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Exploring the Equivalence between Two-Dimensional Classical and Quantum Turbulence through Velocity Circulation

Nicolás P Müller1,2, Giorgio Krstulovic1

  • 1Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire CS 34229 - F 06304 NICE Cedex 4, France.

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This summary is machine-generated.

We compared quantum and classical turbulence using simulations. Quantum turbulence matches classical turbulence in inverse cascades and nearly incompressible direct cascades, establishing boundaries for their equivalence.

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Area of Science:

  • Fluid Dynamics
  • Quantum Mechanics
  • Computational Physics

Background:

  • Two-dimensional turbulence exhibits distinct direct and inverse energy cascades.
  • Quantum turbulence, governed by the Gross-Pitaevskii equation, shares similarities with classical turbulence.
  • Understanding the statistical properties of velocity circulation is key to characterizing turbulent flows.

Purpose of the Study:

  • To investigate and compare the statistical properties of velocity circulation in two-dimensional classical and quantum turbulence.
  • To determine the conditions under which quantum turbulence replicates the behavior of classical turbulence.
  • To establish the limits of equivalence between these two types of turbulence.

Main Methods:

  • Numerical simulations of the incompressible Navier-Stokes equations for classical turbulence.
  • Numerical simulations of the Gross-Pitaevskii equation for quantum turbulence.
  • Analysis of energy spectra and circulation intermittency for both direct and inverse cascades.

Main Results:

  • Gross-Pitaevskii simulations show energy spectra consistent with the double cascade theory of 2D classical turbulence.
  • Circulation intermittency in the inverse cascade of quantum turbulence is identical to that in classical turbulence.
  • Equivalence in self-similar scaling for circulation holds in the direct cascade for nearly incompressible quantum flows.
  • Deviations from equivalence occur when compressibility becomes significant, with quasishocks generating quantum vortices.

Conclusions:

  • Quantum turbulence exhibits strong similarities with classical turbulence, particularly in inverse cascades and nearly incompressible direct cascades.
  • The equivalence between 2D classical and quantum turbulence is bounded and breaks down under significant compressibility.
  • This study delineates the conditions and limitations for the analogy between classical and quantum turbulence.