Spontaneous Core Rotation in Ferrofluid Pipe Flow

Ferrofluid flow along a tube of radius R in a constant axial magnetic field is revisited. Our analytical solution and numerical simulations predict a transition from an initially axial flow to a steady swirling one. The swirl dynamo arises above some critical pressure drop and magnetic field strength. The new flow pattern consists of two phases of different symmetry: The flow in the core resembles Poiseuille flow in a rotating tube of the radius r∗<R, where each fluid element moves along a screw path, and the annular layer of the thickness R-r∗, where the flow remains purely axial. These phases are separated by a thin domain wall. The swirl appearance is accompanied with a sharp increase in the flow rate that might serve for the detection of the swirling instability.