Vortex Stretching as a Mechanism for Quantum Kinetic Energy Decay

Abstract

A pair of perturbed anti-parallel quantum vortices, simulated using the three-dimensional GrossPitaevskii equations, is shown to be unstable to vortex stretching. This results in kinetic energy K ∇ψ 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 wavenumbers. All the wave generation and reconnection steps follow from interactions between the two original vortices, unlike the selfinteractions in vortex wave models. A four vortex example is given to demonstrate that some of these steps might be general. . These results imply that the effect could be a property of the ideal, inviscid equations for a pure superfluid or quantum gas, so that coupling to the viscous normal fluid component is not required to get decay.

A Note on the Propagation of Quantized Vortex Rings Through a Quantum Turbulence Tangle: Energy Transport or Energy Dissipation?

“…Indeed, subsequent numerical simulations performed by both Kerr 11 and Kursa et al 12 have confirmed this scenario. With this in mind, it is plausible to think 9 that this mechanism may provide an alternative route for energy dissipation other than a Kelvin wave cascade [13][14][15] .…”

“…Indeed, using formulas (11) and (12) we can estimate the expected amount of energy to reach a boundary in a typical experimental apparatus for quantum turbulence. As the energy of a vortex ring is proportional to its radius then after n reconnections the vortex ring will contain a factor of (3/4) n of its original energy.…”

Bounds for Euler from vorticity moments and line divergence

“…These figures can be compared with a similar stage (t = 1.25) in the evolution of anti-parallel quantum vortices in Kerr (2011) and to the cover illustration from Kerr (1996), which shows how the vortex lines twist as they extend from the anti-parallel interaction. What happens just after this configuration reconnects in Navier-Stokes calculations can be found in Kerr (2013).…”

“…The resulting variation of the initial circulation in y-planes, Γ (y) is 1 %. (iii) The very long perturbed trajectory from Kerr (2011):…”

“…In two recent vortex reconnection calculations, viscous (Kerr 2013) and quantum (Kerr 2011), this back bend overshoots the original z level of the vortices, leading to a second reconnection site, additional vortex stretching and the formation of vortex rings.…”