Breaking of Equatorial Symmetry in a Rotating System: a Spiralling Intermittency Mechanism

{ Rotating uid systems can display large scale asymmetries about the equator. A model-independent mechanism for such symmetry-breaking is described, via a spiralling intermittency that combines the on-oo and Pomeau-Manneville mechanisms. This involves a periodic orbit in an invariant subspace becoming unstable to perturbations transverse to the subspace, these are describable in terms of the equatorial symmetry of the system. A scaling law is derived for the intermittency and this is tested against results from the numerical simulation of the behaviour of a rotating electrically conducting uid. Finally we make comparisons with recent results on intermittency and symmetry-breaking. Introduction. { In the study of rotating uids there are often important and interesting departures from equatorial symmetry (see e.g. 1]). Such asymmetries can be explained by factors external to the system being studied, but symmetry-breaking can also occur spontaneously in the system itself 2]. Recent work on symmetry breaking via on-oo intermittency 3] could be relevant to such systems, however such work considers symmetry-breaking in phase space and it is by no means clear how this is observed in the space-time behaviour of the system 4]. We consider an axisymmetric rotating uid system connned in a volume such that the boundary conditions have equatorial symmetry (e.g. sphere, torus, cylinder). Let A be a physical property of the system (vector or scalar), whose evolution is governed by a system of equations. We consider the governing equations to possess both symmetric and antisymmetric solutions with respect to reeection in the equatorial plane,