Flow dynamics between two concentric counter-rotating porous cylinders with radial through-flow

This paper investigates the impact of radial mass flux on Taylor-Couette flow in counterrotating configuration, in which a Hopf bifurcation gives rise to branches of nontrivial solutions. Using direct numerical simulation we elucidate structures, dynamics, stability, and bifurcation behavior in qualitative and quantitative detail as a function of inner Reynolds numbers (Rei) and radial mass flux (alpha) spanning a parameter space with a rich variety of solutions. Both radial inflow and strong radial outflow stabilize the system, whereas weak radial outflow has a strong destabilizing effect. We detected the existence of stable ribbons and mixed ribbons with low azimuthal wave number without symmetry restriction. In addition, ribbon solutions and mixed-ribbon solutions can be stable or unstable saddles. Furthermore, in the case of unstable saddles alternations between two different symmetrically related saddles generate different heteroclinic cycles. For alternating stationary (in comoving frame) ribbons the persistence time in one saddle decreases with distance from the onset. The persistence time for the heteroclinic cycle of alternating mixed ribbons shows a more complicated dependence with variation in control parameters and seems to follow an intermittency scenario of type III. Depending on whether the symmetrically related solutions are stationary or time-dependent, the heteroclinic connection can be either of oscillatory or nonoscillatory type.