Within the framework of the two-fluid Landau theory, flows into helium II inside a rotating cylinder are investigated. Special attention is paid to the analysis of excitation by centrifugal forces of counter-current (by super-fluid and normal components) flows. In the approximation of incompressible fluid, an analytical solution of the equations of motion, vortex-free for both components is obtained. The tangential velocities for it are the same as those of a rotating solid body, with the normal and superfluid components moving in opposite directions, with different angular velocities. It's resulting vorticity is compensated by a spiraled counter-current radical movements. Such solution has no axial symmetry and has a tangential gap along the radius. Despite its instability, it is of some interest. First, it can be corrected by stabilizing deformations. In addition, it shows the paths of loss of stability of high-symmetric States. In particular, in our opinion, this type of disturbance are intermediate flow from Landau (superfluid component is at rest) one to the rotation of the Feynman type (in the superfluid part of a system of vortices).
Keywords: helium II, rotating cylinder, two-fluid theory, counter-current flows, centrifugal forces, vorticity compensation
The paper discusses the flow induced by centrifugal forces in helium II on the outside of the rotating cylinder. The analysis was carried out in the framework of Landau's two-fluid theory, in the approximation of a plane incompressible fluid. A two-parameter family of solutions of the equations of motion is revealed, in which the centrifugal forces for the normal component are fully compensated by counter-current (normal and super-fluid components) flows. According to preliminary estimates, the most stable of them is the flow, in which the pressure forces in the superconducting part are also compensated, The results show that in the analysis of helium II rotations it is necessary to take into account countercurrent instabilities.
Keywords: helium II, rotating cylinder, two-fluid theory, counter-current flows, stability, centrifugal forces, pressure compensation