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Effective Transport by 2D Turbulence: Vortex-Gas Theory vs Scale-Invariant Inverse Cascade.

Julie Meunier1, Basile Gallet1

  • 1Service de Physique de l'Etat Condensé, Université Paris-Saclay, CNRS, CEA, 91191 Gif-sur-Yvette, France.

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Standard 2D turbulence scaling laws break down due to intense vortices. New scaling laws for effective diffusivity emerge, matching simulations and revealing large-scale organization in geophysical flows.

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Area of Science:

  • Fluid Dynamics
  • Turbulence Theory
  • Computational Physics

Background:

  • The scale-invariant inverse energy cascade is a key feature of 2D turbulence.
  • Theoretical predictions for energy spectra are validated by direct numerical simulations (DNS) and experiments.
  • Scale-invariance implies effective diffusivity depends only on energy flux and friction.

Purpose of the Study:

  • To investigate the validity of scale-invariant scaling laws in 2D turbulent flows.
  • To derive new scaling laws for effective diffusivity when scale-invariance assumptions fail.
  • To understand the role of intense vortices in 2D turbulent dissipation.

Main Methods:

  • Numerical solutions of the 2D Navier-Stokes equation.
  • Forcing the flow at intermediate wavenumbers.
  • Applying weak linear or quadratic drag for damping.
  • Comparing derived scaling laws with DNS data.

Main Results:

  • Scale-invariant scaling predictions for effective diffusivity are invalidated.
  • Intense, isolated vortices emerge, causing spatially inhomogeneous frictional dissipation.
  • New scaling laws for effective diffusivity are derived.
  • Derived predictions quantitatively match DNS results.

Conclusions:

  • The emergence of intense vortices alters effective diffusivity scaling in 2D turbulence.
  • This suggests a universal large-scale spatial organization in 2D turbulent flows.
  • Findings bridge standard 2D Navier-Stokes turbulence with geophysical turbulence.