Two‐Scale Model of A Geomagnetic Field Variation: Two‐scale model of a geomagnetic field variation

Abstract

This study considers a simple 2‐D model of the core and mantle in which the core mantle boundary (CMB) is a plane. A two‐scale flow varying with time as e‐iwt is given in the conducting fluid: a high velocity horizontal flow in a thin layer of thickness δ and a ‘volume’ flow with both horizontal and vertical lengths L >> δ. the varying magnetic field induced by the flow interacting with a standing uniform main magnetic field‐either vertical or horizontal‐can be computed analytically as long as the corresponding induction equation can be linearized. the main goal of the paper is to give a rather full account of the variety of behaviours and geometries of the induced varying field depending on the frequency of the flow. the changes of its vertical and horizontal components through the δ layer are examined in detail, both in the low and the high frequency cases. In the first case the solution of the induction equation is essentially a ‘volume’ solution, and the part played by the δ layer is just to allow the induced field to match a potential field at the CMB. In the high frequency case, somewhat unexpected features are displayed; and it is shown that the vertical component of the induced field at the CMB obeys a new equation which replaces the well‐known frozen flux equation (valid if there is only one relevant length scale L). It is also shown that in both cases the horizontal component of the induced field is quite different at the CMB and in body of the core (beneath the thin layer δ). Some possible features of the secular variation of the actual geomagnetic field are discussed in the light of the model. Copyright © 1993, Wiley Blackwell. All rights reserved