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Circulation statistics and the mutually excluding behavior of turbulent vortex structures.

L Moriconi1, R M Pereira2, V J Valadão1

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Turbulent flows show that vortex structures repel each other at short distances. This finding, supported by simulations, improves understanding of circulation fluctuations in turbulence.

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Area of Science:

  • Fluid Dynamics
  • Turbulence Theory

Background:

  • Understanding the statistical properties of velocity circulation in turbulent flows is crucial.
  • Classical turbulence models often simplify the complex interactions of vortex structures.

Purpose of the Study:

  • To investigate the small-scale statistical properties of velocity circulation in homogeneous and isotropic turbulent flows.
  • To model the behavior of vortex structures and their correlations.

Main Methods:

  • A modeling framework combining multiplicative cascade and structural descriptions of turbulence.
  • Tomographic investigation of vortex structures using planar cuts, treating them as two-dimensional vortex gases.
  • Direct numerical simulations of the Navier-Stokes equations to study spatial distributions.

Main Results:

  • Vortex structures exhibit short-distance repulsive correlations.
  • Model improvements led to an accurate multiscale description of intermittent circulation fluctuations.
  • The conjectured hard disk behavior of effective planar vortices is strongly supported by simulation data.

Conclusions:

  • The repulsive correlations of vortex structures are a key feature of turbulent flows.
  • The hard disk model provides a robust framework for understanding vortex interactions and circulation intermittency.
  • This research offers new insights into the fundamental nature of turbulence at small scales.