Vortex Multiplication in Applied Flow: the Precursor to Superfluid Turbulence

The dynamics of quantized vortices in rotating $^3$He-B is investigated in the low density (single-vortex) regime as a function of temperature. An abrupt transition is observed at $0.5 T_{\rm c}$. Above this temperature the number of vortex lines remains constant, as they evolve to their equilibrium positions. Below this temperature the number of vortices increases linearly in time until the vortex density has grown sufficiently for turbulence to switch on. On the basis of numerical calculations we suggest a mechanism responsible for vortex formation at low temperatures and identify the mutual friction parameter which governs its abrupt temperature dependence.