Vortex Stretching as a Mechanism for Quantum Kinetic Energy Decay

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Abstract
A pair of perturbed antiparallel quantum vortices, simulated using the three-dimensional Gross-Pitaevskii equations, is shown to be unstable to vortex stretching. This results in kinetic energy K$\nabla${}$\psi${} being converted into interaction energy EI and eventually local kinetic energy depletion that is similar to energy decay in a classical fluid, even though the governing equations are Hamiltonian and energy conserving. The intermediate stages include the generation of vortex waves, their deepening, multiple reconnections, the emission of vortex rings and phonons, and the creation of an approximately -5/3 kinetic energy spectrum at high wave numbers. All of the wave generation and reconnection steps follow from interactions between the two original vortices. A four vortex example is given to demonstrate that some of these steps might be general.

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