A numerical 3d stability analysis of the MHD cylinder wake flow

In the present paper the stability of the time-dependent, three-dimensional, incompressible flow around a circular cylinder exposed to an external magnetic field is investigated numerically. We perform a linear 3d stability analysis of the 2d flow being either steady or quasiperiodic as known from previous work. By monitoring the time evolution of the integral energy of the 3d disturbances in the computational domain we decide whether the flow is globally unstable or stable. The results are compared and validated with recent results for the purely hydrodynamic problem. We restrict the analysis to a magnetic field being aligned with the oncoming flow. For this case we numerically confirm the general result of Hunt that in the (Re, N)-plane parameter regions above the 2d-neutral stability curve exist where the flow is 3d-unstable but 2d stable (steady) because the magnetic field acts in a different way on 2d and 3d instabilities.