Equilibrium and stability of vortex chains in superfluid helium in rotating rings of arbitrary size

In this work, we consider the flow of He II between two concentric cylinders rotating with the same angular velocity. By representing the velocity of the superfluid component in terms of Weierstrass’ ζ-function, an expression is derived for the free energy of a rotating superfluid liquid with vortices in rings of arbitrary size. The obtained condition for the energy minimum indicates that in the equilibrium state, the vortices are situated at a point in the liquid where the velocity generated by them is the same as that of the normal component. An algorithm has been worked out to determine the moment of emergence and the position of any number of vortices. Some results of numerical experiments are presented, including the position of the first vortex and the instant of its emergence, free energy for different values of parameters, and the angular velocity for which the emergence of N vortices becomes advantageous from the energy point of view for some specific values of N.

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