Toward scale-separated weak-field spherical dynamos

Recent numerical experiments of dynamo action relevant to the generation of the geomagnetic field have produced different regime branches identified within bifurcation diagrams. Notable are separate branches in which the resultant magnetic field is either weak or strong. Weak-field solutions can be identified by the prominent role of viscosity on the motion whereas the magnetic field has a leading order effect on the flow in strong-field solutions. For a given Ekman number, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi mathvariant="script">E</a:mi></a:math> (measuring the ratio of viscosity to rotational effects), the existence of these branches and bistability between them is reliant on a small enough magnetic Ekman number, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi mathvariant="script">E</c:mi><c:mtext>m</c:mtext></c:msub></c:math> (measuring the ratio of magnetic diffusion to rotational effects, so <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi mathvariant="script">E</e:mi><e:mo>/</e:mo><e:msub><e:mi mathvariant="script">E</e:mi><e:mtext>m</e:mtext></e:msub><e:mo>=</e:mo><e:msub><e:mi mathvariant="script">P</e:mi><e:mtext>m</e:mtext></e:msub></e:mrow></e:math>, the magnetic Prandtl number). Both branches are known to produce large scale dipolar magnetic fields but do not exhibit an expected scale separation between the flow and magnetic field. In this work, by reducing <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:msub><i:mi mathvariant="script">E</i:mi><i:mtext>m</i:mtext></i:msub></i:math>, we identify a variety of dynamo states on the weak-field branch beyond the known dipolar solutions. Specifically, hemispherical and nondipolar dynamos were found, in addition to the usual dipolar solutions. Some solutions exhibit clear scale separation between small-scale flow and large-scale magnetic field, despite the large ratio of viscosity to magnetic diffusion. Numerical solutions in this regime have not been observed before and they offer a first connection with earlier theoretical work based on mean-field theory.