Parity-breaking flows in precessing spherical containers

We present numerical solutions of the flow in precessing spheres and spherical shells with small (r(i)/r(o)=0.1) inner cores and either stress-free or no-slip inner boundary conditions. For each of these three cases we consider the sequence of bifurcations as the Reynolds number Re=r(o)(2)Ω/ν is increased up to ~1280, focusing particular attention on bifurcations that break the antipodal symmetry U(-r)=-U(r). All three cases have steady and time-periodic symmetric solutions at smaller Re, and quasiperiodic asymmetric solutions at larger Re, but the details of the transitions differ, and include also periodic asymmetric and quasiperiodic symmetric solutions in some of the cases.