Pressure-induced vortex rings multiplication as a source of vorticity in superfluids

Abstract

A modified version of the Gross-Pitaevskii equation (GPE) combined with the Newton equation is used to model the interaction of sound waves with heavy particles, propagating in a quantum fluid. In contrast with the classical cubic GPE we use the equation with the 7-th order nonlinearity, in which the correct equation of state for the fluid is incorporated. Such modification makes this formalism applicable to study pressure variation effects. In the considered process, the particle, moving with an initial velocity, creates a vortex ring excitation in the fluid. A subsequent change of pressure, which appears because of the interaction of the particle with a sound wave, initiates the vortex multiplication process. As a result of the following vortex interplay, the moving particle becomes surrounded by a decaying turbulent cloud with high degree of vorticity. It is demonstrated how at certain stage of evolution of the cloud, the kinetic energy of the fluid circulation around the particle increases in a resonant manner. In accordance with the hydrodynamic Bernoulli principle, an increase of the speed of the fluid (kinetic energy) results in a decrease of pressure (potential energy) around the particle. Such mechanism may help to understand the details of experiments with exploding electron bubbles in liquid helium, as a result of the interaction with sound waves.