Enstrophy Cascade in Two-Dimensional Quantum Turbulence

Ryu Numasato, Makoto Tsubota

Nir Navon, Alexander L. Gaunt, Robert P. Smith +1 more

Gary A. Williams, Andrew Forrester

Tapio Simula

Matthew T. Reeves, T. P. Billam, Xiaoquan Yu +1 more

We report evidence for an enstrophy cascade in large-scale point-vortex simulations of decaying two-dimensional quantum turbulence. Devising a method to generate quantum vortex configurations with kinetic energy narrowly localized near a single length scale, the dynamics are found to be well characterized by a superfluid Reynolds number Re_{s} that depends only on the number of vortices and the initial kinetic energy scale. Under free evolution the vortices exhibit features of a classical enstrophy cascade, including a k^{-3} power-law kinetic energy spectrum, and constant enstrophy flux associated with inertial transport to small scales. Clear signatures of the cascade emerge for N≳500 vortices. Simulating up to very large Reynolds numbers (N=32 768 vortices), additional features of the classical theory are observed: the Kraichnan-Batchelor constant is found to converge to C^{'}≈1.6, and the width of the k^{-3} range scales as Re_{s}^{1/2}.

Tzyy‐Leng Horng, C.-H. Hsueh, Shih-Wei Su +2 more

We investigate the dynamics of turbulent flow in a two-dimensional trapped Bose-Einstein condensate by solving the Gross-Pitaevskii equation numerically. The development of the quantum turbulence is activated by the disruption of an initially embedded vortex quadrupole. By calculating the incompressible kinetic-energy spectrum of the superflow, we conclude that this quantum turbulent state is characterized by the Kolmogorov-Saffman scaling law in the wave-number space. Our study predicts the coexistence of two subinertial ranges responsible for the energy cascade and enstrophy cascade in this prototype of two-dimensional quantum turbulence.