Seminarium KMMF "Teoria Dwoistości"

In the first part I will discuss two classes of solutions of quantum vortex motion in the context of localized induction approximation and relation of these solutions to the motion of a classical vortex. The first class describes self similar solutions, while the second one the solutions for which the infinite vortex line shrinks, but still maintains both its shape and spatial scale. In the second part I will derive equations describing coupled motion of normal and superfluid components in the case when macroscopic velocity fields of both components remain laminar. In the considered approach the normal and superfluid component are coupled by a tangle of quantum vortex lines, which density evolves according to the modified Vinen equation accounting for anisotropy and drift of the tangle. Two specific cases will be considered: stationary rotating turbulence and formation of plane Couette flow.