#### Title

### Theoretical estimates of the westward drift

#### Document Type

Article

#### Publication Date

11-30-1984

#### Department

Department of Mathematical Sciences; Department of Computer Science

#### Abstract

Virtually all dynamo models may be expected to give rise to a permanent differential rotation between mantle and core. Weak conductivity in the mantle permits small leakage currents which couple to the radial component of the magnetic field, producing a Lorentz torque. Mechanical equilibrium is achieved when a zero net torque is established at a critical rotation rate. An estimate of the drift is determined easily given the magnetic field structure predicted by any dynamo model. The result for the drift rate at the core-mantle interface along the equator is given by the product of three factors

Uφ*=UφR λ* L*

The first of these is a geometrical factor which depends only on the structural character of the field. For a variety of model fields, this factor ranges from 16 to 35. The second factor is the ratio of r.m.s. toroidal to poloidal field. This ratio is an (implicitly) adjustable parameter of both α^{2} and α-ω dynamos, and is a measure of the relative efficiency of the generation process for each component. The third (dimensional) term is the ratio of core magnetic diffusivity to core radius, 10^{-4} cm s^{-1}.

The result is essentially independent of the value of mantle diffusivity and its effective depth. The sign of the result may be positive or negative. For α^{2} dynamos a westward drift is produced by choosing α > 0 in the Northern Hemisphere, which constitutes a dynamical assertion about the dynamo process. For an r.m.s. toroidal field of the order of 15 Gs, based on fairly general considerations, a drift rate comparable to observation is expected.

#### Publication Title

Physics of the Earth and Planetary Interiors

#### Recommended Citation

Ierley, G.
(1984).
Theoretical estimates of the westward drift.
*
Physics of the Earth and Planetary Interiors,
36*(1), 43-48.
http://doi.org/10.1016/0031-9201(84)90097-9

Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/5423

## Publisher's Statement

© 1984