Numerical generation of a vortex ring cascade in quantum turbulence
Professor Robert M. Kerr
Department of Mathematics, University of Warwick
A symmetric anti-parallel quantum pair of vortices is
simulated using the three-dimensional Gross-Pitaevski
equations. The
initial development demonstrates vortex dynamics of stretching,
curvature
and torsion consistent with a filament calculation and simulations
of the classical, ideal Euler equations. How a vacuum mediates
reconnection between the pair is illustrated. Out of the
reconnection,
vortex waves are emitted with properties similar to waves in the
local induction approximation. These waves propagate down the
initial
vortex and deepen. When they deepen far enough, secondary reconnections
occur and vortex rings form. Near this time, spectra have a
$k^{-3}$
regime. As the vortex rings fully separate, the high wavenumber spectra
grow until,
at the final time simulated, spectra in two directions develop nearly
-5/3 subranges. This occurs without the dissipation of energy.
Analysis is in progress to determine the flow of energies in spectral
scale and physical space.