Enstrophy Cascade in Decaying Two-Dimensional Quantum Turbulence

Abstract

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}.

Entropy of Negative Temperature States for a Point Vortex Gas

“…It is interesting to note that the flow patterns observed in some of these works also closely resemble similar flow structures observed in classical fluids [47,48]. Indeed, in recent years, increasing evidence has accumulated which suggests that a large ensemble of point vortices/quantised vortices can replicate certain features of classical 2D turbulence including the direct enstrophy cascade [49] and the inverse energy cascade [50,51]. Moreover, the signature of vortex clustering in the energy spectrum and its relation to the Kolmogorov spectrum in classical fluids was considered in [52,53].…”

Probing two-dimensional quantum fluids with cavity optomechanics

“…Furthermore, while the experiments reported here were performed with a relatively small number of vortices, theÅngström-scale of the vortex core in helium-4 will enable the future research on the dynamics of ensembles of thousands of vortices, a regime well outside current capabilities with cold atom and exciton-polariton superfluids [263]. This could allow emergent phenomena in two-dimensional turbulence to be explored, such as the inverse energy cascade [263,280] and anomalous hydrodynamics [281,282].…”

“…The timescale within which a metastable state is reached scales inversely with the vortex-vortex interaction strength and hence depends on the density of free vortices. This timescale can be estimated from the characteristic turnover time for internal rearrangement of the free-vortex cluster, τ ∼ r 2 c /N κ, where N is the number of free vortices, r c is the radius of the cluster, and κ is the circulation quantum [263]. Taking the case of two free vortices separated by the disk radius R = 30 µm provides an upper bound to the turnover time of τ 5 ms 1 .…”

Engineering time-averaged optical potentials for Bose-Einstein condensates

“…Cascades characterise the kinetic energy transport mechanisms which govern the evolution, and provide the more discerning signature. Signatures of the cascades which ultimately form Onsager vortices must manifest before any macroscopic dipole forms, enabling earlier detection [184][185][186][187]. Energy cascades may alternatively characterise driven turbulent systems, where vortices are injected continuously [188][189][190].…”

“…Under those circumstances, the kinetic energy is transported across some inertial range from shorter to longer length scales [185]. Kinetic energy cascades which govern the Onsager vortex formation are another worthwhile subject for future investigation [186,187].…”