  We investigate the transition from steady dipolar to reversing multipolar
dynamos. The Earth has been argued to lie close to this transition, which could
offer a scenario for geomagnetic reversals. We show that the transition between
dipolar and multipolar dynamos is characterized by a three terms balance (as
opposed to the usually assumed two terms balance), which involves the
non-gradient parts of inertial, viscous and Coriolis forces. We introduce from
this equilibrium the sole parameter ${{\rm Ro}}\,{{\rm E}}^{-1/3} \equiv {{\rm
Re}}\,{{\rm E}}^{2/3}$, which accurately describes the transition for a wide
database of 132 fully three dimensional direct numerical simulations of
spherical rotating dynamos (courtesy of U. Christensen). This resolves earlier
contradictions in the literature on the relevant two,terms balance at the
transition. Considering only a two terms balance between the non-gradient part
of the Coriolis force and of inertial forces, provides the classical ${{\rm
Ro}}/{\ell_u}$ (Christensen and Aubert, 2006). This transition can be
equivalently described by ${{\rm Re}} \, {\ell^{2}_u}$, which corresponds to
the two terms balance between the non-gradient part of inertial forces and
viscous forces (Soderlund {\it et al.}, 2012).
