Stochastic approach to analysis of vortex dynamic and turbulence in superfluid

The article is devoted to the study of the stability of a single vortex filament and a vortex ring in superfluid helium He II during the rotation of a cylindrical vessel. The formalism of the Fokker–Planck equation was used to solve this problem. As a result of the study, it was revealed that the main parameter that affects the stability of a vortex filament or its instability is the Rossby number (Ro). For numbers Ro > 1, when the normal velocity component prevails, the state of the vortex filament is stable. For numbers Ro < 1, when the superfluid component exerts its influence more, the vortex filament loses its stability. An increase in temperature also contributes to the development of instability in the vortex filament. A study of the radius of the vortex ring torus showed that its decrease entails a decrease in the radius of the vortex ring itself, at which it is stable.