Propagating vortices in ferrofluidic Couette flow under magnetic fields – Part II: Oblique orientated fields

Abstract

This work provides a numerical investigations of propagating vortex flow states (pVs) for ferrofluidic Couette flow with small aspect ratio and fixed non-rotating end-walls. The system is subjected to oblique magnetic fields as superposition of axial and transverse orientated fields. Such field configuration breaks the basic system symmetries and renders all flow structures to be inherently three-dimensional with complexer flow dynamics. Under oblique field configuration pV states are not direct present at onset. Instead oscillating flow states (oVs) bifurcate out of the stationary state. Basically these oVs hold same symmetries as pVs, which eventually evolve in a smooth transformation out of the oVs. pVs under oblique fields appear periodic or quasi-periodic, which render them topological speaking to exist on either two- or one-dimensional invariant manifolds as 2-torus or limit cycle (1-torus) solutions, respectively. In detail, structural modifications and changes in spatial and temporal behavior for pV solutions are studied with changing the magnetic field strength of the applied magnetic field.