Abstract
In this paper we present numerical simulations for the dynamics of a vortex pair described by the two-dimensional nonlinear Schr\"odinger equation. The simulations reveal significant nonvanishing fluctuations around the classical velocities of vortices in an ideal incompressible fluid due to excitation of the acoustic (or sound) field. The reason for the fluctuations is the potentiality of the superflow, which introduces significant compressibility to the superfluid. We discuss some implications of this observation, especially on existing discrepancies between theories of superfluid turbulence. We indicate a possible mechanism for the spontaneous nucleation of a small vortex ring in the three-dimensional nonlinear Schr\"odinger equation.
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