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Area of Science:

  • Fluid Dynamics
  • Turbulence Research
  • Scalar Transport

Background:

  • Passive scalar intermittency in turbulent flows is a complex phenomenon.
  • Understanding its statistical properties is crucial for various applications.
  • Previous studies have suggested deviations from smooth, Gaussian statistics.

Purpose of the Study:

  • To investigate the intermittency of a passive scalar in 3D Navier-Stokes turbulence.
  • To provide unambiguous evidence for scaling exponent saturation.
  • To explore the relationship between scalar field geometry and statistical properties.

Main Methods:

  • Direct numerical simulations (DNS) on a 4096^3 grid.
  • Analysis of high-order scalar increment moments.
  • Calculation of fractal dimension for steep scalar cliffs.

Main Results:

  • Scaling exponents for scalar increments saturate at 1.2 for high moment orders (>12).
  • Scalar intermittency is dominated by singular, shocklike structures.
  • Fractal dimension of steep cliffs is approximately 1.8, linking geometry and statistics (1.8 + 1.2 = 3).
  • Anomalies in 4th and 6th order moments align with the Kraichnan model.

Conclusions:

  • Scalar intermittency in this turbulent regime is governed by extreme events.
  • A fundamental connection exists between the fractal geometry of scalar structures and their statistical scaling.
  • The findings offer insights into turbulent mixing and scalar transport phenomena.