Flow of Spatiotemporal Turbulentlike Random Fields.

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.