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Area of Science:

  • Fluid dynamics
  • Statistical physics
  • Turbulence modeling

Background:

  • Turbulence at infinite Reynolds numbers exhibits rough, multifractal properties in space and time.
  • Understanding Lagrangian trajectories in such fields is crucial for turbulence phenomenology.

Purpose of the Study:

  • To investigate Lagrangian trajectories in statistically isotropic, homogeneous, and stationary divergence-free spatiotemporal random vector fields.
  • To design an advecting Eulerian velocity field that is asymptotically rough and multifractal.
  • To analyze the roughness and intermittency of trajectories in such fields.

Main Methods:

  • Designing a specific type of advecting Eulerian velocity field.
  • Numerically solving flow equations for a differentiable version of this field.
  • Analyzing Lagrangian trajectories using the Hurst exponent and identifying intermittent corrections.

Main Results:

  • Lagrangian trajectories become rough, exhibiting a Hurst exponent similar to the advecting field.
  • Additional intermittent corrections are observed in the Lagrangian framework, even with fractional Gaussian fields.
  • The numerical findings suggest a connection between the advecting field's properties and trajectory behavior.

Conclusions:

  • The study provides numerical evidence for rough and multifractal Lagrangian trajectories in designed random vector fields.
  • The observed intermittency in Lagrangian trajectories warrants further rigorous theoretical investigation.
  • This approach offers insights into the long-standing problem of turbulence at infinite Reynolds numbers.