Oscillatory dynamos in rotating plane Couette flow

We model a dynamo process using direct numerical simulation (DNS) of the magnetohydrodynamic (MHD) equations in hydrodynamically-unstable rotating plane Couette flow. We find dynamo states which undergo magnetic cycles. In the first phase of each cycle, the weak magnetic field grows exponentially due to a kinematic dynamo instability of the hydrodynamic state. The instability saturates, causing the velocity to decrease substantially. This weak velocity can no longer sustain the magnetic field, causing the field to decay to small values, completing the cycle. We demonstrate that such cycles can be intermittent or chaotic depending on global parameters such as the aspect ratio, Rossby number, and magnetic Prandtl number.