier transform of the linearized equations of MHD. These transformed equations can be inverted for various spatial regions in either two or three Fourier dimensions, yielding a 'semi-analytic' or fully analytic solution. For example, in the Coriolis-dominant case, the velocity and pressure near the buoyant parcel can be found completely in closed form and is independent of the nature of the secondary forces. However the structure of the Taylor column is sensitive to these forces. We will present solutions and visualizations in the parameter regime where the Elsasser number is larger than the Ekman number but less than unity.