Ferrofluidic Couette flow in time-varying magnetic field

Despite time-dependent boundary conditions being ubiquitous in natural and industrial flows, to date the influence of such temporal modulations (e.g. with driving frequency omega(H)) has been given minor attention. The present problem addresses ferrofluidic Couette flow in between counter-rotating cylinders in a spatially homogeneous magnetic field subject to time-periodic modulation. Such a modulation can lead to a significant inner Reynolds number (Re-i) enhancement for both, either helical and toroidal flow structures. Using a modified Niklas approximation, the effect of low-and high-frequency modulation onto the primary instabilities, stability boundaries as well as on the non-linear oscillations that may occur is investigated. Focusing on bistable co-existing solutions, around their stability thresholds quite complex non-linear system response and flow dynamics is detected. For the system remaining supercritical always a single solution is selected by omega(H), while crossing the bifurcation thresholds within a modulation period the triggered system response is more complex, reaching from alternation between different solutions towards the appearance of intermittent behavior.