Remote effect of anisotropy in electrical conductivity or magnetic permeability on dynamo action

We demonstrate that a localised simple shear in an electrically conducting fluid can generate dynamo action, due to the presence of a distant solid wall with anisotropic electrical conductivity or magnetic permeability. Three cylindrical geometries are considered, depending on the position of the solid wall relative to the shear zone. The wall can be either ( a ) internal, ( b ) external, or ( c ) both internal and external, relative to the shear zone. For each of the three geometries, the dynamo threshold is derived analytically. Results are presented with experimental applications in mind, corresponding to present, past or future dynamo experiments. We also consider an application to the Earth’s core, assuming anisotropic electrical conductivity in the inner core and some shear in the tangent cylinder.