Energy spectra of vortex distributions in two-dimensional quantum turbulence

Abstract

We theoretically explore key concepts of two-dimensional turbulence in a homogeneous compressible superfluid described by a dissipative two-dimensional Gross-Pitaeveskii equation. Such a fluid supports quantized vortices that have a size characterized by the healing length $\xi$. We show that for the divergence-free portion of the superfluid velocity field, the kinetic energy spectrum over wavenumber $k$ may be decomposed into an ultraviolet regime ($k\gg {\xi }^{-1}$) having a universal $k^{-3}$ scaling arising from the vortex core structure, and an infrared regime ($k\ll {\xi }^{-1}$) with a spectrum that arises purely from the configuration of the vortices. The Novikov power-law distribution of intervortex distances with exponent -1/3 for vortices of the same sign of circulation leads to an infrared kinetic energy spectrum with a Kolmogorov $k^{-5/3}$ power law, consistent with the existence of an inertial range. The presence of these $k^{-3}$ and $k^{-5/3}$ power laws, together with the constraint of continuity at the smallest configurational scale $k\approx {\xi }^{-1}$, allows us to derive a new analytical expression for the Kolmogorov constant that we test against a numerical simulation of a forced homogeneous compressible two-dimensional superfluid. The numerical simulation corroborates our analysis of the spectral features of the kinetic energy distribution, once we introduce the concept of a {\em clustered fraction} consisting of the fraction of vortices that have the same sign of circulation as their nearest neighboring vortices. Our analysis presents a new approach to understanding two-dimensional quantum turbulence and interpreting similarities and differences with classical two-dimensional turbulence, and suggests new methods to characterize vortex turbulence in two-dimensional quantum fluids via vortex position and circulation measurements.

19 pages, 8 figures

References in corpus (12)

• Power-law distributions in empirical data
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Emergence of turbulence in an oscillating Bose-Einstein condensate
• Bottleneck crossover between classical and quantum superfluid turbulence
• The trapped two-dimensional Bose gas: from Bose-Einstein condensation to Berezinskii-Kosterlitz-Thouless physics
• Bose-Einstein Condensation from a Rotating Thermal Cloud: Vortex Nucleation and Lattice Formation
• Critical Dynamics of a Two-dimensional Superfluid near a Non-Thermal Fixed Point
• Route to turbulence in a trapped Bose-Einstein condensate
• Thermal dissipation in quantum turbulence
• Gradual eddy-wave crossover in superfluid turbulence
• Quantum turbulence: From superfluid helium to atomic Bose-Einstein condensates
• Vortex dynamics in trapped Bose-Einstein condensate

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