Many natural and industrial flows are subject to time-dependent boundary conditions and temporal modulations (e.g. driving frequency), which significantly modify the dynamics compared with their static counterparts. The present problem addresses ferrofluidic wavy vortex flow in Taylor-Couette geometry, with the outer cylinder at rest in a spatially homogeneous magnetic field subject to an alternating modulation. Using a modified Niklas approximation, the effect of frequency modulation on nonlinear flow dynamics and appearing resonance phenomena are investigated in the context of either period doubling or inverse period doubling. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.
Keywords: Taylor–Couette flow; alternating magnetic field; bifurcations; ferrofluid; instability; resonance phenomena.